LCS & GBML Central

Effective constraint handling techniques (CHTs) are of great significance for evolutionary algorithms (EAs) dealing with constrained optimization problems (COPs). To date, many CHTs, such as penalty function, superiority of feasible solutions, and $epsilon $ -constraint (EC), have been designed. However, different CHTs are usually suited to different problems, even the most appropriate technique changes along with the stages of the optimization process. Motivated by this phenomenon, we propose a voting-mechanism-based ensemble framework, named voting mechanism for constraint handling (VMCH), to integrate multiple CHTs for solving various COPs. In this framework, each CHT acts as a voter, all voters vote for each pair of solutions, and the solution in each pair with the highest weighted votes is considered better. In addition, an adaptive strategy is developed to adjust the voter weights according to their historical voting performance. To investigate the performance of VMCH in improving existing algorithms, the proposed VMCH is embedded into the three best algorithms in the competition on constrained single objective real-parameter optimization at CEC 2018, namely, MAgES, iLSHADE $epsilon $ , and IUDE, to form three new algorithm versions, i.e., MAgES-VMCH, iLSHADE $epsilon $ -VMCH, and IUDE-VMCH. They are compared with seven state-of-the-art peer algorithms. Extensive experiments are conducted on 57 real-world COPs. The ranking results show that the new algorithm version MAgES-VMCH takes first place among the ten comparison algorithms. Moreover, all the new VMCH-enhanced versions of the three best algorithms are superior to their original versions. Therefore, the proposed VMCH framework can achieve competitive performance in solving COPs.

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Surrogate-assisted evolutionary algorithms (EAs) have been intensively used to solve computationally expensive problems with some success. However, traditional EAs are not suitable to deal with high-dimensional expensive problems (HEPs) with high-dimensional search space even if their fitness evaluations are assisted by surrogate models. The recently proposed autoencoder-embedded evolutionary optimization (AEO) framework is highly appropriate to deal with high-dimensional problems. This work aims to incorporate surrogate models into it to further boost its performance, thus resulting in surrogate-assisted AEO (SAEO). It proposes a novel model management strategy that can guarantee reasonable amounts of re-evaluations; hence, the accuracy of surrogate models can be enhanced via being updated with new evaluated samples. Moreover, to ensure enough data samples before constructing surrogates, a problem-dimensionality-dependent activation condition is developed for incorporating surrogates into the SAEO framework. SAEO is tested on seven commonly used benchmark functions and compared with state-of-the-art algorithms for HEPs. The experimental results show that SAEO can further enhance the performance of AEO on most cases and SAEO performs significantly better than other algorithms. Therefore, SAEO has great potential to deal with HEPs.

Knowledge transfer plays a vastly important role in solving multitask optimization problems (MTOPs). Many existing methods transfer task-specific knowledge, such as the high-quality solution from one task to other tasks to enhance the optimization ability, which, however, may not work well or even have a negative effect if the tasks have very different task-specific knowledge. Hence, this article proposes a meta-knowledge transfer (MKT)-based differential evolution (MKTDE) algorithm by using a more general MKT method to solve MTOPs more efficiently. The meta-knowledge defined in this article refers to the knowledge that can evolve task-specific knowledge during the evolutionary search. That is, the meta-knowledge is a kind of “knowledge of knowledge,” which denotes the knowledge of “how to solve problem via evolution” and “the feature/way/method of evolving high-quality solution.” The evolutionary search for solving different tasks can share common meta-knowledge even though these tasks involve heterogeneous data and have very different task-specific knowledge. Therefore, the MKT can associate the heterogeneous multisource data of different tasks via transferring the meta-knowledge to help solve MTOPs more efficiently in a more general way. Moreover, to further enhance the MKTDE, two novel and efficient methods are proposed. One is multiple populations for the multiple tasks framework using a unified search space for making knowledge transfer flexibly. The other is an elite solution transfer method for achieving positive high-quality solution transfer. The superior performance of the proposed MKTDE is verified via extensive numerical experiments on both widely used MTOP benchmark problems and real-world robot navigation problems, with comparisons with some state-of-the-art and the latest well-performing-
algorithms.

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Subset selection plays an important role in the field of evolutionary multiobjective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive (UEA), subset selection is an essential post-processing procedure to select a prespecified number of solutions as the final result. In this article, we discuss the efficiency of greedy subset selection for the hypervolume, inverted generational distance (IGD), and IGD plus (IGD+) indicators. Greedy algorithms usually efficiently handle the subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutions in a UEA), they often become time consuming. Our idea is to use the submodular property, which is known for the hypervolume indicator, to improve their efficiency. First, we prove that the IGD and IGD+ indicators are also submodular. Next, based on the submodular property, we propose an efficient greedy inclusion algorithm for each indicator. We demonstrate through computational experiments that the proposed algorithms are much faster than the standard greedy subset selection algorithms. The proposed algorithms also help the research on performance indicators.

Random forest (RF) is a type of ensemble-based machine learning method that has been applied to a variety of machine learning tasks in recent years. This article proposes an evolutionary approach to generate an oblique RF for regression problems. More specifically, our method induces an oblique RF by transforming the original feature space to a new feature space through the evolutionary feature construction method. To speed up the searching process, the proposed method evaluates each set of features based on a decision tree (DT) rather than an RF. In order to obtain an RF, we archive top-performing features and corresponding trees during the search. In this way, both the features and the forest can be constructed simultaneously in a single run. The proposed evolutionary forest is applied to 117 benchmark problems with different characteristics and compared with some state-of-the-art regression methods, including several variants of the RF and gradient boosted DTs (GBDTs). The experimental results suggest that the proposed method outperforms the existing RF and GBDT methods.

A considerable number of surrogate-assisted evolutionary algorithms (SAEAs) have been developed to solve expensive optimization problems (EOPs) with continuous objective functions. However, in the real-world applications, we may face EOPs with discontinuous objective functions, which are also called EOPs with discontinuous responses (EOPDRs). Indeed, EOPDRs pose a great challenge to current SAEAs. In this article, a surrogate-assisted differential evolution (DE) algorithm with region division is proposed, named ReDSADE. ReDSADE includes three main strategies: 1) the region division strategy; 2) the Kriging-based search; and 3) the radial basis function (RBF)-based local search. In the region division strategy, we define a new distance measure, called the objective-decision distance. Based on this distance, the evaluated solutions are partitioned into several clusters, and several support vector machine (SVM) classifiers are trained to classify them. These SVM classifiers divide the decision space into several subregions, with the aim of making the objective function continuous in them. In the Kriging-based search, a Kriging model is established in each subregion and combined with DE to search for the optimal solution. In the RBF-based local search, DE is coupled with RBF to search around the best solution found so far, thus accelerating the convergence. By combining these three strategies, ReDSADE is able to solve EOPDRs with limited function evaluations. Three sets of test problems and a real-world application are utilized to verify the effectiveness of ReDSADE. The results demonstrate that ReDSADE exhibits good convergence accuracy and convergence speed.

The uncertain capacitated arc routing problem has many real-world applications in logistics domains. Genetic programming (GP) is a promising approach to training routing policies to make real-time decisions and handle uncertain events effectively. In the real world, there are various problem domains and no single routing policy can work effectively in all of them. Instead of training in isolation, we can leverage the relatedness between the problems and transfer knowledge from previously solved source problems to solve the target problem. The existing transfer methods are not effective enough due to the loss of diversity during the knowledge transfer. To increase the diversity of the transferred knowledge, in this article, we propose a novel GP method that removes phenotypic duplicates from the source individuals to initialize the target individuals. Furthermore, assuming that the transferred knowledge used in initialization already includes all the important knowledge explored for the source problem, it is more effective to explore new regions that have not been explored for the source problem. Therefore, we propose novel genetic operators that prohibit the search from revisiting the source individuals when solving the target problem. To speed up the revisit check, we propose to adapt a powerful hashing method for routing policies that greatly improves the efficiency of the genetic operators. Our experimental results show that the proposed method significantly outperforms the existing GP approaches with knowledge transfer in terms of both initial and final solution quality.

The ten year GECCO 2022 award, announced yesterday, for most impact paper formed the basis for a paper in GP+EM:

“Better GP benchmarks: community survey results and proposals” by David R. White and James McDermott and Mauro Castelli and Luca Manzoni and Brian W. Goldman and Gabriel Kronberger and Wojciech Jaskowski and Una-May O’Reilly and Sean Luke. Genetic Programming and Evolvable Machines, 14(1):3-29, 2013.
http://gpbib.cs.ucl.ac.uk/gp-html/White_2013_GPEM.html