Subpermutation-Based Evolutionary Multiobjective Algorithm for Load Restoration in Power Distribution Networks

This paper proposes a new multiobjective evolutionary algorithm for handling the problem of distribution network restoration after failures. The problem is formulated as a bi-objective optimization problem considering the total load restored and the time required for restoration. A new encoding scheme is proposed, in which the variables that encode the switch operation are separated into six groups, according to their roles in the faulty system configuration. Employing the idea of defining subspaces of a combinatorial space, those groups are used in order to define subpermutations within which the crossover and mutation operations are performed. In this way, the dimensionality of the search space becomes reduced, allowing a much more efficient search. The proposed encoding scheme also makes a single individual to encode several different solutions, leading to a further reduction of the search space dimensionality. Due to this peculiar feature of the encoding scheme, it becomes convenient to use an adaptation of the Strength Pareto Evolutionary Algorithm 2, in which the raw fitness is modified in order to allow the assignment of fitness to individuals that simultaneously encode several different solutions. The proposed algorithm was implemented such that good solutions are delivered within low processing times, of the order of some minutes for large real systems.