An effective use of crowding distance in multiobjective particle swarm optimization - Raquel, Carlo R. (2005)
Many real-world optimization problems have multiple objectives which are not only interacting but even possibly conflicting. The optimal solutions for these problems are in the form of compromises or "trade-offs" among the different decision variables that optimize the given objectives. The set of optimal solutions for a multiobjective optimization problem in the objective space is known as the Pareto front. The goals of a multiobjective optimization algorithm are to approximate and to generate a well-distributed Pareto front. Particle Swarm Optimization (PSO) is a recent heuristic algorithm that has been successfully applied to single optimization problems. This work presents an algorithm which we call MOPSO-CD that extends the single-objective PSO to handle multiobjective optimization problems by incorporating the mechanism of crowding distance together with a mutation operator to maintain the diversity of nondominated solutions stored in an external archive. MOPSO-CD also has a constraint handling mechanism for solving constrained optimization problems. The performance of MOPSO-CD was compared to another multiobjective PSO algorithm called MOPSO using four test functions and three performance metrics. The experimental results show that MOPSO-CD is highly competitive in converging towards the Pareto front and has generated a much better distribution of Pareto-optimal solutions compared to MOPSO. Thus, the use of crowding distance is very effective not only in maintaining a well-distributed Pareto front but also in improving the convergence capability of the algorithm towards the Pareto front.