A penalty-based multi-objectivization approach for single objective optimization

Advances in Pareto optimization techniques have encouraged the study of their application to solve single-objective optimization problems. The motive is that the Pareto concept can be an effective approach to reduce the impacts of local optima. The most challenging task in developing such an approach is the reformulation of the target single-objective to multiple objectives. This paper proposes a new multi-objectivization approach by introducing an additional helper objective that is to be optimized with the primary objective simultaneously using Pareto local search. As a key feature, the additional objective is formulated as a function of the primary objective and penalties associated to solution features. The penalties are dynamically updated during the search, with the hope to guide the search to avoid non-promising features for the primary objective. Computational results on the traveling salesman problem and the quadratic assignment problem confirm the effectiveness of the proposed approach in comparison to other multi-objectivization approaches and state-of-the-art methods on these benchmarks.