A discrete particle swarm optimization algorithm applied in constrained static weapon-target assignment problem

The weapon-target assignment (WTA) problem is an important content in military operational research. In this paper, a discrete particle swarm optimization (DPSO) algorithm is presented to solve the constrained static weapon-target assignment (SWTA) problem subject to firing range constraint, weapon-target match constraint and so on. This constrained SWTA problem with upper bound on the number of weapons available to each weapon platform is a NP-complete mathematical problem to assign weapon platforms to targets properly. Unlike those one-to-one WTA problems, in this constrained SWTA model, one weapon platform can be assigned to several targets and one target can be attacked by more than one weapon in saturation attack. A special encoding strategy is used to satisfy the firing range constraint, weapon-target match constraint and available weapon quantity constraint. The proposed algorithm introduces the uniform mutation and crossover concepts of genetic algorithm (GA) into standard PSO algorithm to generate the update equation of the proposed DPSO algorithm. And penalty function method is adopted to deal with other constraints by adding restrictions to objective function as the fitness function. The simulation results demonstrate the proposed DPSO algorithm is very efficient to solve this constrained SWTA problem and superior to general GA and standard PSO algorithm.

I. Introduction

THE weapon-target assignment (WTA) is a classic military operational problem and a kernel of command and control. The goal of WTA is assigning weapons to targets properly to get the best combat effectiveness. From the perspective of whether to consider the time factor, the WTA problems can be divided into dynamic weapon-target assignment (DWTA) models and static weapon─target assignment (SWTA) models. Besides, the WTA problems also can be classified as constrained WTA problems (CWTA) and general WTA problems. In this paper, we mainly discuss the constrained SWTA problem which has an upper bound on the number of weapons available to each weapon platform. Because WTA is a NP-complete mathematical problem [1], it's difficult to find the optimal solution when the scale of this problem is large. Until now, there are a number of methods applied in solving SWTA problem such as implicit enumeration algorithm [2], dynamic programming [3], simulated annealing (SA) [4], traditional genetic algorithm (GA) [5], genetic algorithm with greedy eugenics [6], neural-network-based (NN-based) method [7], [8], immunity-based ant colony optimization (ACO) algorithm [9], very large scale neighborhood (VLSN) search algorithm [10], discrete particle swarm algorithm (DPSO) [11] and so on. Although DPSO algorithm has been developed to solve the SWTA problem [11], this one-to-one WTA model doesn't restrain the available quantity of weapons on each weapon platform and the number of weapons of each weapon platform attacking each target cannot be calculated.