Confronting the main aspects that differentiate Religion and Spirituality (most based on Dein [9])
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During the last decades there has been a considerable increase in the number of studies showing positive associations between spirituality-religiosity and health. The most important works in that area began it be deeds in the 1980 decade and are increasing worldwide. Scientific literature have recorded that spiritual well-being is associated with better physical and mental health, according to psycho-neuro-immune models of health. Spirituality and religion can help patients, their families and caregivers dealing with illness and other stressful life events.
Concerning physical health, studies show that appropriate religiousness is related to better general health and longevity (due to better immunologic function and cardiovascular health) and less frequency to health services utilization [1]. In mental health, religiousness is related to less chance to develop and faster recovery of: marital disharmony, depression, suicide attempt, and drugs and alcohol abuse [1]. There are evidences that persons with a well developed spirituality tend to make ill less frequently, to have healthier habits of life and, when make ill, develop less depression and recover more quickly.
Many patients put their suffering into religious frameworks. Religion and spirituality are prevalent coping strategies both for physical and for mental illness. For many patients religion and spirituality play a significant role in their lives and may help them cope with their symptoms. Patients’ personal beliefs may be fundamental to their sense of well-being and could help them to cope with negative aspects of illness or treatment. However, incorporating spirituality into medical practice continues to pose many challenges. Spirituality is often seen as a private and subjective area that lies outside of the therapeutic context, but patients’ beliefs can have a substantial impact on construction of the meaning of illness, coping behavior, and preferences about treatment.
This chapter is intended to present evidences and discuss proposals on how health care services can empower spiritual-religious resources of patients in order to they can be used as an efficient coping strategy. Concepts will be discussed, such as faith, spirituality, religion, and the concept of spiritual-religious coping itself. The characteristics of the spiritual-religious coping structure will be described. The spiritual distress due to non-attended spiritual needs will be discussed, followed by a description of defensive behaviors that patients may adopt in these situations. The chapter ends proposing some suggestions for health care professionals and services to use these knowledge in practice.
The terms faith, spirituality and religious beliefs have been used interchangeably but have significant conceptual differences which may be relevant in trying to understand their influence on medical treatment. While many people use the words spirituality and religion as synonyms, they are in fact very different. Although these terms are associated, they are not interdependent.
It is not always certain what the precise spiritual needs of a patient might be. Some might want help with specific religious rituals. Some might want to talk to members of their own faith communities about the meaning of suffering. Still others might want pastoral counseling regarding their fear of death. Defining the spiritual needs of patients is a matter that is being investigated empirically, but there are, at present, no well-validated research instruments for this purpose. Patients report a wide spectrum of spiritual needs, and meeting spiritual needs is correlated with patient satisfaction with care and their ratings of the quality of medical care [4].
Even if there are interfaces between religion and health, the primary goal of every religious life is beyond the matters of physical, mental, and social well-being. The goals are variously designated: salvation in Christianity; the elimination of avidya (mu-myung) to achieve the state of One-Mind (Il-shim) in Buddhism; the union of Yin and Yang in Tao in Taoism; and achieving the ability of ecstasy to combine the celestial and earthly worlds in shamanism [8].
RELIGION Specific set of beliefs and practices Strongly determined by culture Community focused organization (from outside to inside) Observable, measurable, objective Formal, orthodox, organized Behavior orientated, outward practices Authoritarian in terms of behaviors | SPIRITUALITY Feelings of peace and connectedness Universal human characteristic Individualistic inner experience (from inside to outside) Less visible and measurable, more subjective Less formal, less orthodox, less systematic Emotionally orientated, inward directed Not authoritarian, little accountability |
Confronting the main aspects that differentiate Religion and Spirituality (most based on Dein [9])
Spiritual-Religious (S-R) coping is the use of religious beliefs, attitudes or practices to reduce the emotional distress caused by stressful events of life, such as loss or change, which gives suffering meaning and makes it more bearable. Religious beliefs and practices are used to regulate emotion during times of illness, change, and circumstances that are out of patients’ personal control [1].
Spirituality has an impact on patients’ ability to cope with illness. For many individuals, spiritual beliefs and practices provide a source of comfort, supply a font of wisdom to help make sense of what seems otherwise senseless, and prescribe a ritual pathway for addressing the basic spiritual questions of meaning, value, and relationship [4]. Aspects of religious coping include [7]:
Cognitive aspects: the way we make sense of the world around us. They include questions such as: “Why do bad things happen to good people?” “What happens after death?”
Experiential aspects have to do with connection and inner resilience. They encompass questions such as: “Am I alone or am I connected to something bigger?” “Can I find hope in this difficult situation?”
Behavioral aspects have to do with ways in which a person’s spiritual beliefs and inner spiritual state affect his or her behavior and life choices.
The response to life stressors may be directly mediated by S-R factors which provide a cognitive framework for providing meaning, which enables a healthier appraisal of those stressors through the provision of meaning and coherence. This may provide greater psychological resilience in the face of negative life events. Suffering is given a meaning in the world religions although there is marked variation in how this is done. It is not necessarily seen as destructive or humiliating, to be avoided at all cost [9].
Spirituality provides growth in several relationship fields. In the intrapersonal field (with himself), brings hope, altruism and idealism, purpose for life and for suffering. In the interpersonal field (with others) brings tolerance, unit, and the sense of belonging to a group. In the transpersonal field (with a supreme power), awakes the unconditional love, worship and the belief of not being alone [10].
Spiritual beliefs may assist people in providing a sense of control in understanding, coping with and interpreting events or experiences. Previous studies indicate that individuals who hold religious beliefs allow an individual to reduce the stressful reactions to events that they deem to be uncontrollable by reframing or reinterpreting those events, possibly gaining a new meaning and understanding from them [5].
It is important to have meaning or purpose in life. This sense of meaning is diminished by an illness. This loss and its associated rediscovery were central aspects of both depression and spirituality. Spirituality may provide such a sense of meaning through its emphasis on liturgy, worship and prayer found in the major religious traditions [9]. Adverse life events may be appraised in a different way. Religion provides a meaning context in which adversity can be understood.
Words such as spirituality and religion carry a variety of meanings for different people. Not all S-R coping is positive. S-R perceptions and rituality may well be a double-edged sword. Although much of the literature is suggestive of an overall positive effect of religion on health, at times religious practice might have a deleterious effect. What appears to be ultimately important in terms of health outcome is not religious involvement (e.g. church attendance) but how people actually deploy their religious beliefs to cope with adversity. Table 2 confronts some aspects of positive and negative S-R coping (based on [4];[7];[9] )
POSITIVE | NEGATIVE | |
What does it evoke | bring out the best in individuals, reinforcing active problem-solving behavior | encourage negative avoidance strategies based on the beliefs of abandonment and punishment |
view of the deity | belief in a kind supportive God | distant and uncaring, or punishing for transgressions |
effect on life adjustments and emotional health | lower levels of psychiatric symptoms; linked with improved health-care outcomes | associated with higher prevalence of psychiatric symptoms; worse medical outcomes |
Some aspects of positive and negative S-R coping
A relation between better health and religion or spirituality is found in studies covering heart disease, hypertension, cerebrovascular disease, immunological dysfunction, cancer, longevity, pain, disability, and less frequent health services utilization. Also higher religiousness affects behaviors and correlates such as taking exercise, smoking, substance misuse, alcohol abuse, burnout, and family and marital breakdown [11]. In mental health, higher religiousness is related to less chance to develop the following conditions, and faster recovery when they appear: marital disharmony, depression, anxiety, suicide attempt, and drugs and alcohol abuse [11]. The benefits are almost always threefold: aiding prevention, speeding recovery, and fostering equanimity in the face of ill health.
Studies on spirituality and mental health have looked at the mechanisms involved in spirituality, which may improve mental wellbeing. There is some evidence that positive coping styles can be very positive in terms of people’s mental health [5]. Aspects of spirituality may have a beneficial affect on a variety of health-related physiological mechanisms. In particular, spirituality’s emphasis on contentment, forgiveness, hope and love, may positively affect an individual’s physical wellbeing. Furthermore spirituality may reduce feelings of negative emotions, such as anger, fear and revenge, reducing tension levels. [5]
The theories that can explain how S-R wellbeing may improve health are various. Some involved mechanisms may be the positive cognitive appraisal, the altered status of mind during prayer, and congregational benefits from the religious community.
Human beings are complex, with physical, mental, and spiritual aspects. Suffering can result from issues pertaining to any of these aspects. Spiritual distress is a state of suffering due to spiritual causes. For example: a mother having difficulty understanding why a loving God would allow her child to die [7]. The spiritual distress refers to the existential anguish experienced by patients when their belief system cannot provide relief.
When patients suffer, they experience a sense of their own vulnerability and finitude, as well as a disruption and fracture of their own person and sense of community. As a result, the experience of suffering can be an opportunity to experience his own spirituality [13]. When well constructed, the belief structure is a source of comfort, welfare, security, meaning, idealism and force. Many patients use their beliefs when coping with its illnesses, and the cure can be influenced by the positivist reinforcement of the patient.
In contrast, a dysfunctional belief system may originate negative reactions that harm the healthcare evolution. If there is a disruption of the belief system, the spiritual distress can surge. It may be expressed by many ways, some of them are below described.
The consequent defensive behaviors patient can develop under spiritual distress may affect clinical treatment and quality of life. Below are described some manifestations of such behaviors.
To support the utilization of the spiritual resources by the patient, the Joint Commission on Accreditation of Healthcare Organizations suggests that each institution must [19]: understand and protect the cultural, psychosocial and spiritual values of each patient; prepare professionals to understand and respect beliefs and values of the patients; inform patients about their rights and how to regarding them; and lend aid that consider and respects the beliefs and values of the patient
Health Care Services must invest on some actions, in order to minimize conflicts between religious interests of patients and medical treatment. Some examples are given by the Multi-Faith Group for Healthcare Chaplancy [20]: training and development; appointments to chaplaincy posts; data protection; volunteers; worship and sacred spaces; and bereavement services.
Delgado [6] organized the lay spiritual interventions from health professionals in some categories, as: (a) Assessment: ask about faith, practices and symbols; (b) Communication: empathic and respectful listening, transmitting these findings to proper professionals; (c) Supporting emotionally: watch patients at spiritual suffering risk; empathic presence; be trustful; and (d) Supporting physically: create conditions to attend spiritual needs, as time, place, resources, privacy.
Obstacles to implementing spiritual care must not be underestimated, and include [21]: education (lack of training); economics (lack of staff or resources); environment (lack of space or privacy); personal (sensitivity or own belief systems). To achieve the benefits and overcome difficulties, the below discussions lists some suggestions for health care professionals and services. More systematically, we discuss a list of actions to promote the positive impact of spirituality and religiosity on the health treatment process, which would be followed by health care professionals and services (compiled from information from Saad [22] and Lucchetti [23])
It is important to know the basic precepts of the most prevalent religions in the hospital, especially about objections to suspension of treatments, to organs donation, to the necropsy and body cremation. Good clinical care includes sensitivity and curiosity about the cultural and religious values and beliefs of our patients. While substantial progress has been made in incorporating spirituality into the curriculum in a growing number of medical schools, the quality and depth of that instruction is quite varied [16].
The goal of staff training must be to develop an ability to understand better how one’s patient engages illness and interprets therapeutic interventions, without prejudice and with an appreciation for the particular cultural and religious perspective brought to the clinical encounter by the patient. Even physicians who are not themselves religious can acknowledge and be sensitive to the spiritual dimensions of their work.
An example on how simple may be the training of healthcare professionals is this model adopted by our institution. A list of positive attitudes include: Empathy (being present, realist and honest); Respect to beliefs of the patient; Consider spirituality as component of the well-being; Remember the relation between illness and spiritual suffering; Inform the ways for spiritual support of the hospital. A list of negative attitudes: “To prescribe” religious activities for health improvement; To impose your religious beliefs to patient; To initiate prayers without know appreciation of the patient; To perform task proper of a priest; To give deep religious counseling.
Treatment planning can usefully involve active attention to patient cues about their faith’s importance, consideration of questions in the context of the patient’s spiritual background, processing of questions to look for deeper spiritual questions or issues, and asking clarifying questions to assure accurate identification of spiritual development. It is important that the clinician have accurate information about the family’s worldview to avoid prescriptions that might be offensive or undermine key precepts of the family’s faith [25]. One way to begin is to ask the patient about what she or he finds meaningful or important in life and whether her or his spiritual views have relevance for these issues. It may be helpful to ensure that the patient has access to spiritual counselors as well as to a pastoral care team. It may also be beneficial to discuss with the patient and family how their spiritual practices can be incorporated into the care provided by the medical team.
Trust and good communication are essential components of the doctor-patient relationship. Patients may find it difficult to trust you and talk openly and honestly with you if they feel you are judging them on the basis of their religion, culture, values, political beliefs or other non-medical factors [26]. By encouraging the family’s continuance of healthy religious rituals such as prayer, communion, and anointing, the therapist can enhance family coping responses and possibly increase the efficacy of treatment [25]. Religion and spirituality are not confined to church attendance or affiliation, reading sacred writings, or celebrating Holy Days, or even to praying. There are also non-biblical inspirational literature, religious music, radio and television programming, books on tape and motivational recordings, religious parenting books, and religious books, tapes, and videos.
When the patient brings religious issues up, the physician should always acknowledge the spiritual concerns raised by the patient, respond to the patient, listen respectfully, and refer to pastoral or spiritual care when appropriate. Addressing patients’ spirituality is warranted because it is associated with clinical outcomes and patient coping, because patients want it, and because it can affect their decision making. The spiritual concerns of patients affect them as whole persons and in their overall sense of well-being [4].
Spiritual approaches to pain management can take many forms, from prayer, to participation in religious services and rituals, to therapeutic touch, spiritual healing, mindfulness meditation, Reiki, and other strategies. Some of these strategies are explicitly religious, whereas others take a more secular spiritual approach. In some cases the strategy will have roots in religious tradition but will have been modified to make it more amenable to a diverse group of people. For example, mindfulness meditation has roots in Buddhism but is typically used in Western culture separately from its traditions within Buddhism.
Assisting the patient to engage in religious-spiritual activities involves [6]: referring to clergy; informing patient about resources; providing religious material; allowing for prayer, meditation and other practices; and helping the patient to attend religious services and related activities. Barriers to fulfill spiritual needs will always be in one of these groups [6]: personal, situational or knowledge related. Also there is the inability to differentiate psychological needs from spiritual needs. Many other spiritual activities may be proposed [5]:
Belonging to a faith tradition, participating in associated community-based activities
Ritual and symbolic practices and other forms of worship
Pilgrimage and retreats
Meditation and prayer
Reading scripture
Sacred music (listening to, singing and playing) including songs, hymns, psalms and chants
Acts of compassion (including work, especially teamwork)
Deep reflection (contemplation)
Group or team sports, recreational or other activity involving a special quality of fellowship.
Health professionals should not normally discuss personal beliefs with patients unless those beliefs are directly relevant to the patient’s care. They must not impose their beliefs on patients, or cause distress by the inappropriate or insensitive expression of religious, political or other beliefs or views. Equally, you must not put pressure on patients to discuss or justify their beliefs (or the absence of them) [26].
A helpful principle is to inform but not to recommend. For example, it is legitimate for a physician to inform patients of the potential health benefits of moderate consumption of alcohol, but it is ethically questionable to recommend moderate consumption to a patient who abstains from alcoholic beverages for religious reasons. Respect for autonomy requires that physicians leave it to such patients and their spiritual guides to determine whether a religious practice is worth an elevated health risk [14].
When the health professional has strong reservations about the religious or spiritual tradition to which the patient adheres and feels that such a referral would constitute a tacit endorsement of that religious or spiritual tradition, this fact should be disclosed to the patient. A patient’s spirituality should be explored with an open-mindedness and neutrality that allows for tolerance of difference and avoids prejudice against (or for) particular spiritual or religious beliefs or practices.
General spiritual care—bringing presence, compassion, understanding, and listening to each encounter. This can be provided by anyone at any time. It can traverse all cultural barriers by meeting a universal spiritual need without specific discussion about beliefs or God.
Specific or specialized spiritual care—addressing the individual needs of the patient. Simple issues may be addressed by physicians. More complex issues will likely require the expertise of well-trained spiritual care counselors such as chaplains trained in Clinical Pastoral Education.
It is important to assess and consider the value of consultation with or referral to clergy. Yet a well-timed religious or spiritual consultation with clergy is often necessary for effective and efficient treatment [25]. A chaplain may be seen as the legitimate person to whom spiritual issues may be addressed and can provide a model of ‘holistic care’. But chaplains require a basic knowledge of health issues to ensure that they can pick up major mental illness and refer people for appropriate help.
Although all clinical settings do not have chaplains, most hospitals have chaplains on staff or available within the community. Chaplains who have completed clinical pastoral education training have a breadth of background to provide collegial and informed assistance in dealing with clinically relevant religious issues with most patients. Although chaplains are frequently consulted when approaching end-of-life issues with patients and their families, their potential for service is much broader [16].
For some traditions, it is vital that prayer and counsel come from fellow members of (or even authorities) in that tradition; for other traditions, this is unnecessary. These issues can often be avoided by referrals to appropriate persons within the patient’s religious or spiritual tradition. Religious congregations are considered an important mechanism in molding people in terms of their mental health. Individuals’ mental health is often supported through engagement with members and leaders of religious congregations. A spiritual community may provide a variety of support, including [5]:
Protecting people from social isolation
Providing and strengthening family and social networks
providing individuals with a sense of belonging and self-esteem, and
Offering spiritual support in times of adversity.
Physicians who anticipate conflicts between their own commitments and the requests of their patients (or their patients\' families) should discuss with a chaplain or minister of the patient\'s religion the nature of the conflict, and should discuss with the patient or family about transference of care to a physician who will not experience such conflict.
For some patients, acknowledging their beliefs or religious practices may be an important aspect of a holistic approach to their care. Discussing personal beliefs may, when approached sensitively, help to work in partnership with patients to address their particular treatment needs. The staff must respect patients’ right to hold religious or other beliefs and should take those beliefs into account where they may be relevant to treatment options [26]. It is important to assess whether the treatment plan is consistent with the family’s religious beliefs. Clinicians have contact with families at life’s critical transition points. By accurately identifying the family’s beliefs, clinicians can work with families to accommodate the treatment for the best interest of everyone involved on it.
Should health professionals recommend that patients participate or cease participation in religion or spirituality for their well-being? Here, respect for the religious or spiritual adherence of the patient (or for his or her lack thereof) may conflict with what the professionals believes is in the therapeutic interest of the patient or with the religious or spiritual adherence (or lack thereof) of the professionals. The question is the degree of confidence with which a professional can determine that a religious belief, commitment, practice, or symbol is correlated with (or the cause of) a positive or negative condition that psychotherapy can affect [14].
Open discussion with the patient and her or his family about spiritual views and how they can be incorporated into the management plan will likely be beneficial for both the patient and the team. A person-centered approach is key to ensuring that the patient’s spirituality is understood from her or his perspective. For some patients, the best health treatment will be that which is consistent with their spiritual or religious views.
A scheme on how balancing the elements of attention to the special needs of patients to empower resources on spiritual-religious coping
Figure 1 illustrates how to solve the problem of meeting the special needs of patients by healthcare professionals and services. The elements that are at stake are the institutions (health care and rehabilitation), the people associated with the process (physicians, nurses, other professionals) and individual values of patient (religious and spiritual). The forces that bind these elements are the scientific research on the subject, the good practices adopted by institutions and government policies that support these achievements.
This chapter is intended to present evidences and discuss proposals on how health care services can empower spiritual-religious resources of patients in order to they can be used as an efficient coping strategy. It is known that a relation between better health and religion or spirituality is found in studies covering several physical and mental conditions. Spiritual-religious coping is the use of religious beliefs, attitudes or practices to reduce the emotional distress caused by stressful events of life, such as loss or change, which gives suffering meaning and makes it more bearable. Spiritual distress is a state of suffering due to spiritual causes. Generally it may be associated with unfulfilled spiritual needs. The consequent defensive behaviors patient can develop under spiritual distress may affect clinical treatment and quality of life. Health care services must invest on some actions, in order to minimize conflicts between religious interests of patients and medical treatment. We discussed a list of actions to promote the positive impact of spirituality and religiosity on the health treatment process, which would be followed by health care professionals and services. The elements that are at stake are the institutions (health care and rehabilitation), the people associated with the process (physicians, nurses, other professionals) and individual values of patient (religious and spiritual).
This Chapter is mainly based on an important sector of operation research-weapon’s target assignment (WTA) problem which is a well-known application of optimization techniques. While we discuss about WTA, we need some common terms to be discussed first. In this section, we first introduce WTA problem and then we present some prerequisites such as optimization model, its classification, LP, NLP, SP and their classifications, and applications of SP. We also discuss some relevant software tools we use to optimize the problems.
The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research. It consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the opponent. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There are constraints on weapons available of various types and on the minimum number of weapons by type to be assigned to various targets. The constraints are linear, and the objective function is nonlinear. The objective function is formulated in terms of probability of damage of various targets weighted by their military value.
In the current section, we discuss some preliminaries of the terms we mention in the chapter.
Optimization means ‘the action of finding the best solution’. Optimization modeling is also known as Mathematical Programming. Mathematical programming is the use of mathematical models, particularly optimizing models, to assist in making decisions. It is a branch of operation research which has wide applications in various areas of human activity. Optimization can help solve problems where there are two situations as (1) many ways of doing something or (2) limited resource available.
Any real-world optimization problem may be characterized by five qualities. The problem function may all be linear or be nonlinear. The functional relationships may be known i.e. deterministic, or there may be uncertainty about them i.e. probabilistic. The optimization may take place at a fixed point in time (static) or it may be an optimization over time (dynamic). The variables may be continuous or discrete. And lastly, the problem functions may all be continuously differentiable (smooth) or may have points where the functions are non-differentiable (non-smooth).
Linear programming is an optimization technique of a linear objective function, subject to linear equality and linear inequality constraints. It is a mathematical method that is used to determine the best possible outcome or solution from a given set of parameters or a list of requirements, which are represented in the form of linear relationships. It is most often used in computer modeling or simulation in order to find the best solution in allocating finite resources such as money, energy, manpower, machine resources, time, space and many other variables. In most cases, the “best outcome” needed from linear programming is maximum profit or lowest cost. It was first developed by Soviet mathematician and economist Leonid Kantorvich in 1937 during the second world-war.
Here we present the standard form of linear programming. A linear programming problem may be defined as the problem of maximizing or minimizing.
The standard linear programming problem can be expressed in a compact form as:
Maximize (or Minimize)
The basic components of linear programming are as follows:
Decision variables (
The objective function (1)—This represents how each decision variable would affect the cost, or, simply, the value that needs to be optimized.
Constraints (2)—These represent how each decision variable would use limited amounts of resources.
Data—These quantify the relationships between the objective function and the constraints.
The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. For optimization under uncertainty stochastic programming is one of the best techniques. That is, stochastic programming is mathematical programs that include data that is not known with certainty but is approximated by probability distributions. Stochastic programming extends the scope of linear and nonlinear programming to include probabilistic or statistical information about one or more uncertain problem parameters. Similarly, when all the input data used in the mathematical formulation of the mathematical program is known with certainty then the corresponding models are called deterministic models.
Stochastic programming offers a solution by eliminating uncertainty and characterizing it using probability distributions. There exist many different types of stochastic problems. The most famous type of stochastic programming model is recourse problems. Another form of a stochastic problem is the chance-constrained programming problem. In this type of stochastic programming model, the constraints to be optimized depend on probabilities. The classification of SP problems is shown in Figure 1.
Codification of SP problems.
Stochastic programming has been applied to a wide variety of areas. Some of the specific problems are part of the Stochastic Programming test set. Other applications are listed as follows: Manufacturing Production Planning, Manufacturing production capacity planning, Machine Scheduling, Freight scheduling, Dairy Farm Expansion planning, Macroeconomic modeling and planning, Timber management, Asset Liability Management, Portfolio selection, Traffic management, Optimal truss design, Automobile Dealership inventory management, Lake level management.
Nowadays computerized techniques are widely used to solve various types of problems in the world. Sometimes some problems become difficult to solve and time-consuming by hand calculation. So by using different software tools, we can solve problems from small to large scale problem optimally in a short time. There are so many computer-based mathematical programming languages have been used worldwide. Some of the tools that are used to solve optimization problems are
AMPL, an acronym for “A Mathematical Programming Language” is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, with discrete or continuous variables. It is a language for solving high complexity problems for large scale mathematical computation. It was developed by Robert Fourier, David Gay and Brian Kernighan at Bell Laboratories [1]. By using AMPL, we can get the solution of a problem in which the model of the formulation with sets, variables, parameters, constraints, etc. are written in a mod. file and the data of the formulation are written in a dat. file. Then the solution is found after running the program in the console window.
LINGO is designed to solve a wide range of optimization problems, including linear programs, mixed integer programs, quadratic programs, stochastic, and general nonlinear non-convex programs faster, easier and more efficient. It provides a completely integrated package that includes a powerful language for expressing optimization models, a full-featured environment for building and editing problems, and a set of fast built-in solvers.
First one is based on weapons assignment in which the engagement of a target by a weapon is modeled as a stochastic event. In this type of problem, we develop a general computer oriented algorithm so that we can solve this type of problems for small scales to large scales problems in a single framework. To show the effectiveness of our developed model we present numerical examples of WTAP and compare our result with different existing results.
This chapter contains four sections in total which is organized as follows:
In Section 1, we discuss some prerequisites that are required for WTA problem. We also discuss about the types of optimization models, software tools that we use in this chapter.
In Section 2, we review some relevant papers about weapon’s assignment problem.
In Section 3, we discuss the weapon target assignment problem. We formulate the WTA problem. Some existing algorithms are also presented in this chapter. We discuss the real-life applications and present numerical examples of WTAP. We develop a new computer technique by using programming language AMPL to solve all type of WTA problem in a single framework. Then finally compare the results we get from AMPL to previously solved results of the examples.
In Section 4, we draw a conclusion about our whole chapter.
In this Section, we discussed the relevant preliminaries. In the next Section, we will review some literature about weapons assignment and chance-constrained problem.
In this section, we will review some admissible research articles on Weapon Target Assignment Problem. Since the 1950s, the optimal assignment problem of weapons to targets has always been concerned by many countries. The study of WTA problem can be traced back to the 1950s and 1960s when Manne [2] and Day [3] built the model of WTA problem. The present research work on WTA is focused on models and algorithms. In the research on models of WTA, the static WTA models are mainly studied and the dynamic WTA are not fully studied indeed. In the research on algorithms of WTA, the intelligent algorithms are often used to solve the WTA problem.
There are so many proposed algorithms on WTA problem [4, 5]. So we present the summary of variant heuristic algorithms and the implementation of various WTA have been proposed for several years is shown in Table 1.
Researchers | Year | Proposed Algorithms | Implementation WTA |
---|---|---|---|
Galat and Simaan | 2007 | Tabu | Dynamic single-objective |
Lee | 2010 | VLSN | Static single-objective |
Xin et al. | 2010 | VP + Tabu | Dynamic single-objective |
Li and Dong | 2010 | DPSO+SA | Dynamic single-objective |
Chen et al. | 2010 | SA | Static single-objective |
Fei et al. | 2012 | Auction Algorithm | Static single-objective |
Liu et al. | 2013 | MOPSO | Static multi-objective |
Zhang et al. | 2014 | MOEA/D | Static multi-objective |
Ahner and Parson | 2015 | Dynamic Programming | Dynamic multi-objective |
Li et al. | 2015 | NSGA-II, MOEA/D | Static multi-objective |
Driik et al. | 2015 | MILP | Dynamic multi-objective |
Liang and Kang | 2016 | CSA | Static single-objective |
Li et al. | 2016 | MDE | Dynamic multi-objective |
Existing algorithms for several ye.
Various combinatorial optimization techniques are currently available. Most of these techniques have not been thoroughly tested on realistic problems. In this chapter, we consider a class of non-linear assignment problems collectively referred to as Target-based Weapon Target Assignment (WTA). We first briefly discuss the weapon target assignment problem. We also include the basic concepts and models of WTA and the mathematical nature of the WTA models is also analyzed. We present some real-life applications of WTA here. There does not exist any exact methods for the WTA problem even relatively small size problems, and much research has focused on developing heuristic algorithms based on meta-heuristic techniques. The main focus of this chapter is our new developed optimization algorithm for the WTA problem based on the kill probabilities.
The assignment problem is one of the fundamental constrained combinatorial optimization problems in the branch of optimization or operation research in Mathematics. This problem is mainly used in decision making. Here we consider a special type of problem which is a combination of transportation problem and assignment problem. By the name of weapon-target assignment problem, it is clear that we have to assign weapons to targets. It is a defense-related application in operation research and is slightly different from the more general optimal resource allocation problem. The main aim of weapon-target assignment problem is to find a set of solution of the number of available weapons to a set of required targets so that the expected rewards of the sequential engagement is maximized [6]. The engagement of a target by a weapon is modeled as a stochastic event, with a probability of kill assigned to each weapon-target pair (this is the probability that the interceptor weapon will destroy the target if assigned to it). The engagement of a weapon-target pair is independent of all other weapons and targets. This is an integer optimization problem in that fractional weapon assignments are not allowed.
A number of different approaches have been applied to the WTA problem. When considering a WTA problem, a number of factors need to be considered. Some of these factors are discussed below [7]:
The generalized linear assignment problem (LAP) of allocating weapons to targets is a fundamental problem of combinatorial optimization. In the simplest case, the number of weapons and targets are equal, with only one weapon being assigned to any one target in an allocation. LAP’s can also be represented in a bipartite graph shown in Figure 2(a). In the LAP graph, weapons cannot be assigned to more than one target. But, when targets are assigned to more than one targets or targets, are assigned to more one weapon, then the assignment problem becomes nonlinear as presented by the bipartite graph in Figure 2(b).
A linear and a nonlinear bipartite graph.
Weapon target assignments are generally viewed as nonlinear assignment problems (non-LAP). That is, the optimal solution is nonlinear but is still considered to integer values as in the LAP case.
A WTA problem can be viewed from either a target-based or an asset-based perspective. In the target-based, values are assigned to each target to cause damage to the defended asset. The objective of the target-based WTA solution is to maximize the damage value of the incoming targets.
Conversely, in an asset-based perspective values are assigned to the assets rather than the targets. This WTA problem is where weapons are assigned such that the combined value of assets is maximized. The asset-based approach requires information on which targets are approaching the defended assets. But a target-based approach is more appropriate than the asset-based. The approach which is discussed in this chapter is the target-based perspective.
Generally, WTA is categorized into two versions:
Static WTA
Dynamic WTA
In addition, considering the different missions, each version includes the asset-based problem and the target-based problem. In the asset-based problem, the task is to maximize the expected total value of assets which are defended by the defensive weapons. In the target-based problem, the task is to minimize the expected total value of targets which are not destroyed by the defensive weapons after the engagement. The target-based problem can be considered as a special case of the asset-based problem.
Some relevant properties of the dynamic WTA problem are that it is:
NP-Complete (Non-deterministic polynomial), that is one must essentially resort to complete enumeration to find the optimal solution.
Discrete (fractional weapons assignment are not allowed)
Dynamic (the results of previous engagements are observed before making present assignments)
Nonlinear (the objective function is convex)
Stochastic (weapon-target engagements are modeled as stochastic events)
Large-Scale (the number of weapons and targets is large, making enumeration techniques impractical).
These properties of the problem rule out any hope of obtaining efficient optimal algorithms.
To present the dynamic weapon-target assignment problem, we need the following parameters and variables to be introduced:
Symbols: Descriptions.
Let there be
Here we consider
The WTA problem has wide applications in real life. Some of them are discussed in the current section:
In an air missile defense system [10, 11], missiles are regarded as the major weapon in modern warfare, and missile defense technology becomes a hot research topic for military and information expert. The reasonable target assignment strategy and optimization algorithm for weapon-target assignment improve operational effectiveness greatly. According to target threat degree and air combat priority index of target intercepted, the relative weigh for weapon unit of target attack is definite, the combined effect on target assignment result is weighed, which ensure high target interception as far as possible. In multi-fighter air combat, the weapon target assignment problem is a challenge in information warfare, the air defense command system can assign weapon reasonably for eliminating the threat from enemy targets in time. The selection rules of target function include the facts such as less resource and energy loss for fighter, the minimum threat degree and the minimum number of targets remaining, different selection rule reflect different decision intention, which decided different target function form and combat strategy [12]. AS an NP-complete problem, with the number increasing in weapon units and targets, the solution space shows the trend of the combined explosion [13].
In management science, the word advertisement is the most significant term. In advertising, media allocation is a very important task for advertisers. Communication vehicles such as television, newspapers, internet, radio and etc. are referred by the term media in advertising. To convey the commercial messages to target the potential customers, advertisers use the above-mentioned vehicles. In order to maximize the effectiveness of advertising effort, media planning is the process of selecting time and space in various media for advertising. The best media plans provide the target audiences with an optimum level of coverage and opportunities to see the campaign. So, media allocation is to find the proper assignment of number of ads in each vehicle. This allocation problem can be developed as an optimization model, which can also be considered as the WTA problem of military operation research, that allocates media to target audiences.
This problem is an integer nonlinear programming problem which is independent of the duration of an advertising campaign also schedules advertisements during a day. This is an appropriate example of military operations research models that can be adapted to contemporary business world applications.
Several exact and heuristic algorithms have been proposed to solve the Weapon-Target Assignment problem for several years. Some of them are described briefly below:
Maximum marginal return algorithms are algorithms that assign weapons sequentially with each weapon being assigned to the target which results in the maximum decrease (marginal return) in the objective function value. In other words, in maximum marginal return algorithms, a weapon is always assigned to the target with maximum improvement in the objective function value. Maximum marginal return algorithms are heuristic algorithms, they are easy to implement and efficient algorithms. Although these algorithms do not give the optimal or best solution it is known that these algorithms give near-optimal solutions.
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A genetic algorithm with greedy eugenics that takes into account a probability of kill value for each weapon is suggested [14], and compared to MMR algorithm. Although MMR algorithm runs much faster than GA, GA tends to find better solutions than MMR algorithm. And, GA efficiency increases as the number of targets and weapons increases. Also in GA if a set of weapons can also hit a group of targets, meaning that grouping of weapons and targets is possible, this leads to faster and more optimal solutions [15]. Since the algorithm uses randomization it is a nondeterministic algorithm. The genetic algorithm is given as follows [16]:
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Ant-colony optimization takes inspiration from the foraging behavior of ant colonies. Initially all of the ants search for the food randomly. When an ant finds a food, it starts to deposit a chemical substance produced and released into the environment called pheromone on the ground while returning back to the colony. By depositing pheromone on the ground, they mark the path to the food that should be followed by other members of the colony. If an ant comes across a path with pheromone, it stops searching for the food randomly and starts to follow the path marked with pheromone. If it reaches the food, it starts to deposit pheromone on the path back to the colony also. This positive feedback strengthens the pheromone trail on the same path and causes all of the ants to follow a single path. On the other hand, if the path is not followed by other colony members, the pheromone evaporates in time and eventually, the path disappears [1, 16].
An Ant-Colony Optimization algorithm basically consists of 3 main steps. After the initialization of pheromone trails, while there is still time, at each iteration:
Ants create solutions.
Created solutions are improved through a local search. This process is also known as daemon actions and it is an optional process.
Pheromone update is applied to increase the pheromone values that are associated with good solutions and to decrease the pheromone values that are associated with bad solutions (pheromone evaporation).
The description of the algorithm is given below:
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On modern battlefields, the task of battle managers is very important to make a proper assignment of weapons to targets to defend own-force assets or to offend the opponent targets. As an example, we now consider a target-based weapon-target assignment model for maximizing the total expected damage value of the targets which satisfies the Eqs. (3)–(5). Here considering five weapons are to be assigned to 20 targets [17, 18]. These targets have different probabilities of killing to platforms which are dependent on the target types. That is, the destroying probabilities of targets by different types of weapons obviously will be different. The probabilities define the effectiveness of the
The characteristics of the five weapon types could be thought as follows:
Breda-SAFAT machine gun
Lewis gun
Spandau machine gun
Vickers machine gun
Blue Danube (nuclear weapon)
Each weapon-target pair survival probabilities are shown in Figure 3.
Survival probabilities of targets by weapons.
The number of available weapons and the military value of targets is shown in [19] Figure 4.
Availability of weapons and target military values.
There are also some requirements for weapons to destroy particular targets. Figure 5 shows the minimum number of weapons that must be assigned to some particular targets.
Minimum requirements of weapons assigned to targets.
After having all the values of required parameters, we formulate the model corresponding to the given example for maximizing the total expected target damage value as follows:
subject to,
The linear constraints on the available number of weapons of the five types are,
And the linear constraints on the minimum required assignment of weapons to the seven specified targets that must be engaged are:
The general WTA problem is the situation where a number of
After formulating the problem, we have the Eqs. (7)–(9). We observe that we have total 100 variables with a nonlinear exponential objective function and 12 linear constraints, which is quite large. There does not exist any exact methods for the WTA problem even relatively small size problems. As there are so many computer based software tools to solve different types of mathematical problems, we propose a computer oriented algorithm to solve such large scale problems in a short time. Our proposed algorithm not only solve large scale WTA problems but also small problems in a single framework. We develop a computerized algorithm in which all types of target-based WTA problem can be solved in a reasonably fast time to help decision makers to make proper assignment on the battlefield.
Since no real time exact solutions to WTAs are available, either for static or dynamic versions, alternative approximation methodologies must be considered, including heuristic techniques. We develop our computerized algorithm by using the Mathematical Programming Language AMPL.
Using the new developed algorithm by AMPL, we can solve the WTAP for the large numbers of weapons and targets using the single model file with different data values according to the different scale problems.
As our developed method is based on computerized tools, so we first develop the general code in AMPL. Then update the data file for the Eqs. (7)–(9). And finally run the AMPL code, then we get our desired result as an output file (Appendix-A) in AMPL. Subsequent to adjusting the quantity of weapons to the closest whole numbers, the outcomes have appeared in.
For several years this type of weapon-target assignment has been performed at the Research analysis. Here we have taken the numerical problem presented in [18]. We have presented the result of the WTAP by using our developed method in Table 2. Bracken et al. [18] solved this problem and got a set of solution of the number of weapons assigned to targets shown in Figure 6.
Number of weapons assigned to targets.
Now to check the efficiency of our model we compare the two results of the problem graphically. Then for the both results we calculate the objective function that is to be maximized. Here the graphical representation of total number of weapons assigned to targets of the results are shown in Figure 7.
Comparison of the results between the two methods.
Comparing the above two results, we have the better result than the existing result. That is, we have the maximum objective function. This concludes that our proposed method gives the effective result. Our developed AMPL code studied in this Chapter improved the existing solution by 0.1%.
Comparing media allocation with the WTA problem, we can consider the weapons as media vehicles to be advertised when the military targets as target audiences to be intended to reach. People exposed by media vehicles at different times of the day are given as target audiences. The weapon numbers
The number of ads refers to the number of times within a given period time an audience is exposed to a media schedule. The mathematical programming model is as follows under the assumption that the target audience is constant to be exposed by such media vehicles in given period time.
We formulate the media allocation as the weapon-target assignment model which satisfies the Eqs. (3)–(6).
Here
So here the objective is to maximize the total probability of reaching the target audiences.
Suppose a company is planning to start an advertising campaign for a particular product. That company takes four target audiences as morning, afternoon, prime and night time of the day. Also, they take 15 vehicles such as somoy news, BTV, Channel I, NTV, ETV, ATN News, GTV, Radio Today, Radio Foorti, Facebook, Prothom Alo, Ittefaq, Billboard, Printings, and E-mail. That company knows the percentages of reaching the target audiences in different time partitions according to the mentioned media vehicles. The probabilities of reaching target audiences are shown in the following table. In Table 2, we can see that some vehicles have 0 probability to reach some targets. Prime time is the most important segment, as night time is the least important segment for the product. Moreover, the segment weights facilitate marketers to give relative importance with respect to product or service characteristics. The weights can be changed with respect to the features of the product.
Media vehicles | Morning time (1) | Afternoon time (2) | Prime time (3) | Night time (4) | Ad capacities |
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Somoy News (1) | 0.21 | 0.12 | 0.12 | 0.23 | 8 |
BTV (2) | 0.35 | 0.24 | 0.12 | 0.07 | 7 |
Channel I (3) | 0.19 | 0.04 | 0 | 0.19 | 9 |
NTV (4) | 0 | 0.26 | 0.19 | 0.13 | 5 |
ETV (5) | 0.13 | 0.19 | 0.25 | 0 | 6 |
ATN News (6) | 0.24 | 0.14 | 0.22 | 0.09 | 8 |
GTV (7) | 0.09 | 0 | 0.18 | 0.28 | 3 |
Radio Today (8) | 0.39 | 0.17 | 0.47 | 0 | 10 |
Radio Foorti (9) | 0.24 | 0.31 | 0.14 | 0.43 | 15 |
Facebook (10) | 0.1 | 0.23 | 0.03 | 0.35 | 12 |
Prothom Alo (11) | 0.12 | 0.11 | 0.03 | 0.09 | 8 |
Ittefaq (12) | 0.32 | 0.23 | 0.09 | 0.21 | 4 |
Billboard (13) | 0.32 | 0.1 | 0.28 | 0.02 | 4 |
Printings (14) | 0.23 | 0.12 | 0.08 | 0.03 | 4 |
E-mail (15) | 0.29 | 0.07 | 0.04 | 0.32 | 4 |
Number of ads required | 16 | 18 | 25 | 10 | |
Segment weights | 2 | 3 | 4 | 1 |
The probability of reaching target audiences.
Probability Matrix (
Our objective is to make a proper assignment of ads to targets for maximizing the effectiveness of advertising. The objective function along with total 19 constraints (15 supply constraints for media vehicles and 4 demand constraints for target audiences) are given below:
Maximize, z =
Subject to, the linear constraints on the available number ads of 15 media types are,
And, the linear constraints on the minimum required ads of media vehicles to the four specified target audiences that must be engaged are:
We develop a near optimization model which allocate media vehicles to predetermined target segments. As this media allocation problem is formulated by using weapon-target assignment problem with 60 decision variables. By using our algorithm, we have solved the Media Allocation problem in a short time. In this case, we only change the data values in the ‘dat’ file, use the same mod.file and run.file. The result is given in Figure 8.
Number of ads reaching to target audiences.
This hypothetical example was given and solved by using MS Excel [20] and meta-heuristic genetic algorithm [21] previously. We have used our proposed algorithm to solve the media allocation problem. The solutions obtained by using genetic algorithm [21] and MS Excel [20] are shown in Tables 3 and 4, respectively [22].
Media vehicles | Morning time (1) | Afternoon time (2) | Prime time (3) | Night time (4) |
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Somoy News (1) | 0 | 0 | 0 | 0 |
BTV (2) | 7 | 0 | 0 | 0 |
Channel I (3) | 6 | 1 | 0 | 2 |
NTV (4) | 0 | 5 | 0 | 0 |
ETV (5) | 0 | 0 | 6 | 0 |
ATN News (6) | 2 | 0 | 5 | 0 |
GTV (7) | 0 | 0 | 0 | 0 |
Radio Today (8) | 2 | 0 | 8 | 0 |
Radio Foorti (9) | 0 | 14 | 0 | 1 |
Facebook (10) | 0 | 0 | 0 | 12 |
Prothom Alo (11) | 2 | 2 | 2 | 2 |
Ittefaq (12) | 1 | 1 | 1 | 1 |
Billboard (13) | 1 | 1 | 1 | 1 |
Printings (14) | 1 | 1 | 1 | 1 |
E-mail (15) | 1 | 1 | 1 | 1 |
Total no of ads | 23 | 26 | 25 | 21 |
Media allocation solution by genetic algorithm.
Media vehicles | Morning time (1) | Afternoon time (2) | Prime time (3) | Night time (4) |
---|---|---|---|---|
Somoy news (1) | 1 | 0 | 0 | 0 |
BTV (2) | 7 | 0 | 0 | 0 |
Channel I (3) | 7 | 0 | 0 | 2 |
NTV (4) | 0 | 5 | 0 | 0 |
ETV (5) | 0 | 0 | 6 | 0 |
ATN news (6) | 0 | 0 | 5 | 0 |
GTV (7) | 0 | 0 | 0 | 0 |
Radio today (8) | 2 | 0 | 8 | 0 |
Radio foorti (9) | 0 | 15 | 0 | 0 |
Facebook (10) | 0 | 0 | 0 | 12 |
Prothom Alo (11) | 2 | 2 | 2 | 2 |
Ittefaq (12) | 1 | 1 | 1 | 1 |
Billboard (13) | 1 | 1 | 1 | 1 |
Printings (14) | 1 | 1 | 1 | 1 |
E-mail (15) | 1 | 1 | 1 | 1 |
Total no. of ads | 23 | 26 | 25 | 20 |
Media allocation solution by MS excel solver.
To check the efficiency of our model, we need to calculate the objective function for all the existing solution that is to be maximized. So the graphical representation of the existing solutions of Media Allocation and objective function value for the corresponding results is shown in Figure 9.
Comparison the results between the three solving methods.
In Figure 9 it is clear that, our model gives the best result compared to other two methods. By analyzing the values of the objective function, we can see that the Genetic algorithm improved the solution using MS Excel by 0.004%. Thus, the AMPL algorithm employed in this study improved the previous solution using Genetic Algorithm and MS Excel Solver 0.033% and 0.037% respectively.
In this effort, we have proposed the AMPL program code as a meta-heuristic tool for the solution of all type of dynamic weapon-target assignment problem. We have discussed two numerical examples and we have compared the results of the problems with previously solved results. We have observed that our proposed computational algorithm is easy to compute and gives a nearby optimal solution than other methods in a short time. We believe that AMPL program approach is a good and feasible alternative for the solution of this type class of problems. As further research, we may employ our developed AMPL program approach for the problem with many targets, many weapons or advertising tools as well.
This chapter is performed on two types of optimization such as the weapon’s assignment problem.
In a warfare scenario, weapons allocation is very important. Since no exact algorithm is available to solve the WTAP, it is quite unavailable to estimate the quality of solutions produced by heuristic methods. The purpose of this chapter was to develop a new computerized algorithm to find a feasible solution in a reasonably fast time to help decision makers to make a proper assignment on the battlefield. We have developed a new computer-oriented algorithm by using AMPL to avoid the computational problems and solve this type of large scale problems. Our algorithm has been applied in two numerical examples of WTA problem and we have compared the complete outputs of the specified large scale problems with the outputs of the existing algorithms. We have concluded that our developed algorithm gives us the better result than others.
Finally, we conclude that the programming language AMPL is an effective technique to compute different types of optimization problems which will reduce the computational time for large scale problems. Overall, we have developed computer-oriented algorithms to solve the mentioned applications of optimization problems.
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