The Combinatorial problems are real world decision making problem with discrete and disjunctive choices. When these decision making problems involve more than one conflicting objective and constraint, it turns the polynomial time problem into NP-hard. Thus, the straight forward approaches to solve multi-objective problems would not give an optimal solution. In such case evolutionary based meta-...

Particle swarm optimization (PSO) has been successfully applied to solve various optimization problems. Recently, a state-based algorithm called multi-state particle swarm optimization (MSPSO) has been proposed to solve discrete combinatorial optimization problems. The algorithm operates based on a simplified mechanism of transition between two states. However, the MSPSO algorithm has to deal w...

This paper investigates the ability of a discrete particle swarm optimization algorithm (DPSO) to evolve solutions from infeasibility to feasibility for the Vehicle Routing Problem with Time Windows (VRPTW). The proposed algorithm incorporates some principles from multi-objective optimization to allow particles to conduct a dynamic trade-off between objectives in order to reach feasibility. The...

In this paper, we present an extension of the heuristic called “particle swarm optimization” (PSO) that is able to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and is based on the idea of having a set of subswarms instead of single particles. In each sub-swarm, a PSO algorithm is executed and, a...

In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...