An evolving surrogate model-based differential evolution algorithm

A multi-model assisted differential evolution algorithm for computationally expensive optimization problems

Surrogate models are commonly used to reduce the number of required expensive fitness evaluations in optimizing computationally expensive problems. Although many competitive surrogate-assisted evolutionary algorithms have been proposed, it remains a challenging issue to develop an effective model management strategy to address problems with different landscape features under a limited computational budget. This paper adopts a coarse-to-fine evaluation scheme basing on two surrogate models, i.e., a coarse Gaussian process and a fine radial basis function, for assisting a differential evolution algorithm to solve computationally expensive optimization problems. The coarse Gaussian process model is meant to capture the general contour of the fitness landscape to estimate the fitness and its degree of uncertainty. A surrogate-assisted environmental selection strategy is then developed according to the non-dominance relationship between approximated fitness and estimated uncertainty. Meanwhile, the fine radial basis function model aims to learn the details of the local fitness landscape to refine the approximation quality of the new parent population and find the local optima for real-evaluations. The performance and scalability of the proposed method are extensively evaluated on two sets of widely used benchmark problems. Experimental results show that the proposed method can outperform several state-of-the-art algorithms within a limited computational budget.

Underestimation-Assisted Global-Local Cooperative Differential Evolution and the Application to Protein Structure Prediction

Various mutation strategies show distinct advantages in differential evolution (DE). The cooperation of multiple strategies in the evolutionary process may be effective. This paper presents an underestimation-assisted global and local cooperative DE to simultaneously enhance the effectiveness and efficiency. In the proposed algorithm, two phases, namely, the global exploration and the local exploitation, are performed in each generation. In the global phase, a set of trial vectors is produced for each target individual by employing multiple strategies with strong exploration capability. Afterward, an adaptive underestimation model with a self-adapted slope control parameter is proposed to evaluate these trial vectors, the best of which is selected as the candidate. In the local phase, the better-based strategies guided by individuals that are better than the target individual are designed. For each individual accepted in the global phase, multiple trial vectors are generated by using these strategies and filtered by the underestimation value. The cooperation between the global and local phases includes two aspects. First, both of them concentrate on generating better individuals for the next generation. Second, the global phase aims to locate promising regions quickly while the local phase serves as a local search for enhancing convergence. Moreover, a simple mechanism is designed to determine the parameter of DE adaptively in the searching process. Finally, the proposed approach is applied to predict the protein 3D structure. Experimental studies on classical benchmark functions, CEC test sets, and protein structure prediction problem show that the proposed approach is superior to the competitors.

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

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.

Differential Evolution With Underestimation-Based Multimutation Strategy

As we know, the performance of differential evolution (DE) highly depends on the mutation strategy. However, it is difficult to choose a suitable mutation strategy for a specific problem or different running stages. This paper proposes an underestimation-based multimutation strategy (UMS) for DE. In the UMS, a set of candidate offsprings are simultaneously generated for each target individual by utilizing multiple mutation strategies. Then a cheap abstract convex underestimation model is built based on some selected individuals to obtain the underestimation value of each candidate offspring. According to the quality of each candidate offspring measured by the underestimation value, the most promising candidate solution is chosen as the offspring. Compared to the existing probability-based multimutation techniques, no mutation strategies are lost during the search process as each mutation strategy has the same probability to generate a candidate solution. Moreover, no extra function evaluations are produced because the candidate solutions are filtered by the underestimation value. The UMS is integrated into some DE variants and compared with their original algorithms and several advanced DE approaches over the CEC 2013 and 2014 benchmark sets. Additionally, a well-known real-world problem is employed to evaluate the performance of the UMS. Experimental results show that the proposed UMS can improve the performance of the advanced DE variants.