Multi-objective artificial bee algorithm based on decomposition by PBI method

This paper proposes a multi-objective artificial bee colony (MOABC) algorithm based on decomposition by penalty-based boundary intersection (PBI) method. It decomposes a MOP into a number of single-objective problems. The objective of every single-objective problem is based on the distance and angle from the current solution to their own ideal point so as to obtain the good convergence and distribution of the optimal solutions. In this way, the aggregate function is proposed by PBI method. Then the three phases of Artificial Bee Colony (ABC) algorithm are adopted, which are the employed bees sending, the unemployed bees following, and the scout bees converting. Among these phases, the improvement degree of every aggregate function is proposed as the fitness function, which could overcome the two shortcomings in the weighted sum function usually applied in the conventional MOABC. Besides, Boltzmann selection mechanism is used to obtain the probability of unemployed bees following the employed bees so that the selection pressure of unemployed bees in the optimizing process could be adjusted dynamically. The algorithm is validated on CEC2009 problems and the problems with complicated Pareto set shapes in terms of four indicators: IGD, HV, SPR, and EPS. Experimental results show that our proposed algorithm can perform better than other state-of-the-art algorithms in the convergence and diversity, and can be considered as a promising alternative to solve MOPs.