**3.3 Air missile system**

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].

efficient algorithms. Although these algorithms do not give the optimal or best

solution it is known that these algorithms give near-optimal solutions.

4: **while** *allocated Weapon Count < =no Of Weapons* **do**

10: *decrease target Values [i] \* kill Probabilities [i][k]*

20: *unallocated Weapons. Remove (allocated Weapon)*

23: *allocated Weapon Count allocated Weapon Count* + 1

25: *solution. Value Calculate Solution Value (solution. allocations)*

22: *target Values* [*allocated Target*] *target Values* [*allocated Target*]-*max*

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]:

21: *solution. Allocations* [*k*] *allocated Target*

7: **while** *k < unallocated Weapons. Count* **do**

**Algorithm**: MMR Algorithm

*DOI: http://dx.doi.org/10.5772/intechopen.93665*

5: *max Decrease Min Value*

9: **while** *i < no Of Targets* **do**

11: **if** *decrease > max Decrease* **then** 12: *max Decrease decrease* 13: *allocated Target i* 14: *allocated Target k*

1: *solution. Allocations* {} 2: *solution. Value MaxValue* 3: *allocated Weapon Count* 0

*Weapon Target Assignment*

6: *k* 1

8: *i* 1

15: **end if** 16: *i i +* 1 17: **end while** 18: *k k +* 1 19: **end while**

*Decrease*

24: **end while**

26: **return** *solution*

*3.5.2 Genetic algorithms (GA)*

**Algorithm**: Genetic Algorithm

3: *solution. Allocations* {} 4: *solution.value MaxValue*

2: *end Time start Time + allowed Search Time*

5: if *no Of Targets > no Of Weapons* **then** 6: *no Of Individuals no Of Targets*

8: *no Of Individuals no Of Weapons*

1: *start Time Now*

7: **else**

**189**

#### **3.4 WTA approach to media allocation**

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.

### **3.5 Various existing algorithms**

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:

#### *3.5.1 Maximum marginal return (MMR) algorithm*

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.
