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On repair by binary interpolation

One ongoing theme of our research [e.g. PPSN VIII, Yao,ed. LNCS 3242, pp. 292–301, Springer-Verlag, 2004.] is the value of infeasible solutions of constrained optimization problems. Infeasible solutions violate the constraints but they can nevertheless contain valuable genetic information. Particularly valuable ones might be only a single mutation away from feasibility, or even optimality. Consider also that an optimal solution is likewise only a single mutation away from infeasibility provided that the constraints are relevant (which we assume). The guiding principle is that for constrained optimization problems, evolutionary computation methods should pay particular attention to the region near the feasible/infeasible boundary. A desire for boundary exploration led us to create the Feasible-Infeasible Two Population Genetic Algorithm (FI-2PopGA). This model alternates between (1) evolving feasible solutions solely to improve them by seeking better objective function values and (2) evolving infeasible solutions solely to repair them by lessening their constraint violations. Let us give a general description of the observed behavior of the FI-2PopGA (op. cit.). A first order effect is that the infeasible population seeks out the boundary indiscriminately (exploration), and the feasible population seeks out the optima which will be located on or near the boundary (exploitation). Upon reaching the region of the boundary, a population can produce mutant children that end up in the other population where they are subjected to a different competitive criterion. A very interesting second order effect is obtained when mutant grandchildren end up reentering the population of their grandparents. This means that their genetic material has survived competitions involving two criteria: both approaching optima and also diminishing constraint violations. This makes both populations gradually become genetically similar and cluster on opposite sides of the boundary near optima. Of course, both boundary searching and dual population evolution have been studied before (see references in op. cit.). Our approach is one of the few that avoid attempting to heuristically evaluate candidate solutions by two unrelated criteria at the same time.