No Arabic abstract
Over the last three decades, a large number of evolutionary algorithms have been developed for solving multiobjective optimization problems. However, there lacks an up-to-date and comprehensive software platform for researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multi-objective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.
When solving constrained multi-objective optimization problems, an important issue is how to balance convergence, diversity and feasibility simultaneously. To address this issue, this paper proposes a parameter-free constraint handling technique, two-archive evolutionary algorithm, for constrained multi-objective optimization. It maintains two co-evolving populations simultaneously: one, denoted as convergence archive, is the driving force to push the population toward the Pareto front; the other one, denoted as diversity archive, mainly tends to maintain the population diversity. In particular, to complement the behavior of the convergence archive and provide as much diversified information as possible, the diversity archive aims at exploring areas under-exploited by the convergence archive including the infeasible regions. To leverage the complementary effects of both archives, we develop a restricted mating selection mechanism that adaptively chooses appropriate mating parents from them according to their evolution status. Comprehensive experiments on a series of benchmark problems and a real-world case study fully demonstrate the competitiveness of our proposed algorithm, comparing to five state-of-the-art constrained evolutionary multi-objective optimizers.
Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization is always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and is subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogate construction so that multiple clients collaboratively train a radial-basis-function-network as the global surrogate. Then a new federated acquisition function is proposed for the central server to approximate the objective values using the global surrogate and estimate the uncertainty level of the approximated objective values based on the local models. The performance of the proposed algorithm is verified on a series of multi/many-objective benchmark problems by comparing it with two state-of-the-art surrogate-assisted multi-objective evolutionary algorithms.
Dynamic multi-objective optimization problems (DMOPs) remain a challenge to be settled, because of conflicting objective functions change over time. In recent years, transfer learning has been proven to be a kind of effective approach in solving DMOPs. In this paper, a novel transfer learning based dynamic multi-objective optimization algorithm (DMOA) is proposed called regression transfer learning prediction based DMOA (RTLP-DMOA). The algorithm aims to generate an excellent initial population to accelerate the evolutionary process and improve the evolutionary performance in solving DMOPs. When an environmental change is detected, a regression transfer learning prediction model is constructed by reusing the historical population, which can predict objective values. Then, with the assistance of this prediction model, some high-quality solutions with better predicted objective values are selected as the initial population, which can improve the performance of the evolutionary process. We compare the proposed algorithm with three state-of-the-art algorithms on benchmark functions. Experimental results indicate that the proposed algorithm can significantly enhance the performance of static multi-objective optimization algorithms and is competitive in convergence and diversity.
Recently, more and more works have proposed to drive evolutionary algorithms using machine learning models.Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models.Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality.To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs).At each generation of the proposed algorithm, the parent solutions are first classified into emph{real} and emph{fake} samples to train the GANs; then the offspring solutions are sampled by the trained GANs.Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data.The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables.Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.
Multi-objective optimization problems are ubiquitous in real-world science, engineering and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of non-dominated trade-off solutions, where the expensive objective functions are approximated as a surrogate model. In this paper, we propose a framework for implementing batched data-driven evolutionary multi-objective optimization. It is so general that any off-the-shelf evolutionary multi-objective optimization algorithms can be applied in a plug-in manner. In particular, it has two unique components: 1) based on the Karush-Kuhn-Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set; and 2) a batch recommendation approach that reduces the computational time of the optimization process by evaluating multiple samples at a time in parallel. Experiments on 136 benchmark test problem instances with irregular Pareto-optimal front shapes against six state-of-the-art surrogate-assisted EMO algorithms fully demonstrate the effectiveness and superiority of our proposed framework. In particular, our proposed framework is featured with a faster convergence and a stronger resilience to various PF shapes.