A Competitive Approach For Bi-Level Co-Evolution

Real-life problems often involve several decision makers whose decisions impact each other. When two decision makers decides sequentially, these problems are referred to as bi-level optimization problems. Generally modeled as nested optimization problems, they are NP-hard even for two linear and continuous levels. Such problems often occur in situations were only a part of the decision variables is controlled by each decision makers. Their final objective value is thus subject to each other's decision. From the first decision maker point of view, it is necessary to predict the "rational reaction" of the second decision maker which may have a conflicting objective function. The first decision maker should therefore ensure that this reaction will not have a disastrous effect on its own final objective value. The inherent complexity of bi-level optimization problems led researchers to consider metaheuristics. Among the most promising metaheuristics, co-evolutionary algorithms proved their abilities to tackle large scale problems. Unfortunately, BOPs are naturally strongly epistatic. In this work, we propose an hybrid competitive co-evolutionary algorithm (CARBON) to tackle this pitfall. We compare CARBON against another co-evolutionary approach for bi-level optimization problems, i.e., COBRA. Experimental results demonstrate the abilities of CARBON to break the inherent nested structure that makes bi-level optimization problems so difficult.