Multi Objective Particle Swarm Optimization for a Discrete Time, Cost and Quality Trade -off Problem

Time -Cost trade-off is a known and important problem in project management, because project managers should decide that whether they want to shorten the time of a project and tolerate its execution costs or minimize the costs and accept delays. It was recently suggested that the quality of a project should also be taken into considerations in this decision-making. In this paper, a meta-heuristic algorithm for the discrete time, cost and quality trade-off problem was applied and multiple alternative were considered for the activities of a project. Advantage of this method over others is that every activity has several different modes offered by various options of time, cost and quality and the best options of project’s activities are determined in order to minimize the total cost of the project while maximizing the quality and also meeting a given deadline by assuming that duration and quality of project activities are discrete. Particle Swarm Optimization (PSO) algorithm was proposed to solve this problem. In this algorithm, initially a population of feasible solutions is generated. A number of these solutions are then selected and improved locally thorough the algorithm. The improved solutions are then combined to generate a new set of solutions. Since it was assumed that there were no bounds for three entities, a multi-objective problem has been considered. The whole process is stopped when no significant improvements, through fitness function achieved from multi-objective problem, can be made in the set of solutions that are observed. For validating of the efficiency of proposed multi-objective particle swarm, two types of problems, large size and small size are considered and for both types several problems are considered randomly and proposed algorithm is applied to them. Also a genetic algorithm is applied to those problems to comprise the efficiency of PSO and GA together.