This paper shows that by tuning the neighbouring area radius parameter, the performance of the proposed HVEA can be pushed towards better convergence, diversity or coverage and this could be beneficial to different types of problems. | VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 1 (2016) 10–32 Hyper-volume Evolutionary Algorithm Khoi Nguyen Le1,∗, Dario Landa-Silva2 1 VNU University of Engineering and Technology, Hanoi, Vietnam 2 The University of Nottingham, Nottingham, United Kingdom Abstract We propose a multi-objective evolutionary algorithm (MOEA), named the Hyper-volume Evolutionary Algorithm (HVEA). The algorithm is characterised by three components. First, individual fitness evaluation depends on the current Pareto front, specifically on the ratio of its dominated hyper-volume to the current Pareto front hyper-volume, hence giving an indication of how close the individual is to the current Pareto front. Second, a ranking strategy classifies individuals based on their fitness instead of Pareto dominance, individuals within the same rank are non guaranteed to be mutually non-dominated. Third, a crowding assignment mechanism that adapts according to the individual’s neighbouring area, controlled by the neighbouring area radius parameter, and the archive of non-dominated solutions. We perform extensive experiments on the multiple 0/1 knapsack problem using different greedy repair methods to compare the performance of HVEA to other MOEAs including NSGA2, SEAMO2, SPEA2, IBEA and MOEA/D. This paper shows that by tuning the neighbouring area radius parameter, the performance of the proposed HVEA can be pushed towards better convergence, diversity or coverage and this could be beneficial to different types of problems. Received 05 December 2015, revised 20 December 2015, accepted 31 December 2015 Keywords: Multi-objective Evolutionary Algorithm, Pareto Optimisation, Hyper-volume, Knapsack Problem. 1. Introduction An important issue in a MOEA is how to establish superiority between solutions within the population, . how to assess solution fitness in a multi-objective sense. In this paper, we proposed the Hyper-Volume Evolutionary Algorithm (HVEA), a MOEA that employs the
