**Abstract**

In Command and Control (C2), Threat Evaluation (TE) and Weapon Target Allocation (WTA) are two key components. To build an automated system in this area after modeling Threat Evaluation and Weapon Target Allocation processes, solving these models and finding the optimal solution are further important issues. This setting demands instantaneous operational planning and decision making under inherent severe stress conditions. The associated responsibilities are usually divided among a number of operators and also computerized decision support systems that aid these operators during the decision making process. In this Chapter, the literature in the area of WTA system with the emphasis on the modeling and solving methods are surveyed.

**Keywords:** command and control (C2), weapon target allocation (WTA), mathematical models, algorithmic approaches, decision support systems (DSS)

#### **1. Introduction**

The field of air defense is one of those areas where resource allocation is of great importance. Research on the resource allocation problem with military purposes dates back to the 1950s and 1960s where the first modeling issues for WTA problem were investigated [1]. Rapid developments in the field of battle and attention to advances in threat technology in the recent years, pose significant challenges for commanders in C2 Systems (CCSs). Furthermore, the complexity and diversity of engagement scenarios, and the volume and imperfect nature of data to be processed under time-critical conditions make the commander's problems severe.

The WTA problem is a well-known military operations research problem which has many aspects and features. (a) It is a dynamic decision-making problem. Serial and interdependent decisions are made at different periods of time to deal with different threats. At each period, a decision (about one or several engagements) is made. The consequences or outcomes of decisions made at a given period change the characteristics of the problem for the next periods (e.g. ammunition availability, threats conditions, change in tactics, decreasing the data ambiguity). One important characteristic of dynamic decision-making problems is that the information is obtained gradually over time. (b) The WTA is a multiple criteria decision-making problem. In fact, the decision-making problem for the resource management is

#### *Computational Optimization Techniques and Applications*

based on conflicting criteria. For example, minimizing the risk, maximizing the effectiveness measures and so on. (c) The resource allocation problem is subject to uncertainty (e.g., stochastic). The uncertainty is related to many aspects of the model such as the hit probability of the weapons and targets characteristics (e.g. maneuvering, tracking, identification/classification and so on). Therefore, decision consequences are uncertain and usually modeled by probabilistic distributions. Then, a kill assessment process checks the result of executed actions and reports either the threat is diminished or not. (d) The resource allocation problem is a timecritical decision-making problem. Decision makers have to decide and act under tight temporal constraints. The allocation of available weapons on priority bases to the correct targets needs complex calculations in a very short time.

and improve the weakness of models and solutions procedures some useful sugges-

The organization of this Chapter is as follows. In Section 2, we give a brief description of the problem and its components. In Section 3, the basic formulations of the WTA problem are presented and variations of modeling approaches are explained. Section 4 contains classification for algorithmic approaches. The last section contains some concluding remarks and providing directions for future

There are many different functions that must be handled in an air defense system. From a high-level command perspective, these functions can be divided in

The purpose of picture compilation process is generating a representation of the volume of interest (VOI) based on data and information received from a variety of sensors/sources. This step often includes the following sub-processes: (i) The target detection, (ii) target tracking, and (iii) target identification. The picture exploitation is the subsequent process that includes the following sub-processes: (i) Threat Evaluation (TE), (ii) Engageability assessment and (iii) weapons assignment (here referred to as WTA) [2]. In a military context this set of sub-problems also are known as combat power management (CPM). The WTA component, in a CPM

• *Response planning*; this sub-problem deals with the combat resource allocation. During this process, one or more of available weapons are assigned to engage

• *Response execution*; in this phase the planned response is executed at the

• *Outcome assessment*; in this process the outcome of the executed actions or engagement is identified and/or verified. This process is well known as killing assessment (where outcomes are 0/1 for kill/alive) or damage assessment (where outcome is a value in [0, 1] i.e. partial damage is possible) in C2

This research concentrates only on the response planning procedure of WTA process. This process is about how and when to allocate the available defensive resources. In other words, response planning procedure has two aspects: resource

In C2 context the response planning mainly is pertained to resource allocation problem. Resource allocation is the assignment of resources to activities, where the start and end times of each activity is given [8]. This problem is concerned with optimally assigning weapons to the hostile targets so that after all engagements, the BF expectations are met as far as possible. Resource allocation scheduling is another important aspect of the response planning that consists of determining the start and end times of the activities. In pure scheduling problems, activities are already chosen (or given), leaving only the problem of determining a feasible and possibly

two main processes: picture compilation and picture exploitation [2].

tions have been put forward for future studies.

*DOI: http://dx.doi.org/10.5772/intechopen.96318*

*A Survey on Weapon Target Allocation Models and Applications*

**2. The WTA problem and its components**

system can be divided into three sub-problems:

each threat.

domain.

**75**

designated time.

allocation planning and scheduling.

**2.1 Resource allocation: planning and scheduling**

research.

Some important properties of the WTA problem are:


Finding efficient solutions for WTA problem with these features, is the main challenge of the command. These WTA characteristics often make the solving process and finding the optimal solution difficult.

Researchers have suggested different mathematical formulations of the WTA problem and proposed exact algorithms and heuristic/meta-heuristic methods to solve the problem. The exact algorithms that have been introduced to solve the WTA problem are not comprehensive and usually run under the following conditions: (i) when all the defensive weapons are identical [6] or (ii) when the hostile targets can receive at most one defensive weapon [7]. Despite extensive attention of research in this field, a comprehensive and classificatory review will pave the path for more efficient and practical models and algorithms in accordance with the advent in the technology. Hence, in this survey different WTA models and solutions methods used for this problem are reviewed. Based on the modeling approaches, the available literature is classified into two groups. (i) defense allocation models, (ii) the game models. In the second part, the important characteristics for the WTA models and the solution process for the resource allocation problem are investigated. Like many other problems the WTA solution algorithms can be divided into three main categories, (a) enumerative techniques, (b) heuristic/approximate methods and (c) meta-heuristic methods. Finally, mission planning systems which have been developed in the military are listed. To cover the existing shortcomings

based on conflicting criteria. For example, minimizing the risk, maximizing the effectiveness measures and so on. (c) The resource allocation problem is subject to uncertainty (e.g., stochastic). The uncertainty is related to many aspects of the model such as the hit probability of the weapons and targets characteristics (e.g. maneuvering, tracking, identification/classification and so on). Therefore, decision consequences are uncertain and usually modeled by probabilistic distributions. Then, a kill assessment process checks the result of executed actions and reports either the threat is diminished or not. (d) The resource allocation problem is a timecritical decision-making problem. Decision makers have to decide and act under tight temporal constraints. The allocation of available weapons on priority bases to

• It is NP-complete and consequently the computation time of any optimal

• It is sequential (the results of previous engagements are observed before

• The objective function is nonlinear (The WTA objective, often is a linear

• It is stochastic (weapon-target engagements are modeled as stochastic events) [5].

*Xik* ) [4].

combination of nonlinear summand of expressions like 1½ � � *Pik*

• It is large-scale (the combination of weapons-targets-time, grows

• It is mixed-integer; WTA is a combination of discrete and continuous

Finding efficient solutions for WTA problem with these features, is the main challenge of the command. These WTA characteristics often make the solving

Researchers have suggested different mathematical formulations of the WTA problem and proposed exact algorithms and heuristic/meta-heuristic methods to solve the problem. The exact algorithms that have been introduced to solve the WTA problem are not comprehensive and usually run under the following conditions: (i) when all the defensive weapons are identical [6] or (ii) when the hostile targets can receive at most one defensive weapon [7]. Despite extensive attention of research in this field, a comprehensive and classificatory review will pave the path for more efficient and practical models and algorithms in accordance with the advent in the technology. Hence, in this survey different WTA models and solutions methods used for this problem are reviewed. Based on the modeling approaches, the available literature is classified into two groups. (i) defense allocation models, (ii) the game models. In the second part, the important characteristics for the WTA models and the solution process for the resource allocation problem are investigated. Like many other problems the WTA solution algorithms can be divided into three main categories, (a) enumerative techniques, (b) heuristic/approximate methods and (c) meta-heuristic methods. Finally, mission planning systems which have been developed in the military are listed. To cover the existing shortcomings

algorithm grows exponentially with its size [2]. The complexity of this problem drastically increases if the temporal and spatial constraints of both the Blue Forces (BF) (i.e. friendly forces) and Red Forces (RF) (i.e. hostile targets) are

the correct targets needs complex calculations in a very short time.

Some important properties of the WTA problem are:

*Computational Optimization Techniques and Applications*

considered.

exponentially) [2].

variables.

**74**

making present assignments) [3].

process and finding the optimal solution difficult.

and improve the weakness of models and solutions procedures some useful suggestions have been put forward for future studies.

The organization of this Chapter is as follows. In Section 2, we give a brief description of the problem and its components. In Section 3, the basic formulations of the WTA problem are presented and variations of modeling approaches are explained. Section 4 contains classification for algorithmic approaches. The last section contains some concluding remarks and providing directions for future research.
