Applied Soft Computing 2 (2002) 39–47 An immunity-based ant colony optimization algorithm for solving weapon–target assignment problem Zne-Jung Lee a,∗ , Chou-Yuan Lee b , Shun-Feng Su c a Department of Information Management, Kang-Ning Junior College of Nursing, National Taiwan University of Science and Technology, Taipei, Taiwan b Department of Information Management, Lan-Yang Institute of Technology, National Taiwan University of Science and Technology, Taipei, Taiwan c Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan Abstract In this paper, an immunity-based ant colony optimization (ACO) algorithm for solving weapon–target assignment (WTA) problems is proposed. The WTA problem, known as a NP-complete problem, is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force assets. The general idea of the proposed algorithm is to combine the advantages of ACO, the ability to cooperatively explore the search space and to avoid premature convergence, and that of immune system (IS), the ability to quickly find good solutions within a small region of the search space. From our simulation for those WTA problems, the proposed algorithm indeed is very efficient. © 2002 Published by Elsevier Science B.V. Keywords: Ant colony optimization; Optimization; Immune system; Weapon–target assignment 1. Introduction A weapon–target assignment (WTA) problem is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force assets. WTA in fact is an NP-complete problem, and various methods for solving such NP- complete optimization problems have been reported in the literature [1,9,10]. Classical methods are based on graph search approaches and usually result in ex- ponential computational complexities [10–14]. Thus, when the problem size is large, those methods may need lots of time to find the optimal solutions or some- times even are not able to find the optimal solutions. Other methods [3], such as simulated annealing (SA) [2,21] or genetic algorithms (GAs) are also widely ∗ Corresponding author. employed to solve optimization problems and have demonstrated satisfactory performances in various applications. SA has been shown to have the ability of finding the global optimum. However, due to its se- quential search characteristics, SA cannot be used in a parallel architecture to improve its search efficiency. GAs can be viewed as parallel search techniques that stimulate the evolution of individual structures for optimization inspired by natural evolution. However, the parallelism of search is based on the solution (or chromosome) level. Thus, the search efficiency may not be very nice. This phenomenon can be seen in our simulations. Recently, many research activities have been devoted to ant colony optimization (ACO) and im- mune system (IS) [16,18,19,28,30]. ACO and IS have applied to many fields and shown premising results in various applications [7,8,29,30]. ACO was initially 1568-4946/02/$ – see front matter © 2002 Published by Elsevier Science B.V. PII:S1568-4946(02)00027-3