LCS & GBML Central

When solving constrained multiobjective 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, a two-archive evolutionary algorithm, for constrained multiobjective optimization. It maintains two collaborative archives simultaneously: one, denoted as the convergence-oriented archive (CA), is the driving force to push the population toward the Pareto front; the other one, denoted as the diversity-oriented archive (DA), mainly tends to maintain the population diversity. In particular, to complement the behavior of the CA and provide as much diversified information as possible, the DA aims at exploring areas under-exploited by the CA 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, in comparison to five state-of-the-art constrained evolutionary multiobjective optimizers.

The DTLZ1–DTLZ4 problems are by far one of the most commonly used test problems in the validation and comparison of multiobjective optimization evolutionary algorithms (MOEAs). However, very recently, it has been pointed out that they have the following two special characteristics: 1) the regularly oriented Pareto front shape and 2) the single distance function. As a modification of them, this paper presents a new set of test problems mDTLZ1–mDTLZ4 to avoid the two special characteristics. Using these new test problems, we investigate the performance of three representative multiobjective evolutionary algorithms NSGA-II, MOEA/D-Tch, and SMS-EMOA. Experimental results indicate that the performance of NSGA-II and MOEA/D-Tch deteriorates on mDTLZ1–mDTLZ4. Subsequently, our analysis reveals that there exist the hardly dominated boundaries in each of mDTLZ1–mDTLZ4, which hinder the approximation of Pareto dominance-based algorithms and Tchebycheff-decomposition-based algorithms. Furthermore, we summarize that the hardly dominated boundary should be an often encountered problem feature in multiobjective optimization. Last but not least, we point out and validate some coping strategies for dominance-based algorithms and decomposition-based algorithms to overcome the challenges caused by the hardly dominated boundary.

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In solving many real-world optimization problems, neither mathematical functions nor numerical simulations are available for evaluating the quality of candidate solutions. Instead, surrogate models must be built based on historical data to approximate the objective functions and no new data will be available during the optimization process. Such problems are known as offline data-driven optimization problems. Since the surrogate models solely depend on the given historical data, the optimization algorithm is able to search only in a very limited decision space during offline data-driven optimization. This paper proposes a new offline data-driven evolutionary algorithm to make the full use of the offline data to guide the search. To this end, a surrogate management strategy based on ensemble learning techniques developed in machine learning is adopted, which builds a large number of surrogate models before optimization and adaptively selects a small yet diverse subset of them during the optimization to achieve the best local approximation accuracy and reduce the computational complexity. Our experimental results on the benchmark problems and a transonic airfoil design example show that the proposed algorithm is able to handle offline data-driven optimization problems with up to 100 decision variables.

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Through introducing the divide-and-conquer strategy, cooperative co-evolution (CC) has been successfully employed by many evolutionary algorithms (EAs) to solve large-scale optimization problems. In practice, it is common that different subcomponents of a large-scale problem have imbalanced contributions to the global fitness. Thus, how to utilize such imbalance and concentrate efforts on optimizing important subcomponents becomes an important issue for improving performance of cooperative co-EA, especially in distributed computing environment. In this paper, we propose a two-layer distributed CC (dCC) architecture with adaptive computing resource allocation for large-scale optimization. The first layer is the dCC model which takes charge of calculating the importance of subcomponents and accordingly allocating resources. An effective allocating algorithm is designed which can adaptively allocate computing resources based on a periodic contribution calculating method. The second layer is the pool model which takes charge of making fully utilization of imbalanced resource allocation. Within this layer, two different conformance policies are designed to help optimizers use the assigned computing resources efficiently. Empirical studies show that the two conformance policies and the computing resource allocation algorithm are effective, and the proposed distributed architecture possesses high scalability and efficiency.

Uncertainty inadvertently exists in most real-world applications. In the optimization process, uncertainty poses a very important issue and it directly affects the optimization performance. Nowadays, evolutionary algorithms (EAs) have been successfully applied to various multiobjective optimization problems (MOPs). However, current researches on EAs rarely consider uncertainty in the optimization process and existing algorithms often fail to handle the uncertainty, which have limited EAs’ applications in real-world problems. When MOPs come with uncertainty, they are referred to as robust MOPs (RMOPs). In this paper, we aim at solving RMOPs using EA-based optimization search. We propose a novel robust multiobjective optimization EA (RMOEA) with two distinct, yet complement, parts: 1) multiobjective optimization finding global Pareto optimal front ignoring disturbance at first and 2) robust optimization searching for the robust optimal front afterward. Furthermore, a comprehensive performance evaluation method is proposed to quantify the performance of RMOEA in solving RMOPs. Experimental results on a group of benchmark functions demonstrate the superiority of the proposed design in terms of both solutions’ quality under the disturbance and computational efficiency in solving RMOPs.

Inverted generational distance (IGD) has been widely considered as a reliable performance indicator to concurrently quantify the convergence and diversity of multiobjective and many-objective evolutionary algorithms. In this paper, an IGD indicator-based evolutionary algorithm for solving many-objective optimization problems (MaOPs) has been proposed. Specifically, the IGD indicator is employed in each generation to select the solutions with favorable convergence and diversity. In addition, a computationally efficient dominance comparison method is designed to assign the rank values of solutions along with three newly proposed proximity distance assignments. Based on these two designs, the solutions are selected from a global view by linear assignment mechanism to concern the convergence and diversity simultaneously. In order to facilitate the accuracy of the sampled reference points for the calculation of IGD indicator, we also propose an efficient decomposition-based nadir point estimation method for constructing the Utopian Pareto front (PF) which is regarded as the best approximate PF for real-world MaOPs at the early stage of the evolution. To evaluate the performance, a series of experiments is performed on the proposed algorithm against a group of selected state-of-the-art many-objective optimization algorithms over optimization problems with 8-, 15-, and 20-objective. Experimental results measured by the chosen performance metrics indicate that the proposed algorithm is very competitive in addressing MaOPs.

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication.

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication.