AMOBH: Adaptive Multiobjective Black Hole Algorithm

This paper proposes a new multiobjective evolutionary algorithm based on the black hole algorithm with a new individual density assessment (cell density), called “adaptive multiobjective black hole algorithm” (AMOBH). Cell density has the characteristics of low computational complexity and maintains a good balance of convergence and diversity of the Pareto front. The framework of AMOBH can be divided into three steps. Firstly, the Pareto front is mapped to a new objective space called parallel cell coordinate system. Then, to adjust the evolutionary strategies adaptively, Shannon entropy is employed to estimate the evolution status. At last, the cell density is combined with a dominance strength assessment called cell dominance to evaluate the fitness of solutions. Compared with the state-of-the-art methods SPEA-II, PESA-II, NSGA-II, and MOEA/D, experimental results show that AMOBH has a good performance in terms of convergence rate, population diversity, population convergence, subpopulation obtention of different Pareto regions, and time complexity to the latter in most cases

On Using Populations of Sets in Multiobjective Optimization

Most existing evolutionary approaches to multiobjective optimization aim at finding an appropriate set of compromise solutions, ideally a subset of the Pareto-optimal set. That means they are solving a set problem where the search space consists of all possible solution sets. Taking this perspective, multiobjective evolutionary algorithms can be regarded as hill-climbers on solution sets: the population is one element of the set search space and selection as well as variation implement a specific type of set mutation operator. Therefore, one may ask whether a ‘real ’ evolutionary algorithm on solution sets can have advantages over the classical single-population approach. This paper investigates this issue; it presents a multi-population multiobjective optimization framework and demonstrates its usefulness on several test problems and a sensor network application