Reflected Adaptive Differential Evolution with Two External Archives for Large-Scale Global Optimization

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.

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.

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

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.

With the onset of the big data age, data is growing exponentially, and the issue of how to optimize large-scale data processing is especially significant.Large-scale global optimization (LSGO) is a research topic with great interest in academia and industry.Spark is a popular cloud computing framework that can cluster large-scale data, and it can effectively support the functions of iterative calculation through resilient distributed datasets (RDD).In this paper, we propose a hybrid mechanism of particle swarm optimization (PSO) and differential evolution (DE) algorithms based on Spark (SparkPSODE).The SparkPSODE algorithm is a parallel algorithm, in which the RDD and island models are employed.The island model is used to divide the global population into several subpopulations, which are applied to reduce the computational time by corresponding to RDD's partitions.To preserve population diversity and avoid premature convergence, the evolutionary strategy of DE is integrated into SparkPSODE.Finally, SparkPSODE is conducted on a set of benchmark problems on LSGO and show that, in comparison with several algorithms, the proposed SparkPSODE algorithm obtains better optimization performance through experimental results.

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.

This work investigates the performance of Differential Evolution (DE) and its opposition-based version (ODE) on large scale optimization problems. Opposition-based differential evolution (ODE) has been proposed based on DE; it employs opposition-based population initialization and generation jumping to accelerate convergence speed. ODE shows promising results in terms of convergence rate, robustness, and solution accuracy. A recently proposed seven-function benchmark test suite for the CEC-2008 special session and competition on large scale global optimization has been utilized for the current investigation. Results interestingly confirm that ODE outperforms its parent algorithm (DE) on all high dimensional (500D and 1000D) benchmark functions (F1-F7). Furthermore, authors recommend to utilize ODE for more complex search spaces as well. Because results confirm that ODE performs much better than DE when the dimensionality of the problems is increased from 500D to 1000D. All required details about the testing platform, comparison methodology, and also achieved results are provided.

This paper presents the Constructive Cooperative Coevolutionary (mathrm {C}^3) algorithm, applied to continuous large-scale global optimisation problems. The novelty of mathrm {C}^3 is that it utilises a multi-start architecture and incorporates the Cooperative Coevolutionary algorithm. The considered optimisation problem is decomposed into subproblems. An embedded optimisation algorithm optimises the subproblems separately while exchanging information to co-adapt the solutions for the subproblems. Further, mathrm {C}^3 includes a novel constructive heuristic that generates different feasible solutions for the entire problem and thereby expedites the search. In this work, two different versions of mathrm {C}^3 are evaluated on high-dimensional benchmark problems, including the CEC’2013 test suite for large-scale global optimisation. mathrm {C}^3 is compared with several state-of-the-art algorithms, which shows that mathrm {C}^3 is among the most competitive algorithms. mathrm {C}^3 outperforms the other algorithms for most partially separable functions and overlapping functions. This shows that mathrm {C}^3 is an effective algorithm for large-scale global optimisation. This paper demonstrates the enhanced performance by using constructive heuristics for generating initial feasible solutions for Cooperative Coevolutionary algorithms in a multi-start framework.

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.

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.

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.

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.

Cooperation coevolution with fast interdependency identification for large scale optimization

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.

Memetic algorithms arise as very effective algorithms to obtain reliable and high accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, making recommendable to test the behavior of the optimization algorithms to large-scale problems. The local search method must be applied with a higher intensity, specially to most promising solutions, to explore the higher domain space around each solution. In this work, we present a preliminar study of a memetic algorithm that assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. This algorithm have obtained good results in continuous optimization and we study whether is a good algorithm for large scale optimizations problems. We make experiments of our proposal using the benchmark problems defined in the Special Session or Competition on Large Scale Global Optimisation, on the IEEE Congress on Evolutionary Computation in 2008. First, we test different local search methods to identify the best one. Then, we compare the proposed algorithm with the algorithms used into the competition, obtaining that our proposal is a very promising algorithm for this type of high-dimensional problems: with dimension 500 our proposal is the second best of the compared algorithms, and the best memetic algorithm.