Modern computational mathematics and informatics for Digital Environments deal with the high dimensionality when designing and optimizing models for various real-world phenomena. Large-scale global black-box optimization (LSGO) is still a hard problem for search metaheuristics, including bio-inspired algorithms. Such optimization problems are usually extremely multi-modal, and require significant computing resources for discovering and converging to the global optimum. The majority of state-of-the-art LSGO algorithms are based on problem decomposition with the cooperative co-evolution (CC) approach, which divides the search space into a set of lower dimensional subspaces (or subcomponents), which are expected to be easier to explore independently by an optimization algorithm. The question of the choice of the decomposition method remains open, and an adaptive decomposition looks more promising. As we can see from the most recent LSGO competitions, winner-approaches are focused on modifying advanced DE algorithms through integrating them with local search techniques. In this study, an approach that combines multiple ideas from state-of-the-art algorithms and implements Coordination of Self-adaptive Cooperative Co-evolution algorithms with Local Search (COSACC-LS1) is proposed. The self-adaptation method tunes both the structure of the complete approach and the parameters of each algorithm in the cooperation. The performance of COSACC-LS1 has been investigated using the CEC LSGO 2013 benchmark and the experimental results has been compared with leading LSGO approaches. The main contribution of the study is a new self-adaptive approach that is preferable for solving hard real-world problems because it is not overfitted with the LSGO benchmark due to self-adaptation during the search process instead of a manual benchmark-specific fine-tuning.

Many modern real-valued optimization tasks use “black-box” (BB) models for evaluating objective functions and they are high-dimensional and constrained. Using common classifications, we can identify them as constrained large-scale global optimization (cLSGO) tasks. Today, the IEEE Congress of Evolutionary Computation provides a special session and several benchmarks for LSGO. At the same time, cLSGO problems are not well studied yet. The majority of modern optimization techniques demonstrate insufficient performance when confronted with cLSGO tasks. The effectiveness of evolution algorithms (EAs) in solving constrained low-dimensional optimization problems has been proven in many scientific papers and studies. Moreover, the cooperative coevolution (CC) framework has been successfully applied for EA used to solve LSGO problems. In this paper, a new approach for solving cLSGO has been proposed. This approach is based on CC and a method that increases the size of groups of variables at the decomposition stage (iCC) when solving cLSGO tasks. A new algorithm has been proposed, which combined the success-history based parameter adaptation for differential evolution (SHADE) optimizer, iCC, and the ε-constrained method (namely ε-iCC-SHADE). We investigated the performance of the ε-iCC-SHADE and compared it with the previously proposed ε-CC-SHADE algorithm on scalable problems from the IEEE CEC 2017 Competition on constrained real-parameter optimization.

Many real-world optimization problems deal with high dimensionality and are known as large-scale global optimization (LSGO) problems. LSGO problems, which have many optima and are not separable, can be very challenging for many heuristic search algorithms. In this study, we have proposed a novel two-stage hybrid heuristic algorithm, which incorporates the coordinate descent algorithm with the golden-section search (CDGSS) and the random adaptive grouping for cooperative coevolution of the Self-adaptive Differential Evolution with Neighborhood Search (DECC-RAG) algorithm. At the first stage, the proposed algorithm roughly scans the search space for a better initial population for the DECC-RAG algorithm. At the second stage, the algorithm uses the DECC-RAG framework for solving the given LSGO problem. We have evaluated the proposed approach (DECC-RAG1.1) with 15 most difficult LSGO problems from the IEEE CEC’2013 benchmark set. The experimental results show that DECC-RAG1.1 outperforms the standard DECC-RAG and some the state-of-the-art LSGO algorithms.

Nowadays, high-dimensional constrained «Black-Box» (BB) optimization problems has become more urgent. At the same time, the constrained large-scale global optimization (cLSGO) problems are not well studied and many modern optimization approaches demonstrate low performance when dealing with cLSGO problems. Evolution algorithms (EAs) has proved their efficiency in solving low-dimensional constrained optimization problems and high-dimensional single-objective optimization problems. In this study, we have proposed a new approach based on the cooperative coevolution (CC) framework and an algorithm for increasing size of variables grouping on the decomposition stage (iCC) when solving cLSGO problems. We have proposed a novel EA that combines SHADE, iCC and ɛ-constrained method (ɛ-iCC-SHADE). The proposed optimization algorithm has been investigated using a new cLSGO benchmark, which is based on scalable problems from IEEE CEC 2017 Competition on Constrained Real-Parameter Optimization. The numerical experiments have shown that ɛ-iCC-SHADE outperforms the early proposed ɛ-CC-SHADE algorithm which operates with the fixed number of subcomponents.

Unconstrained continuous large-scale global optimization (LSGO) is still a challenging task for a wide range of modern metaheuristic approaches. A cooperative coevolution approach is a good tool for increasing the performance of an evolutionary algorithm in solving high-dimensional optimization problems. However, the performance of cooperative coevolution approaches for LSGO depends significantly on the problem decomposition, namely, on the number of subcomponents and on how variables are grouped in these subcomponents. Also, the choice of the population size is still an open question for population-based algorithms. This paper discusses a method for selecting the number of subcomponents and the population size during the optimization process (“on fly”) from a predefined pool of parameters. The selection of the parameters is based on their performance in the previous optimization steps. The main goal of the study is the improvement of coevolutionary decomposition-based algorithms for solving LSGO problems. In this paper, we propose a novel self-adapt evolutionary algorithm for solving continuous LSGO problems. We have tested this algorithm on 15 optimization problems from the IEEE LSGO CEC’2013 benchmark suite. The proposed approach, on average, outperforms cooperative coevolution algorithms with a static number of subcomponents and a static number of individuals.