* Corresponding author 188 An International Journal of Optimization and Control: Theories & Applications ISSN: 2146-0957 eISSN: 2146-5703 Vol.10, No.2, pp.188-197 (2020) https://doi.org/10.11121/ijocta.01.2020.00775 RESEARCH ARTICLE A modified crow search algorithm for the weapon-target assignment problem Emrullah Sonuç * a Department of Computer Engineering, Karabuk University, Turkey esonuc@karabuk.edu.tr ARTICLE INFO ABSTRACT Article history: Received: 26 January 2019 Accepted: 31 January 2020 Available Online: 4 June 2020 The Weapon-Target Assignment (WTA) problem is one of the most important optimization problems in military operation research. In the WTA problem, assets of defense aim the best assignment of each weapon to target for decreasing expected damage directed by the offense. In this paper, Modified Crow Search Algorithm (MCSA) is proposed to solve the WTA problem. In MCSA, a trial mechanism is used to improve the quality of solutions using parameter LIMIT. If the solution is not improved after a predetermined number of iterations, then MCSA starts with a new position in the search space. Experimental results on the different sizes of the WTA problem instances show that MCSA outperforms CSA in all problem instances. Also, MCSA achieved better results for 11 out of 12 problem instances compared with four state-of-the-art algorithms. The source codes of MCSA for the WTA are publicly available at http://www.3mrullah.com/MCSA.html Keywords: Combinatorial optimization Crow search algorithm Nature inspired meta-heuristic algorithms Weapon-target Assignment Problem AMS Classification 2010: 68T20, 90C27 1. Introduction Weapon-Target Assignment (WTA) problem is one of the most important optimization problems in military operation research. The WTA problem has two versions as the static weapon-target assignment problem (SWTA) and the dynamic weapon-target assignment problem (DWTA). The main difference between the SWTA and the DWTA is the timing of launching weapons to targets. In the DWTA, the launching of weapons is performed asynchronously, however in the SWTA, all weapons are launching at the same time and only once [1]. In the WTA problem, the aim is to minimize the damage caused by attacks of the targets. Hence, assets of the defense aim the best assignments for minimal damage after the engagement. Several exact and approximation algorithms [2–4] have recently involved in solving the WTA problem. Since the WTA is an NP-complete problem [5], exact algorithms can not solve large-scale WTA problems in polynomial time. To overcome this problem, metaheuristic algorithms are presented to solve the WTA problem. Metaheuristic algorithms provide a valid solution in a reasonable time [6]. In recent years, metaheuristic algorithms for solving optimization and engineering problems have attracted much attention in the literature. The development of nature-inspired metaheuristic algorithms has increased rapidly in the last decades [7]. These algorithms have good ability to solve global optimization problems even it is complex or high dimensional. The strategy of metaheuristic algorithms is to obtain a solution in a reasonable time for optimization problems which are naturally intricate and very hard to solve. This strategy is built on two main features: exploration and exploitation. In the exploration stage, the algorithm attempts to find a new solution in the search space. In the exploitation stage, the algorithm searches for the neighborhood of the highest quality solution so far to get better solutions. The balance of these two stages is highly important for the algorithm to be successful. The Crow Search Algorithm (CSA) [8] is a population- based metaheuristic algorithm inspired by the behavior of crows, has a good exploration and exploitation for optimization problems. Many metaheuristic algorithms have been proposed for the WTA problem. Şahin and Leblebicioğlu [9] presented a Hierarchical Fuzzy Decision Maker method to achieve the best assignment for improving performance on the battlefield. The proposed method increased the approximation performance in comparison to exact and optimal methods. Wang et al. [10] developed a Grey Wolf Optimizer which is the