Global and Local Surrogate-Assisted Differential Evolution for Expensive Constrained Optimization Problems With Inequality Constraints

Abstract

For expensive constrained optimization problems (ECOPs), the computation of objective function and constraints is very time-consuming. This paper proposes a novel global and local surrogate-assisted differential evolution (DE) for solving ECOPs with inequality constraints. The proposed method consists of two main phases: 1) global surrogate-assisted phase and 2) local surrogate-assisted phase. In the global surrogate-assisted phase, DE serves as the search engine to produce multiple trial vectors. Afterward, the generalized regression neural network is used to evaluate these trial vectors. In order to select the best candidate from these trial vectors, two rules are combined. The first is the feasibility rule, which at first guides the population toward the feasible region, and then toward the optimal solution. In addition, the second rule puts more emphasis on the solution with the highest predicted uncertainty, and thus alleviates the inaccuracy of the surrogates. In the local surrogate-assisted phase, the interior point method coupled with radial basis function is utilized to refine each individual in the population. During the evolution, the global surrogate-assisted phase has the capability to promptly locate the promising region and the local surrogate-assisted phase is able to speed up the convergence. Therefore, by combining these two important elements, the number of fitness evaluations can be reduced remarkably. The proposed method has been tested on numerous benchmark test functions from three test suites and two real-world cases. The experimental results demonstrate that the performance of the proposed method is better than that of other state-of-the-art methods.

Evaluating MAP-Elites on constrained optimization problems

“…Other possibilities will be to use the "directional variation" operator introduced in [31], that exploits inter-species (or inter-elites) correlations to accelerate the search, add, most of all, specific constraint handling techniques (especially for handling equality constraints, which as we have seen is the main weakness of this approach) [8,15]. It is also worth considering the use of surrogate models, such as in [33], in order to further speed up the the search and guide it towards the feasible region, still allowing the algorithm to keep infeasible solutions as part of the map. Another improvement can be obtained by using an explicit Quality Diversity measure [1,4,20,21], so to enforce at the same time a better coverage of the feature space and a further improvement in terms of optimization results.…”

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“… is the joint PDF of and . The conditional mean of on [ 44 ] is The estimated joint PDF can be written as [ 44 ] where q is a user-defined smoothness parameter. Combining Equations ( A18 ) and ( A19 ), the conditional mean of , which is thought to be equal to , can be given by [ 44 ] As a kind of RBFNN, the GRNN has a better approximation capability and learning rate than the traditional RBFNN.…”

“…The estimated joint PDF can be written as [ 44 ] where q is a user-defined smoothness parameter. Combining Equations ( A18 ) and ( A19 ), the conditional mean of , which is thought to be equal to , can be given by [ 44 ] …”