A Selective Biogeography-Based Optimizer Considering Resource Allocation 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.

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.

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

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

Opposition-based learning (OBL) and cooperative co-evolution (CC) have demonstrated promising performance when dealing with large-scale global optimization (LSGO) problems. In this work, we propose a novel framework for hybridizing these two techniques, and investigate the performance of simple implementations of this new framework using the most recent LSGO benchmarking test suite. The obtained results verify the effectiveness of our proposed OBL-CC framework. Moreover, some advanced statistical analyses reveal that the proposed hybridization significantly outperforms its component methods in terms of the quality of finally obtained solutions.

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.

A two-stage differential biogeography-based optimization algorithm and its performance analysis

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.

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.

Cooperative coevolution (CC) algorithms based on variable decomposition methods are efficient in solving large-scale optimization problems (LSOPs). However, many decomposition methods, such as the differential grouping (DG) method and its variants, are based on the theorem of function additively separable, which may not work well on problems that are not additively separable and will result in a bottleneck for CC to solve various LSOPs. This deficiency motivates us to study how the decomposition method can decompose more kinds of separable functions, such as the multiplicatively separable function, to improve the general problem-solving ability of CC on LSOPs. With this concern, this article makes the first attempt to decompose multiplicatively separable functions and proposes a novel method called dual DG (DDG) for better LSOP decomposition and optimization. The novelty and advantage of DDG are that it can be suitable for not only additively separable functions but also multiplicatively separable functions, which can considerably expand the application scope of CC. In this article, we will first define the multiplicatively separable function, and then mathematically show its relationship to the additively separable function and how they can be transformed into each other. Based on this, the DDG can use two kinds of differences to detect the separable structure of both additively and multiplicatively separable functions. In addition, the time complexity of DDG is analyzed and a DDG-based CC algorithm framework is developed for solving LSOPs. To verify the superiority of DDG, experiments and comparisons with some state-of-the-art and champion algorithms are conducted not only on 30 LSOPs based on the test suite of the IEEE CEC large-scale global optimization competition, but also on a case study of the parameter optimization for a neural network-based application.

This chapter introduces the basic concepts of biogeography based optimization (BBO) algorithm and its application to a combinatorial water switching problem. Water switching optimization is a pump scheduling problem which considers minimization of total electrical energy requirement as an objective function. Pump status (switch on/switch off) of pumping stations are considered as a discrete (binary) decision variables for the optimization problem. Suction and discharge pressure are considered as constraints in the procedure. A case study with 10 pumping station and 40 pumps is presented for the experimentation. The performance of BBO is tested against other state-of-the art algorithms that includes genetic algorithm (GA), branch & bound method (B&B), harmony search (HS) algorithm, particle swarm optimization (PSO) and ant colony optimization (ACO) algorithms. Water pump switching problem is also investigated by using different constraint handling techniques and by considering different pump situations in a pumping station. The Computational results indicate that BBO is an appropriate algorithm to solve water pump switching problem and is effective over other optimization methods. Moreover, 20 alternative optimum solutions are presented to demonstrate water switching problem as a multi-modal problem with different optimum solutions and the search capability of BBO to find alternate optimum solutions.

Accurate identification of 3-D Cauer model parameters is crucial for obtaining the junction temperature distribution of multichip IGBT modules and subsequently assessing their reliability. However, existing methods suffer from low computational efficiency and limited applicability. Thus, an efficient parameter identification method for 3-D Cauer model of multichip IGBT modules is proposed. The proposed method transforms the parameter identification problem into a large scale global optimization (LSGO) problem. By constructing the fitness function based on the temperature responses obtained from both the 3-D Cauer model and one-time finite element analysis, the method achieves high computational efficiency. For the first time, a cooperative co-evolution (CC)-based LSGO algorithm, with high universality for decision variables across diverse dimensions, is employed to identify 3-D Cauer model parameters. Within the algorithm, problem decomposition considers the inherent partitioned structure of the 3-D Cauer model for multichip IGBT modules, effectively preserving internal physical correlations and enhancing both convergence speed and solution quality. Additionally, the probabilistic contribution-based computational resource allocation strategy prioritizes high-contribution subproblems for resource efficiency, while enabling low-contribution ones to run and thus avoiding local optima. Finally, the effectiveness and superiority of the proposed method were validated using experimental data from a 6500V/750A multichip IGBT module.

For sharing the information between solutions, biogeography based optimization (BBO) procedure uses migration operator based on biogeography. Differential evolution (DE) is another well-organized, robust and most common evolutionary procedure for solving global optimization problems. We have implemented BBO with DE algorithm and proposes a new efficient approach namely BBO/DE. To generate an effective candidate solution BBO/DE hybridize the BBO with the DE effectively and the BBO migration operators are adjusted on the basis of iteration count to enhance the performance. To certify the effectiveness of our suggested approach, we have used 6 benchmark functions and applied our proposed solution. From the comparison results it can be induced that the suggested methodology is effective and efficient both in comparison to traditional BBO and DE.

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.

The scalability performance of the traditional evolutionary algorithms (EAs) deteriorates rapidly as the dimensionality of the optimization problems increases. Therefore, cooperative coevolutionary (CC) framework is proposed to overcome the defect. Different from existing CC algorithms, a novel self-adaptive based cooperative coevolutionary (SaCC) algorithm is presented in this paper. The SaCC employs three algorithms which with self-adaptive mechanism as sub-algorithms. The focus of this paper is on investigating two different cooperative coevolutionary manners. In the first manner, SaCC executes its sub-algorithms in parallel during evolve process and the corresponding algorithm is termed as SaCC-M1. In the second manner, SaCC executes its sub-algorithms in serial and the corresponding algorithm is termed as SaCC-M2. 26 test functions with 1000 dimensionalities are employed to verify the validity of SaCC-M1 and SaCC-M2. Experiment results demonstrate that SaCC-M2 outperforms its sub-algorithms and SaCC-M1. Besides, the results indicate that serial manner is another simple yet efficient manner for CC algorithms to solve large-scale global optimization problems.