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This research aims at solving the special case of multistate assignment problem. The problem includes many special characteristics which are not normally included in the assignment problem. There are many types and conditions of vehicles included in the planning and different road conditions of traveling, which would have different effects on fuel consumption, which is the objective function of the study. The proposed problem is determined as a large and complicated problem making the optimization software unable to find an optimal solution within the proper time. Therefore, the researchers had developed a method for determining the optimal solution by using particle swarm optimization (PSO) in which the methods were developed for solving the proposed problem. This method is called the modified particle swarm optimization (modified PSO). The proposed method was tested with three groups of tested instances, i.e., small, medium, and large groups. The computational result shows that, in small-sized and medium-sized problems, the proposed method performed not significantly different from the optimization software, and in the large-sized problems, the modified PSO method gave 3.61% lower cost than the cost generated from best solution generated from optimization software within 72 hours and it gave 11.03% better solution than that of the best existing heuristics published so far (differential evolution algorithm).

The Modified Particle Swarm Optimization for a Special Case of the Assignment Problem: A Case Study in Chicken Transportation