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Register a new userTransfer Learning Based Co-surrogate Assisted Evolutionary Bi-objective Optimization for Objectives with Non-uniform Evaluation Times
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Added by
Xilu Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Most existing multiobjetive evolutionary algorithms (MOEAs) implicitly assume that each objective function can be evaluated within the same period of time. Typically. this is untenable in many real-world optimization scenarios where evaluation of different objectives involves different computer simulations or physical experiments with distinct time complexity. To address this issue, a transfer learning scheme based on surrogate-assisted evolutionary algorithms (SAEAs) is proposed, in which a co-surrogate is adopted to model the functional relationship between the fast and slow objective functions and a transferable instance selection method is introduced to acquire useful knowledge from the search process of the fast objective. Our experimental results on DTLZ and UF test suites demonstrate that the proposed algorithm is competitive for solving bi-objective optimization where objectives have non-uniform evaluation times.
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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.
Previous theory work on multi-objective evolutionary algorithms considers mostly easy problems that are composed of unimodal objectives. This paper takes a first step towards a deeper understanding of how evolutionary algorithms solve multi-modal multi-objective problems. We propose the OneJumpZeroJump problem, a bi-objective problem whose single objectives are isomorphic to the classic jump functions benchmark. We prove that the simple evolutionary multi-objective optimizer (SEMO) cannot compute the full Pareto front. In contrast, for all problem sizes~$n$ and all jump sizes $k in [4..frac n2 - 1]$, the global SEMO (GSEMO) covers the Pareto front in $Theta((n-2k)n^{k})$ iterations in expectation. To improve the performance, we combine the GSEMO with two approaches, a heavy-tailed mutation operator and a stagnation detection strategy, that showed advantages in single-objective multi-modal problems. Runtime improvements of asymptotic order at least $k^{Omega(k)}$ are shown for both strategies. Our experiments verify the {substantial} runtime gains already for moderate problem sizes. Overall, these results show that the ideas recently developed for single-objective evolutionary algorithms can be effectively employed also in multi-objective optimization.
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.
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.
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.
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