Crowded comparison operators for constraints handling in NSGA-II for optimal design of the compensation system in electrical distribution networks

This paper proposes an improvement of an efficient multiobjective optimization algorithm, Non-dominated Sorting Genetic Algorithm II, NSGA-II, that has been here applied to solve the problem of optimal capacitors placement in distribution systems. The studied improvement involves the Crowded Comparison Operator and modifies it in order to handle several constraints. The problem of optimal location and sizing of capacitor banks for losses reduction and voltage profile flattening in medium voltage (MV) automated distribution systems is a difficult combinatorial constrained optimization problem which is deeply studied in literature. In this paper, the efficiency of the proposed Crowded Comparison Operator, CCO1, is compared to the efficiency of another Crowded Comparison Operator, CCO2, whose definition derives from the constraint-domination principle proposed by Deb et al. The two operators are tested on difficult test problems as well as on the optimal capacitors placement problem.