Multi-modal search for multiobjective optimization: an application to optimal smart grids management

Abstract

This paper studies the possibility to use efficient multimodal optimizers for multi-objective optimization. In this paper, the application area considered for such new approach is the optimal dispatch of energy sources in smart grids. The problem indeed shows a non uniform Pareto front and requires efficient optimal search methods. The idea is to exploit the potential of agents in population-based heuristics to improve diversity in the Pareto front, where solutions show the same rank and are thus equally weighted. Since Pareto dominance is at the basis of the theory of multi-objective optimization, most algorithms show the non dominance ranking as quality indicator, with some problem in finding sufficiently diverse solutions. Other algorithms, such as the Indicator Based Evolutionary Algorithm, use most commonly the Hypervolume indicator which also intrinsically shows diversity preserving problems. In this paper, the Glow-worm swarm optimizer is used as multimodal optimization method over a set of solutions ordered based on non dominance. After the introduction of this algorithm, its multiobjective implementation is briefly outlined. Then some tests are carried out on test functions taken from the literature giving quite encouraging results. Finally, the problem of optimal energy dispatch in smart grids is described and different applications are shown comparing the results with those obtained emplying the Non Dominated Sorting Genetic Algorithm II.