A large-scale continuous optimization benchmark suite with versatile coupled heterogeneous modules

Large-scale global optimization (LSGO) problems are emergent in many domains of applied sciences. LSGO is a hard challenge for the majority of state-of-the-art optimization methods. Evolution algorithms (EAs) combined with Cooperative Coevolution (CC) are able to perform well when solving many real-world LSGO problems. The grouping of variables at the problem decomposition stage has a significant impact on the performance of the CC approach. This study proposes an improvement of the previously developed random adaptive grouping (RAG) approach for CC. The new method is titled as RAG2, and the whole optimization algorithm, based on RAG2, is called CC-SHADE-RAG2. The influence of the choice of the population size and the number of subcomponents on the algorithm performance have been investigated using the IEEE LSGO CEC’2013 benchmark. The set of test problems in the benchmark contains fifteen functions with dimensionality equal to one thousand. We have also compared the performance of the novel algorithm with some EAs, which are applied for solving LSGO problems.

Large-scale global optimization (LSGO) problems have widely appeared in various real-world applications. However, their inherent complexity, coupled with the curse of dimensionality, makes them challenging to solve. Continuous efforts have been devoted to designing computational intelligence-based approaches to solve them. This paper offers a comprehensive review of the latest developments in the field, focusing on the advances in both single-objective and multi-objective large-scale evolutionary optimization algorithms over the past five years. We systematically categorize these algorithms, discuss their distinct features, and highlight benchmark test suites essential for performance evaluation. After that, comparative studies are conducted using numerical solutions to evaluate the performance of state-of-the-art LSGO for both single-objective and multi-objective problems. Finally, we discuss the real-world applications of LSGO, some challenges, and possible future research directions.

In the recent years, Large-Scale Global Optimization (LSGO) algorithms attempt to solve real-world problems efficiently. The imbalance in the contribution of variables and the interaction among variables pose major challenges for LSGO algorithms. This paper proposes mapping schemes based on the interaction among variables and the imbalance in the contribution of variables. The proposed mapping schemes present the different relations between the constructed class of variables according to the interaction feature and the constructed class of variables according to the imbalance feature. Covering a wide range of real-world problems is considered in the mapping schemes; therefore it can provide some insights to design LSGO benchmark suites. By developing LSGO benchmark suites with the ability of representing many-real world problems, researchers will be motivated to realize the success or failure level of LSGO algorithms for tackling various types of LSGO problems. Also, a preliminary set of experiments is conducted to present the importance of considered features in each scheme.

Biogeography-based optimization (BBO), a recent proposed metaheuristic algorithm, has been successfully applied to many optimization problems due to its simplicity and efficiency. However, BBO is sensitive to the curse of dimensionality; its performance degrades rapidly as the dimensionality of the search space increases. In this paper, a selective migration operator is proposed to scale up the performance of BBO and we name it selective BBO (SBBO). The differential migration operator is selected heuristically to explore the global area as far as possible whist the normal distributed migration operator is chosen to exploit the local area. By the means of heuristic selection, an appropriate migration operator can be used to search the global optimum efficiently. Moreover, the strategy of cooperative coevolution (CC) is adopted to solve large-scale global optimization problems (LSOPs). To deal with subgroup imbalance contribution to the whole solution in the context of CC, a more efficient computing resource allocation is proposed. Extensive experiments are conducted on the CEC 2010 benchmark suite for large-scale global optimization, and the results show the effectiveness and efficiency of SBBO compared with BBO variants and other representative algorithms for LSOPs. Also, the results confirm that the proposed computing resource allocation is vital to the large-scale optimization within the limited computation budget.

Whale optimization algorithm (WOA) is a relatively novel swarm-based optimization algorithm that has the advantage of less control parameters, strong global optimization ability and easy of implementation. However, there is still an insufficiency of low accuracy, premature, and slow convergence speed in tackling large-scale global optimization (LSGO) problems. To address the issue, an enhanced whale optimization algorithm (EWOA), which combines the original WOA with opposition-based learning, chaotic map and dynamic inertia weight, is proposed for solving LSGO problems. Chaotic opposition-based learning initialization strategy by comparing the fitness of an individual to its opposite and retaining well-diversified solutions is employed to accelerate convergence speed and improve the exploration. In addition, in order to make full use of and balance the exploration and exploitation of the original WOA, a novel chaotic cooperative updating strategy of nonlinear control parameter and dynamic inertia weight is given. Moreover, optimal individual chaotic searching strategy is integrated with evolutionary population updating to avoid the possibility of being trapped into local optima. The experimental results on four classical benchmark functions with dimensions ranging from 100 to 1000 demonstrate the effectiveness and efficiency of the chaotic opposition-based learning initialization strategy, chaotic nonlinear control parameter updating strategy and optimal individual chaotic searching strategy. The comparisons show that the proposed EWOA significantly improves the performance of WOA and provides competitive results for LSGO problems compared with state-of-the-art algorithms.

Ant-colony optimization (ACO) is a popular swarm intelligence metaheuristic scheme that can be applied to almost any optimization problem. In this paper, we address a performance evaluation of an ACO-based algorithm for solving large-scale global optimization problems with continuous variables, labeled Differential Ant-Stigmergy Algorithm (DASA). The DASA transforms a real-parameter optimization problem into a graph-search problem. The parameters' differences assigned to the graph vertices are used to navigate through the search space. The performance of the DASA is evaluated on the set of benchmark problems provided for CEC'2010 Special Session and Competition on Large-Scale Global Optimization.

Evolutionary algorithms (EAs) have shown their great capability of handling optimization problems. In the domain of large scale global optimization, many distributed EAs (dEAs) have been proposed for maintaining population diversity so as to enhance their efficacy. One well-known variant of dEA is the island model EA, in which several populations form islands communicating through migration. There are several key factors that affect the performance and search behavior of island model EA, such as population size of each island and migration topology. While most studies of dEA focus on low or medium dimensional problems, an investigation into the effects of these factors on high dimensional problems is greatly needed. This study presents an empirical analysis of island model EA on large scale global optimization problems. The analysis examines the solution quality, convergence speed, and population diversity of island model EA with different migration topologies, population sizes, migration rates, and migration frequencies on four benchmark function of 1,000 dimensions. The results render guidelines for using island model EA to solve large scale global optimization problems.

In this paper, we propose the application of a Cooperative Co-evolutionary LSHADE (CCLSHADE) algorithm for Large-Scale Global Optimization (LSGO). We illustrate that by tuning two simple parameters of the CC framework, one can obtain very competitive results. The results are achieved without the need of incorporating local search modules, a re-initialization step, or adaptively configuring the CC framework budget allocation. The two parameters studied in this work are the number of iterations for which to run each sub-optimizer in a single cycle and the maximum size of the component containing the separable problem variables. The performance of CCLSHADE is compared against six state-of-the-art algorithms developed for LSGO using the CEC10 benchmarks. Experimental results and statistical tests confirm the competitiveness of the proposed algorithm.

This paper presents enhanced adaptive differential evolution (EADE) algorithm for solving high-dimensional optimization problems over continuous space. To utilize the information of good and bad vectors in the DE population, the proposed algorithm introduces a new mutation rule. It uses two random chosen vectors of the top and bottom 100p% individuals in the current population of size NP, while the third vector is selected randomly from the middle [NP-2(100p%)] individuals. The mutation rule is combined with the basic mutation strategy DE/rand/1/bin, where the only one of the two mutation rules is applied with the probability of 0.5. This new mutation scheme helps to maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. Furthermore, we propose a novel self-adaptive scheme for gradual change of the values of the crossover rate that can excellently benefit from the past experience of the individuals in the search space during evolution process which, in turn, can considerably balance the common trade-off between the population diversity and convergence speed. The proposed algorithm has been evaluated on the 7 and 20 standard high-dimensional benchmark numerical optimization problems for both the IEEE CEC-2008 and the IEEE CEC-2010 Special Session and Competition on Large-Scale Global Optimization. The comparison results between EADE and its version and the other state-of-art algorithms that were all tested on these test suites indicate that the proposed algorithm and its version are highly competitive algorithms for solving large-scale global optimization problems.

A view of the limitations, opportunities, and challenges in parallel nonlinear optimization

Effective identification of interdependence information between decision variables is crucial for variable grouping in large-scale global optimization (LSGO). This paper introduces a novel approach called FCA-G (Formal Concept Analysis-Driven Grouping) to solve LSGO problems. FCA, an effective tool for data analysis, is employed in this approach. The primary contribution involves transforming decision variables into the formal context within FCA and utilizing the FCA methodology to solve LSGO problems based on a cooperative coevolution framework. Based on the formal context, a formal concept lattice is constructed, from which equivalent concepts are extracted. All variables within these concepts exhibit explicit interactions. This approach ensures a high degree of correlation among variables within subgroups and a low degree of correlation between subgroups, thereby enhancing cooperative coevolution. Experimental results indicate the significant potential of FCA-G in LSGO, as it outperforms state-of-the-art LSGO algorithms across the majority of LSGO test problems, including those with up to 1000 decision variables and a large-scale cloud task scheduling problem.

Large-scale global optimization (LSGO) is a very important and challenging task in optimization domain, which is embedded in many scientific and engineering applications. In this paper, a two-stage based ensemble optimization evolutionary algorithm (EOEA) is designed to handle LSGO problems. The performance of EOEA is evaluated on the test functions provided by the LSGO competition of IEEE Congress of Evolutionary Computation (CEC 2010). Compared with some previous LSGO algorithms, EOEA demonstrates better performance.

JADE is an adaptive scheme of nature inspired algorithm, Differential Evolution (DE). It performed considerably improved on a set of well-studied benchmark test problems. In this paper, we evaluate the performance of new JADE with two external archives to deal with unconstrained continuous large-scale global optimization problems labeled as Reflected Adaptive Differential Evolution with Two External Archives (RJADE/TA). The only archive of JADE stores failed solutions. In contrast, the proposed second archive stores superior solutions at regular intervals of the optimization process to avoid premature convergence towards local optima. The superior solutions which are sent to the archive are reflected by new potential solutions. At the end of the search process, the best solution is selected from the second archive and the current population. The performance of RJADE/TA algorithm is then extensively evaluated on two test beds. At first on 28 latest benchmark functions constructed for the 2013 Congress on Evolutionary Computation special session. Secondly on ten benchmark problems from CEC2010 Special Session and Competition on Large-Scale Global Optimization. Experimental results demonstrated a very competitive perfor-mance of the algorithm.

In this paper, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multiobjective optimization. The main idea is to track the Pareto optimal set (PS) directly via problem reformulation. To begin with, the algorithm obtains a set of reference directions in the decision space and associates them with a set of weight variables for locating the PS. Afterwards, the original large-scale multiobjective optimization problem is reformulated into a low-dimensional single-objective optimization problem. In the reformulated problem, the decision space is reconstructed by the weight variables and the objective space is reduced by an indicator function. Thanks to the low dimensionality of the weight variables and reduced objective space, a set of quasi-optimal solutions can be obtained efficiently. Finally, a multiobjective evolutionary algorithm is used to spread the quasi-optimal solutions over the approximate Pareto optimal front evenly. Experiments have been conducted on a variety of large-scale multiobjective problems with up to 5000 decision variables. Four different types of representative algorithms are embedded into the proposed framework and compared with their original versions, respectively. Furthermore, the proposed framework has been compared with two state-of-the-art algorithms for large-scale multiobjective optimization. The experimental results have demonstrated the significant improvement benefited from the framework in terms of its performance and computational efficiency in large-scale multiobjective optimization.

Model parameter identification for lithium-ion batteries using adaptive multi-context cooperatively co-evolutionary parallel differential evolution algorithm