Cooperative Coevolution Framework Research Articles

A novel implicit decision variable classification approach for high-dimensional robust multi-objective optimization in order scheduling

This paper efficiently addresses the high-dimensional robust order scheduling problem. A novel algorithm named dynamic cooperative coevolution based on an implicit decision variable classification approach (DCC/IDVCA) is developed to search for robust order schedules. To significantly reduce the computational resources required for solving the high-dimensional robust order scheduling problem, we propose decomposing the original decision variables through implicit classification methods. First, a novel estimation method is introduced to evaluate the weighted contribution of variables to robustness. This method utilizes historical information, including the variation of the overall mean effective fitness and the frequency of variables being classified into highly robustness-related subcomponents in previous cycles, for evaluating their weighted contribution to robustness. Then, based on the corresponding weighted robustness contributions, the original variables are classified into highly and weakly robustness-related variables. Finally, these two types of variables are decomposed into highly and weakly robustness-related subgroups within a dynamic cooperative coevolution framework and optimized separately. In the experimental section, the proposed algorithm is applied to two practical order scheduling problems in discrete manufacturing industry. The experimental results demonstrate that the proposed algorithm achieves competitive outcomes compared to state-of-the-art high-dimensional robust multi-objective optimization algorithms.

Using cooperative coevolution in large-scale black-box constraint satisfaction problems

Solving constrained large-scale global optimization problems poses a challenging task. In these problems with constraints, when the number of variables is measured in the thousands, when the constraints are presented in the form of a black box, and neither the size nor the configuration of the feasible region is known, it is very difficult to find at least one feasible solution. In general, such a problem of finding a feasible region is known as a constraint satisfaction problem. In this paper, we have extended a well-known benchmark set based on constrained optimization problems up to 1000 variables. We have evaluated the CC-SHADE performance, to tackle constraints in large-scale search space. CC-SHADE merges the power of cooperative coevolution and self-adaptive differential evolution. Our extensive experimental evaluations on a range of benchmark problems demonstrate the strong dependence of the performance of CC-SHADE on the number of individuals and the subcomponent number. The numerical results emphasize the importance of using a cooperative coevolution framework for evolutionary-based approaches compared to conventional methods. All numerical experiments are proven by the Wilcoxon test.

Difficulty and Contribution-Based Cooperative Coevolution for Large-Scale Optimization

Cooperative coevolution (CC) is a paradigm equipped with the divide-and-conquer strategy for solving large-scale optimization problems. Currently, the computational resource allocation schemes of most CC could be divided into two categories, namely equal allocation to all subproblems and preference allocation to the subproblems with large contribution. However, the difficult subproblems are not carefully considered by the existing computational resource allocation schemes. For these subproblems, the investment of computational resources cannot quickly improve the fitness value, which leads to their small early contribution and being neglected. In this paper, we comprehensively analyze the imbalanced nature of the subproblems from their difficulty and contribution in large-scale optimization problems. First, we propose a method to quantify the optimization difficulty of the problems during the evolution process, which considers both the difficulty of the fitness landscape and the behaviors of the optimization algorithm. Then, we propose a novel both difficulty and contribution based CC framework, called DCCC, which encourages the allocation of the computational resources to more contributing and more difficult subproblems. DCCC is tested on the CEC’2010 and CEC’2013 large-scale optimization benchmarks, and is compared with several typical CC frameworks and state-of-the-art large-scale optimization algorithms. The experimental results demonstrate that DCCC is very competitive.

Cooperative coevolutionary differential evolution with linkage measurement minimization for large-scale optimization problems in noisy environments

Many optimization problems suffer from noise, and the noise combined with the large-scale attributes makes the problem complexity explode. Cooperative coevolution (CC) based on divide and conquer decomposes the problems and solves the sub-problems alternately, which is a popular framework for solving large-scale optimization problems (LSOPs). Many studies show that the CC framework is sensitive to decomposition, and the high-accuracy decomposition methods such as differential grouping (DG), DG2, and recursive DG (RDG) are extremely sensitive to sampling accuracy, which will fail to detect the interactions in noisy environments. Therefore, solving LSOPs in noisy environments based on the CC framework faces unprecedented challenges. In this paper, we propose a novel decomposition method named linkage measurement minimization (LMM). We regard the decomposition problem as a combinatorial optimization problem and design the linkage measurement function (LMF) based on Linkage Identification by non-linearity check for real-coded GA (LINC-R). A detailed theoretical analysis explains why our proposal can determine the interactions in noisy environments. In the optimization, we introduce an advanced optimizer named modified differential evolution with distance-based selection (MDE-DS), and the various mutation strategy and distance-based selection endow MDE-DS with strong anti-noise ability. Numerical experiments show that our proposal is competitive with the state-of-the-art decomposition methods in noisy environments, and the introduction of MDE-DS can accelerate the optimization in noisy environments significantly.

Dominance-based variable analysis for large-scale multi-objective problems

Optimization problems with multiple objectives and many input variables inherit challenges from both large-scale optimization and multi-objective optimization. To solve the problems, decomposition and transformation methods are frequently used. In this study, an improved control variable analysis is proposed based on dominance and diversity in Pareto optimization. Further, the decomposition method is used in a cooperative coevolution framework with orthogonal sampling mutation. The algorithm’s performances are compared against the weighted optimization framework. The results show that the proposed decomposition method has much better accuracy compared to the traditional method. The results also show that the cooperative coevolution framework with a good grouping is very competitive. Additionally, the number of search directions in orthogonal sampling can be easily configured. A small number of search directions will reduce the search space greatly while also restricting the area that can be explored and vice versa.

CCFR3: A cooperative co-evolution with efficient resource allocation for large-scale global optimization

Cooperative co-evolution (CC) adopts the divide-and-conquer strategy to decompose an optimization problem, which can decrease the difficulty of solving large-scale optimization problems. Each decomposed subproblem is solved by a subpopulation. According to the contributions of the subpopulations to the improvement of the best overall objective value, the CC algorithms select the subpopulation with the greatest contribution to undergo evolution. In the existing CC algorithms, the contribution evaluation cannot adapt to solve the optimization problem, which may decrease the performance of CC. In this paper, we propose a new CC framework named CCFR3, which can adaptively evaluate the contribution of a subpopulation in each co-evolutionary cycle. CCFR3 can allocate computational resources among subpopulations more frequently than other contribution-based CC algorithms. The subpopulations can have more chances to undergo evolution, which is beneficial to speed up the convergence of CC and enhance the performance of CC on obtaining the global optimal solution. Our experimental results and analysis suggest that CCFR3 is a competitive solver for large-scale optimization problems.

A multipopulation cooperative coevolutionary whale optimization algorithm with a two-stage orthogonal learning mechanism

This paper designed a multipopulation cooperative coevolutionary framework with a two-stage orthogonal learning (OL) mechanism for the whale optimization algorithm (MCCWOA) to improve the performance of the whale optimization algorithm (WOA). In the framework, a prediction model of the neighborhood structure is established by discovering the guidance information of the following iteration process in the objective space at the first-stage OL. In the second-stage OL, an auxiliary vector pool with various features in the decision space is introduced to guide the candidates falling in the stagnant status to conduct more valuable exploration. According to the domain knowledge of the candidates, the population is divided into the elite population, the intermediate population, and the inferior population. The information of the subpopulations has interacted with the corresponding historical populations in the evolution processes to enhance the ability of cooperative coevolution among individuals. A standard set of comprehensive benchmark cases and three engineering cases are utilized to verify the advantages of the proposed algorithm. The results of the statistical analysis, diversity analysis, and convergence analysis testified that the MCCWOA outperforms the 15 state-of-the-art algorithms regarding efficiency and significance.

Evolutionary reinforcement learning via cooperative coevolutionary negatively correlated search

Evolutionary algorithms (EAs) have been successfully applied to optimize the policies for Reinforcement Learning (RL) tasks due to their exploration ability. The recently proposed Negatively Correlated Search (NCS) provides a distinct parallel exploration search behavior and is expected to facilitate RL more effectively. Considering that the commonly adopted neural policies usually involves millions of parameters to be optimized, the direct application of NCS to RL may face a great challenge of the large-scale search space. To address this issue, this paper presents an NCS-friendly Cooperative Coevolution (CC) framework to scale-up NCS while largely preserving its parallel exploration search behavior. The issue of traditional CC that can deteriorate NCS is also discussed. Empirical studies on 10 popular Atari games show that the proposed method can significantly outperform three state-of-the-art deep RL methods with 50% less computational time by effectively exploring a 1.7 million-dimensional search space.

Cooperative Coevolutionary Particle Swarms using Fuzzy Logic for Large Scale Optimization

A cooperative coevolutionary framework can improve the performance of optimization algorithms on large-scale problems. In this paper, we propose a new Cooperative Coevolutionary Coevolutionary algorithm based on our preliminary work FuzzyPSO2. This new proposal, called CCFPSO, uses a variable decomposition method, adopting the random grouping technique and a dynamic subcomponent size at each generation. Unlike FuzzyPSO2, in CCFPSO the re-initialization of the variables suggested by the fuzzy system is performed on the particles that has the worst fitness value in each generation. Moreover, the particles are updated based on their best position and its neighborhoods, instead of the best particle in the population as its standard version. On high-dimensional problems that more closely resemble real-world problems (CEC2008, CEC2010) the performance of CCFPSO is favorable compared to other state-of-the-art PSO versions such as CCPSO2, SLPSO and CSO. The results indicate that using a Cooperative Coevolutionary PSO approach with a fuzzy logic system can improve results on high dimensionality problems (100 to 1000 variables).

Task Execution Quality Maximization for Mobile Crowdsourcing in Geo-Social Networks

With the rapid development of smart devices and high-quality wireless technologies, mobile crowdsourcing (MCS) has been drawing increasing attention with its great potential in collaboratively completing complicated tasks on a large scale. A key issue toward successful MCS is participant recruitment, where a MCS platform directly recruits suitable crowd participants to execute outsourced tasks by physically traveling to specified locations. Recently, a novel recruitment strategy, namely Word-of-Mouth(WoM)-based MCS, has emerged to effectively improve recruitment effectiveness, by fully exploring users' mobility traces and social relationships on geo-social networks. Against this background, we study in this paper a novel problem, namely Expected Task Execution Quality Maximization (ETEQM) for MCS in geo-social networks, which strives to search a subset of seed users to maximize the expected task execution quality of all recruited participants, under a given incentive budget. To characterize the MCS task propagation process over geo-social networks, we first adopt a propagation tree structure to model the autonomous recruitment between the referrers and the referrals. Based on the model, we then formalize the task execution quality and devise a novel incentive mechanism by harnessing the business strategy of multi-level marketing. We formulate our ETEQM problem as a combinatorial optimization problem, and analyze its NP hardness and high-dimensional characteristics. Based on a cooperative co-evolution framework, we proposed a divide-and-conquer problem-solving approach named ETEQM-CC. We conduct extensive simulation experiments and a case study, verifying the effectiveness of our proposed approach.

A graph partitioning based cooperative coevolution for the batching problem in steelmaking production

This paper studies a common planning problem encountered in steelmaking production. The problem is to group different customer orders into a set of batches to accommodate the mass production mode of steelmaking furnaces. We formulate the problem as a novel mixed-integer programming model by considering the practical technological requirements. To solve the problem, we propose a cooperative coevolution framework in which an effective decomposition scheme based on graph partitioning is developed. The decomposition scheme first explores the problem structure by considering the production process rules and then exploits the batch information of the best-so-far solution to identify the potentially better decompositions. To solve each decomposed subcomponent, we propose a new differential evolution algorithm which incorporates a subpopulation-based classification mechanism and local search with an external archive strategy to balance the abilities of exploration and exploitation. Computational tests on a set of real production data as well as on a more diverse set of randomly generated problem instances show that our method is effective and efficient in practical application and outperforms other benchmark algorithms.

Constraint-Objective Cooperative Coevolution for Large-scale Constrained Optimization

Large-scale optimization problems and constrained optimization problems have attracted considerable attention in the swarm and evolutionary intelligence communities and exemplify two common features of real problems, i.e., a large scale and constraint limitations. However, only a little work on solving large-scale continuous constrained optimization problems exists. Moreover, the types of benchmarks proposed for large-scale continuous constrained optimization algorithms are not comprehensive at present. In this article, first, a constraint-objective cooperative coevolution (COCC) framework is proposed for large-scale continuous constrained optimization problems, which is based on the dual nature of the objective and constraint functions: modular and imbalanced components. The COCC framework allocates the computing resources to different components according to the impact of objective values and constraint violations. Second, a benchmark for large-scale continuous constrained optimization is presented, which takes into account the modular nature, as well as both imbalanced and overlapping characteristics of components. Finally, three different evolutionary algorithms are embedded into the COCC framework for experiments, and the experimental results show that COCC performs competitively.

Quantum differential evolution with cooperative coevolution framework and hybrid mutation strategy for large scale optimization

In order to overcome the low solution efficiency, insufficient diversity in the later search stage, slow convergence speed and a high search stagnation possibility of differential evolution(DE) algorithm, the quantum computing characteristics of quantum evolutionary algorithm(QEA) and the divide-and-conquer idea of cooperative coevolution evolutionary algorithm(CCEA) are combined to propose an improved differential evolution(HMCFQDE) in this paper. In the proposed HMCFQDE, a new hybrid mutation strategy based on the advantages of local neighborhood mutation and SaNSDE is designed. In the early stage of the search, the local neighborhood mutation strategy with high search efficiency is used to speed up the algorithm convergence. In the later stage of the search, the SaNSDE algorithm is used to adjust the search direction in order to avoid the search stagnation. The QEA is combined with the DE to make use of the quantum chromosome encoding to enhance the population diversity, the quantum rotation to speed up the convergence speed. The CC framework is used to divide the large-scale and high-dimensional complex optimization problem into several low-dimensional optimization sub-problems, and these sub-populations are solved by independent searching among sub-populations in order to improve the solution efficiency. By comparing with other 6 algorithms in solving 6 test functions from CEC’08 under the dimensions of 100, 500 and 1000, it is proved that the proposed HMCFQDE has higher convergence accuracy and stronger stability. In particular, it has a strong ability to optimize high-dimensional complex functions. Therefore, it provides a new method for solving large-scale optimization problem.

Multi-objective multi-mode resource-constrained project scheduling with fuzzy activity durations in prefabricated building construction

Different from traditional project management, the prefabricated building (PB) construction project has a complex distributed supply chain model, and the overall project is completed by multi-stage cooperation. Therefore, the implementation process will be restricted by many constraints, and various uncertain factors will also interfere with the smooth implementation of the project. In order to improve the stability and reliability of the PB construction project implementation process, it is very important to study an effective robust project scheduling method considering resource constraints in an uncertain environment. In this paper, we formulate a PB construction resource-constrained project scheduling with multi-objective multi-mode, focus on the uncertainty of the execution time of the execution activity, and constructs the interval value of the execution time to express it through fuzzy theory; also considers the multiple objectives of PB construction project, including time-based profit, and cost-based profit. Secondly, we propose a hybrid cooperative co-evolution algorithm (HCOEA) to obtain the highly robust project scheduling, reduce the impact of the uncertainty of the execution time of the activity on the overall project. Resource-constrained project scheduling problem (RCPSP) is an NP-hard combinatorial optimization problem. This paper also needs to consider the complex combination of time-resource and/or time–cost constraints. At the same time, it is necessary to consider the impact of time changes in different mode combinations. Therefore, how to design an effective multi-objective optimization algorithm is very difficult. This paper design a Hybrid Cooperative Co-evolution Algorithm (HCOEA) with multi-stage representation for the activity sequencing and the resource allocation, further improve the search efficiency. We improve the cooperative co-evolution framework with a self-adaptive mechanism and a self-adaptive selection process. Finally, benchmarks and extended datasets with fuzzy processing time are adopted to test our HCOEA. Computational results show that the HCOEA performs better than the existing state-of-the-art methods.

A cooperative coevolution framework for evolutionary learning and instance selection

Data science becomes an emerging topic in developing computational and artificial intelligence techniques due to the rapid growth of information and data over past decade. Data-driven evaluation, through scanning data to validate the performance of a method, is the crux of effectively retrieving information. Ordinarily, the computational cost at data-driven evaluation is proportional to the volume, determined by the number of instances and the number of attributes, of the data. One straightforward way of reducing the volume of data is instance selection. Past studies have adopted evolutionary algorithm (EA) for instance selection, yet these studies are mainly based on k nearest neighbors classifier due to the high computational cost at learning process. Leveraging EA to learn patterns, models, or classifiers forms a famous branch of learning method known as evolutionary learning (EL). Nevertheless, EL requires immense amount of data-driven fitness evaluations, which detracts EL from efficiency and causes slow convergence. The issue of high computational cost at data-driven evaluation restricts the capability of evolutionary learning and evolutionary instance selection. This study proposes a novel framework called cooperative evolutionary learning and instance selection (CELIS) for addressing the above issues. There are three main features in the proposed CELIS: 1) cooperative evolutionary learning and instance selection in an adaptive manner, 2) fast solution evaluation based on the selected subset of data for evolutionary learning, and 3) effective data evaluation of representativeness as per promising solution for evolutionary instance selection. This study conducts a series of experiments for testing the effectiveness and efficiency of the proposed CELIS on data mining, classification, and symbolic regression problems. The results show that the proposed method can significantly enhance the performance of state-of-the-art EAs on the three types of problems in terms of solution quality and convergence speed. Further analysis also validates that CELIS is able to gain a small and representative subset of data.

Investigation of the iCC Framework Performance for Solving Constrained LSGO Problems

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.

Improving DE-based cooperative coevolution for constrained large-scale global optimization problems using an increasing grouping strategy

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.

Dynamic Cooperative Coevolution for Large Scale Optimization

The cooperative coevolution (CC) framework achieves a promising performance in solving large scale global optimization problems. The framework encounters difficulties on nonseparable problems, where variables interact with each other. Using the static grouping methods, variables will be theoretically grouped into one big subcomponent, whereas the random grouping strategy endures low efficiency. In this paper, a dynamic CC framework is proposed to tackle the challenge. The proposed framework works in a computationally efficient manner, in which the computational resources are allocated to a series of elitist subcomponents consisting of superior variables. First, a novel estimation method is proposed to evaluate the contribution of variables using the historical information of the best overall fitness. Based on the contribution and the interaction information, a dynamic grouping strategy is conducted to construct the dynamic subcomponent that evolves in the next evolutionary period. The constructed subcomponents are different from each other, and therefore the required parameters to control the optimization of each subcomponent vary a lot in each evolutionary period. A stage-by-stage parameter adaptation strategy is proposed to adapt the optimizer to the dynamic optimization environment. Experimental results indicate that the proposed framework achieves competitive results compared with the state-of-the-art CC frameworks.

Automatic Design of Intercell Scheduling Heuristics

Though intercell scheduling problems have been studied in the literature, extant algorithms can hardly come into play in practice. This is because of two reasons: 1) transportation among cells, which is important for practical intercell scheduling, has not been adequately considered and 2) the problem size is large in practice, which may lead to intolerable computation efficiency. The motivation of this paper is to automatically design intercell scheduling heuristics that are suitable for practical application. A genetic programming algorithm with a pretraining strategy (GP-PS) is proposed. Production within cells and transportation among cells are simultaneously considered, and a cooperative coevolutionary framework is designed. To evolve better heuristics, a PS is developed. A speedup strategy is designed to accelerate the evolutionary process. Comparative experiments are conducted with other GP-based algorithms, speedup strategies, and with some state-of-the-art intercell scheduling algorithms. GP-PS is also put into use in a large manufacturing enterprise of China. Computational experiments and application results both verify the effectiveness of GP-PS. Note to Practitioners —Although intercell scheduling problems have been studied in the literature, it is still common to rely on manually generated schedules in industrial environments. This paper does not attempt to seek solutions directly, but try to automatically design good heuristic rules to address the problem, so that the computation efficiency that is required by real-time decision and the optimization performance that is important for a complex problem, can be satisfied at the same time.

Solving Incremental Optimization Problems via Cooperative Coevolution

Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems, where the changes are caused by some objective factors, the changes in such incremental optimization problems (IOPs) are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such IOPs. In this paper, we study how to adopt cooperative coevolution to efficiently solve a specific type of IOPs, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of IOPs with increasing decision variables and exploitable modular structure. Then, we propose a contribution-based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam.