A Multi-Form Evolutionary Search Paradigm for Bi-level Multi-Objective Optimization

Many practical optimization problems in the fields of transportation, business, engineering, environmental economics, etc., involve more than one level of decision-making and can be modeled as a bi-level optimization problem with a nested structure of decision variables. Existing studies have made remarkable progress on bi-level single-objective problems. However, due to the increased complexities in terms of computation and decision-making, few efforts have been devoted to bi-level multi-objective optimization problems (BLMOPs). This paper proposes an evolutionary multi-form optimization paradigm that explores alternative formulations of the target task to assist in the search with the original formulation, namely BLMFO, for bi-level multi-objective optimization. Firstly, in the proposed framework, alternative formulations of the original problem are derived to facilitate the problem-solving and also alleviate computational overheads. Then, BLMFO performs the evolutionary search in the original problem space and the auxiliary task space simultaneously to combine searching for feasible solutions and exploring regions of promising solutions, thus ensuring the effectiveness of the proposed framework. Further, useful information is transferred across the original and auxiliary tasks via explicit knowledge transfer to enable complementary exploration for better optimization performance. To the best of our knowledge, this work serves as the first attempt to solve BLMOPs via multi-form evolutionary optimization in the literature. The framework is verified using four instantiation groups with different underlying baseline solvers on various benchmarks and practical problems. The experimental results show the effectiveness and superiority of the proposed framework in terms of performance indicators and the quality of final optimized solutions.