Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm

Differential evolution (DE) is an efficient population-based search algorithm with good robustness, however, it is challenged to deal with high-dimensional problems. In this paper, we propose an improved multi-population differential evolution with best-and-current mutation strategy (mDE-bcM). The population is divided into three subpopulations based on the fitness values, each of subpopulations uses different mutation strategy. After crossover, mutation and selection, all subpopulations are updated based on the new fitness values of their individuals. An improved mutation strategy is proposed, which uses a new approach to generate base vector that is composed of the best individual and current individual. The performance of mDE-bcM is evaluated on a set of 19 large-scale continuous optimization problems, a comparative study is carried out with other state-of-the-art optimization techniques. The results show that mDE-bcM has a competitive performance compared to the contestant algorithms and better efficiency for large-scale optimization problems.

Optimization technology is used to accelerate decision-making processes and to increase the quality of decision making in management and engineering problems. The development technology has made real-world problems large and complex. Many optimization methods that proposed for solving LSGO problems suffer from the “curse of dimensionality”, which implies that their performance deteriorates quickly as the dimensionality of the search space increases. Therefore, more efficient and robust algorithms are needed. When literature on large-scale optimization problems is examined, it is seen that algorithms with effective global search ability have better results. For the purpose, in this paper, Modified Artificial Algae Algorithm (MAAA) is proposed by modifying the original version of Artificial Algae Algorithm (AAA) inspiring by Differential Evolution Algorithm’s mutation strategies. AAA and MAAA are compared with each other by operating with the first 10 benchmark functions of CEC2010 Special Session on Large Scale Global Optimization. The results show that the hybridization process that applied by updating an additional fourth dimension with mutation strategies of DE after the helical motion of the AAA algorithm, contributes exploration phase and improves the AAA performance on LSGO.

JADE is an state-of-the-art adaptive differential evolution algorithm which implements “DE/current-to-pbest” as its mutation strategy, adapts its mutation factor and crossover rate, and uses an optional external archive to keep track of potential removed individuals in previous generations. This paper proposes MPADE, which extends JADE by using a multi-populated approach to solve high dimensional real-parameter optimization problems. This mechanism helps preventing the two well-known problems affecting the differential evolution algorithm performance, which are premature convergence and stagnation. The algorithm was tested using the benchmark functions in IEEE Congress on Evolutionary Computation 2014 test suite. MPADE was compared using Wilcoxon test to JADE algorithm and with other state-of-the-art algorithms that either use a multi-population approach or adapt their parameters. The experimental results show that the proposed new algorithm improves significantly its precursor and it is also suggested that other state-of-the-art algorithms could benefit from the multi-populated based approach.

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.

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

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.

Recently, the large-scale optimization problems have become a common research topic in the field of evolutionary computation. It is hard to find optimal solutions when solving large-scale multi-objective optimization problems (LSMOPs), due to the ineffectiveness of existing operators. In the other word, the search ability of most existing MOEAs on solving LSMOPs is still weak. To address this issue, an efficient competitive swarm optimizer with a strong exploration ability, denoted as E-CSO, is presented in this paper, which designs a novel three-particle-based particle updating strategy to improve the search efficiency. The experimental results validate the high efficiency and effectiveness of our proposed approach when solving various LSMOPs.

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.

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

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.

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.

Large-scale machine system optimization problems usually resist solution because large-scale machine systems often have a hierarchical general structure that produces numerous local optirna during hierarchical optimization. Genetic algorithms having hierarchical genotypes can be directly applied to the optimization of such problems, however the appearance of local optima during hierarchical optimization procedures often foils effective searching. To enable the global optimization of such problems, skillful analysis of the component relationships comprising the hierarchical problem allows the hierarchical structure to be divided into more tractable units. Divided optimization problems can then be optimized via multiple crenetic algorithm processes, and global large-scale optimization problems can be represented as hierarchical sets of genetic algorithm processes. The exchange of local searching information between these genetic algorithm processes enables global searching and parallel processing, both of which enhance the efficiency and quality of searching for optimum solutions to large-scale optimization problems.

An efficient variable interdependency-identification and decomposition by minimizing redundant computations for large-scale global optimization

We propose singular value decomposition (SVD) algorithms for very large-scale matrices based on a low-rank tensor decomposition technique called the tensor train (TT) format. By using the proposed algorithms, we can compute several dominant singular values and corresponding singular vectors of large-scale structured matrices given in a low-rank TT format. We propose a large-scale trace optimization problem, and in the proposed methods, the large-scale optimization problem is reduced to sequential small-scale optimization problems. We show that the computational complexity of the proposed algorithms scales logarithmically with the matrix size if the TT-ranks are bounded. Numerical simulations based on very large-scale Hilbert matrix demonstrate the effectiveness of the proposed methods.

Today, because of the exponential growth of the volume of data in big data applications, large-scale optimization problems (i.e., optimization problems with a large number of decision variables) have become ubiquitous in the real world [219, 220]. In this chapter, building on the algorithms and observations presented for solving both continuous and combinatorial optimization problems, we further present a novel multi-space evolutionary search framework based on EMT for solving large-scale single-objective optimization problem.