A multi-objective particle swarm for constraint and unconstrained problems

Abstract

Multi-objective particle swarm optimization algorithms (MOPS) are used successfully to solve real-life optimization problems. The multi-objective algorithms based on particle swarm optimization (PSO) have seen various adaptations to improve convergence to the true Pareto-optimal front and well-diverse non-dominated solution. In some cases, the values of the MOPS control parameters need to be fine-tuned while solving a specific multi-objective optimization problem. It is challenge to correctly fine-tune the value of the PSO control parameters when the true non-dominated solutions are not known as in case of a real-life optimization problem. To address this challenge, a multi-objective particle swarm optimization algorithm that uses constant PSO control parameters was developed. The new algorithm called NF-MOPSO is capable of solving different multi-objective optimization problems without the need of fine-tuning the value of the PSO control parameters. The NF-MOPSO enhances the convergence to the true Pareto-optimal front and improves the diversity of Pareto-optimal using the same fixed values for all the PSO control parameters. The NF-MOPSO uses constant values of the PSO control parameters such as acceleration coefficients $$c_{1}$$ and $$c_{2}$$ , and inertia weight $$\omega$$ . A Gaussian mutation is applied to the position of particles to increase diversity while a penalty function is used as constraint mechanism. The algorithm has been tested on 45 well-known benchmark test functions using four performance metrics. The test results demonstrate the capability of the NF-MOPSO to solve different multi-objective optimization problems using the same value of the PSO control parameters. The capability of the NF-MOPSO was demonstrated in real-life optimization problem by solving a multi-objective optimization problem of a neutron radiography collimator. The results of collimator optimization showed that the optimizer was able to provide a set of Pareto optimal solutions from which the geometrical design parameters of a collimator could be retrieved for given application.