Solving many-objective optimisation problems by an improved particle swarm optimisation approach and a normalised penalty method

Abstract

In this paper, a novel modified particle swarm optimisation (NMPSO) approach is presented to handle the many-objective knapsack (MOK) problem. NMPSO relies on the global best particle to guide the search of all particles in each generation. Furthermore, a randomisation-based mutation is adopted to overcome the premature convergence. A normalised penalty method (NPM) is devised to reach a compromise between objective functions and inequality constraints, which enables particles to explore solution space more precisely. In summary, the contribution of our work can be summarised in two aspects: 1) a more powerful approach called NMPSO is proposed; 2) a reasonable NPM is devised. Five improved PSOs are used to handle the MOKs with different number of objective functions and dimensions. Experimental results show that NMPSO has higher efficiency than the other four approaches. It uses the lowest computational cost and achieves the smallest penalty function values for most MOKs.