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When solving constrained optimization problems by evolutionary algorithms, the core issue is to balance constraints and objective function. This paper is the first attempt to utilize the correlation between constraints and objective function to keep this balance. First of all, the correlation between constraints and objective function is mined and represented by a correlation index. Afterward, a weighted sum updating approach and an archiving and replacement mechanism are proposed to make use of this correlation index to guide the evolution. By the above process, a novel constrained optimization evolutionary algorithm is presented. Experiments on a broad range of benchmark test functions indicate that the proposed method shows better or at least competitive performance against other state-of-the-art methods. Moreover, the proposed method is applied to the gait optimization of humanoid robots.

The design space exploration (DSE) of fault-tolerant multiprocessor systems is very complex, as it contains three interacting NP-hard problems: 1) task hardening; 2) task mapping; and 3) task scheduling. In addition, replication-based task hardening can introduce new tasks, called replicas, into the system, enlarging the design space further. As a population-based global optimization algorithm, evolutionary algorithms (EAs) have been widely used to explore this huge design space over the last decade. However, as analyzed in this paper, the search space of previous works is highly redundant, resulting in poor efficiency and scalability. This paper proposes an efficient EA-based DSE method for the design of large-scale fault-tolerant multiprocessor systems. The main novelties of this paper include: 1) mapping exploration is explicitly separated, i.e., task mapping is optimized during the evolutionary search, while replica mapping is constructed heuristically according to the current co-synthesis state; 2) the design space of task hardening and task mapping are explored independently by a cooperative co-EA; and 3) as a complement to global search of EA, problem-specific local search operators are designed for both task hardening and task mapping, reducing the number of fitness evaluations required. Compared with the most relevant state-of-the-art method, the superiority of the proposed method is demonstrated using extensive experiments on a large set of benchmarks, e.g., $1.75times sim 2.50times $ better results can be obtained on the benchmarks of 300 tasks and 30 processors.

Evolutionary multitask optimization (EMTO) is a newly emerging research area in the field of evolutionary computation. It investigates how to solve multiple optimization problems (tasks) at the same time via evolutionary algorithms (EAs) to improve on the performance of solving each task independently, assuming if some component tasks are related then the useful knowledge (e.g., promising candidate solutions) acquired during the process of solving one task may assist in (and also benefit from) solving the other tasks. In EMTO, task relatedness is typically unknown in advance and needs to be captured via EA’s population. Since the population of an EA can only cover a subregion of the solution space and keeps evolving during the search, thus captured task relatedness is local and dynamic. The multifactorial EA (MFEA) is one of the most representative EMTO techniques, inspired by the bio-cultural model of multifactorial inheritance, which transmits both biological and cultural traits from the parents to the offspring. MFEA has succeeded in solving various multitask optimization (MTO) problems. However, the intensity of knowledge transfer in MFEA is determined via its algorithmic configuration without considering the degree of task relatedness, which may prevent the effective sharing and utilization of the useful knowledge acquired in related tasks. To address this issue, we propose a self-regulated EMTO (SREMTO) algorithm to automatically adapt the intensity of cross-task knowledge transfer to different and varying degrees of relatedness between different tasks as the search proceeds so that the useful knowledge in common for solving related tasks can be captured, shared, and utilized to a great extent. We compare SREMTO with MFEA and its variants as well as the single-task optimization counterpart of SREMTO on two MTO test suites, which demonstrates the superiority of SREMTO.

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Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark (MPB) and show its nonseparable nature irrespective of its number of peaks. We then propose a composite MPB suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower-dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200-D, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.

Two-echelon vehicle routing problem (2E-VRP) is a challenging problem that involves both the strategic and tactical planning decisions on both echelons. The satellite locations and the customer distribution affect the cost of different components on the second echelon, thus the possibilities of satellite-to-customer assignment complicates the problem. In this paper, we propose a graph-based fuzzy evolutionary algorithm for solving 2E-VRP. The proposed method integrates a graph-based fuzzy assignment scheme into an iteratively evolutionary learning process to minimize the total cost. To resolve the possibilities of the satellite-to-customer assignment, graph-based fuzzy operator is used to take advantage of population evolution and avoid excessive fitness evaluations of unpromising moves in different satellites. Each offspring is produced via graph-based fuzzy assignment procedure out of an assignment graph from parent individuals, and fuzzy local search procedure is used to further improve the offspring. The experimental results on the public test sets demonstrate the competitiveness of the proposed method.

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In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method, and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use.

Evolutionary Computation, Volume 27, Issue 4, Page 639-664, Winter 2019.