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In the past few decades, many multiobjective evolutionary optimizationalgorithms (MOEAs) have been proposed to find a finite set of approximatePareto solutions for a given problem in a single run, each with its ownstructure. However, in many real-world applications, it could be desirable tohave structure constraints on the entire optimal solution set, which define thepatterns shared among all solutions. The current population-based MOEAs cannotproperly handle such requirements. In this work, we make the first attempt toincorporate the structure constraints into the whole solution set by a singlePareto set model, which can be efficiently learned by a simple evolutionarystochastic optimization method. With our proposed method, the decision-makerscan flexibly trade off the Pareto optimality with preferred structures amongall solutions, which is not supported by previous MOEAs. A set of experimentson benchmark test suites and real-world application problems fully demonstratesthe efficiency of our proposed method.

Dealing with Structure Constraints in Evolutionary Pareto Set Learning