Cooperative Coevolution Research Articles

Multi-Aircraft Cooperative Strategic Trajectory-Planning Method Considering Wind Forecast Uncertainty

We address the issue of multi-aircraft cooperative strategic trajectory planning in free-route airspace (FRA) in this study, taking into consideration the impact of time-varying and altitude-varying wind forecast uncertainty. A bi-level planning model was established in response to the properties of the wind. The upper level focused on minimizing the flight time, while the lower level aimed to reduce potential conflicts. Meanwhile, a heuristic approach based on conflict severity (CS) within the framework of a cooperative co-evolution evolutionary algorithm (CCEA) was proposed to accelerate the convergence speed in view of the complexity of this optimization issue. In order to conduct the experiments, historical data of 1479 flights over western Chinese airspace were retrieved. The number of conflicts, total flight time, total flight time variance, and deviation were used as indicators to evaluate the safety, efficiency, and predictability of the trajectory. When compared to a trajectory in the structured airspace, the optimal solution was conflict-free and reduced the total flight time by about 17.7%, the variance by 11.7%, and the deviation by 37.5%. Additionally, the contrast with the two-stage model demonstrated that the proposed method was entirely meaningful. The outcome of this survey can provide an effective trajectory-planning method, which is crucial for the sustainable development of future air traffic management (ATM).

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.

An Effective Cooperative Co-Evolutionary Algorithm for Distributed Flowshop Group Scheduling Problems.

This article addresses a novel scheduling problem, a distributed flowshop group scheduling problem, which has important applications in modern manufacturing systems. The problem considers how to arrange a variety of jobs subject to group constraints at a number of identical manufacturing cellulars, each one with a flowshop structure, with the objective of minimizing makespan. We explore the problem-specific knowledge and present a mixed-integer linear programming model, a counterintuitive paradox, and two suites of accelerations to save computational efforts. Due to the complexity of the problem, we consider a decomposition strategy and propose a cooperative co-evolutionary algorithm (CCEA) with a novel collaboration model and a reinitialization scheme. A comprehensive and thorough computational and statistical campaign is carried out. The results show that the proposed collaboration model and reinitialization scheme are very effective. The proposed CCEA outperforms a number of metaheuristics adapted from closely related scheduling problems in the literature by a significantly considerable margin.

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.

UCAV Path Planning for Avoiding Obstacles using Cooperative Co-evolution Spider Monkey Optimization

The unmanned combat aerial vehicle (UCAV) path planning problem is a complex global optimization problem that aims to seek an optimal flight route that avoids the threats and constraints on the battlefield. However, as the number and degree of the path threats increases, the recent UCAV path planning algorithms all suffer from being trapped into local optima with a low convergence rate, which leads to the poor performance. Therefore, to resolve these problems, we propose a Cooperative co-Evolution (CE)-based Spider Monkey Optimization (SMO) algorithm, named CESMO to address UCAV path planning problem for avoiding obstacles. First, a cooperative co-evolution strategy is proposed to prevent the algorithms from falling into local optima easily, enhancing the coherence of the path. After that, a further division is applied to the algorithm for diversifying the search direction of each individual in the sub-groups. Finally, the spider monkey optimization-based search mechanism is designed to further strengthen the search efficiency and boost the convergence rate. Experimental results demonstrate that our proposed method is more competitive than other state-of-the-art evolutionary algorithms for UCAV path planning problem considering the quality and stability of the final paths.

Cooperative co-evolutionary differential evolution algorithm applied for parameters identification of lithium-ion batteries

Parameters identification of battery is a significant task for lithium-ion batteries. Some widely used techniques usually simplify the electrical circuit model (ECM) with non-linearity to a linear model or local linear model. However, by using such a methodology, the parameters in ECMs are not globally optimal, since the parameters may be not consistent at different linearized points. To address this issue, this paper proposed a cooperative co-evolution differential evolution (CCDE) algorithm to identify parameters of lithium-ion battery, without any linearization or pre-assumption. First, to describe the dynamic behaviors of battery, we presented a first-order RC equivalent circuit model ECM. Without making any approximation, improved Euler’s numerical method was utilized to solve the differential equations directly. Second, an optimizing objective function was built to minimize errors between the true and optimized terminal voltages. In that optimization model, parameters of battery (R0, RP and CP) and vOCV(t) at each sampling point were considered as variables to be optimized, resulting in a very high-dimension problem. Third, such an optimization problem was transformed into a large scale optimization problem (LSOP). Based on the character of parameters identification, we proposed a new m-decomposition method which is different from general grouping methods for benchmark functions and its corresponding differential evolution (DE) algorithm to solve this LSOP. Comprehensive experimental results demonstrated effectiveness of the proposed framework and methodology, compared with seven state-of-the-art cooperative co-evolution methods.

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.

Automatic Design of Efficient Heuristics for Two-Stage Hybrid Flow Shop Scheduling

This paper addresses the two-stage hybrid flow shop scheduling problem with a batch processor in the first stage and a discrete processor in the second stage. Incompatible job families and limited buffer size are considered. This hybrid flow shop configuration commonly appears in manufacturing operations and the batch processor is always the bottleneck which breaks the symmetry of processing time. Since making a real-time high-quality schedule is challenging, we focus on the automatic design of efficient heuristics for this two-stage problem based on the genetic programming method. We develop a hyper-heuristic approach to automate the tedious trial-and-error design process of heuristics. The goal is to generate efficient dispatching rules for identifying complete schedules to minimize the total completion time. A genetic programming with cooperative co-evolution approach is proposed to evolve the schedule policy automatically. Numerical results demonstrate that the proposed approach outperforms both the constructive heuristic and meta-heuristic algorithms, and is capable of producing high-quality schedules within seconds.

Variable Decomposition for Large-Scale Constrained Optimization Problems Using a Grouping Genetic Algorithm

Several real optimization problems are very difficult, and their optimal solutions cannot be found with a traditional method. Moreover, for some of these problems, the large number of decision variables is a major contributing factor to their complexity; they are known as Large-Scale Optimization Problems, and various strategies have been proposed to deal with them. One of the most popular tools is called Cooperative Co-Evolution, which works through a decomposition of the decision variables into smaller subproblems or variables subgroups, which are optimized separately and cooperate to finally create a complete solution of the original problem. This kind of decomposition can be handled as a combinatorial optimization problem where we want to group variables that interact with each other. In this work, we propose a Grouping Genetic Algorithm to optimize the variable decomposition by reducing their interaction. Although the Cooperative Co-Evolution approach is widely used to deal with unconstrained optimization problems, there are few works related to constrained problems. Therefore, our experiments were performed on a test benchmark of 18 constrained functions under 100, 500, and 1000 variables. The results obtained indicate that a Grouping Genetic Algorithm is an appropriate tool to optimize the variable decomposition for Large-Scale Constrained Optimization Problems, outperforming the decomposition obtained by a state-of-the-art genetic algorithm.

Grammar-based cooperative learning for evolving collective behaviours in multi-agent systems

This paper presents a novel grammar-based evolutionary approach which allows autonomous emergence of heterogeneity in collective behaviours. The approach adopts a context-free grammar to describe the syntax of evolving rules, which facilitates an evolutionary algorithm to evolve rule structures without manual intervention. We propose modifications to the genome structure to address the requirements of heterogeneity, and two cooperative learning architectures based on team learning and cooperative coevolution. Experimental evaluations with four behaviours illustrate that both architectures are successful in evolving heterogeneous collective behaviours. Both heterogeneous architectures surpass a homogeneous model in performance for deriving a flocking macro behaviour, however the homogeneous model is superior for evolving micro behaviours such as cohesion and alignment. The results infer that by placing the entire set of agent rules and their syntax under evolutionary control, effective solutions to complex problems can be evolved when human knowledge and intuition becomes insufficient.

Parallel Cooperative Coevolutionary Grey Wolf Optimizer for Path Planning Problem of Unmanned Aerial Vehicles.

The path planning of Unmanned Aerial Vehicles (UAVs) is a complex and hard task that can be formulated as a Large-Scale Global Optimization (LSGO) problem. A higher partition of the flight environment leads to an increase in route’s accuracy but at the expense of greater planning complexity. In this paper, a new Parallel Cooperative Coevolutionary Grey Wolf Optimizer (PCCGWO) is proposed to solve such a planning problem. The proposed PCCGWO metaheuristic applies cooperative coevolutionary concepts to ensure an efficient partition of the original search space into multiple sub-spaces with reduced dimensions. The decomposition of the decision variables vector into several sub-components is achieved and multi-swarms are created from the initial population. Each sub-swarm is then assigned to optimize a part of the LSGO problem. To form the complete solution, the representatives from each sub-swarm are combined. To reduce the computation time, an efficient parallel master-slave model is introduced in the proposed parameters-free PCCGWO. The master will be responsible for decomposing the original problem and constructing the context vector which contains the complete solution. Each slave is designed to evolve a sub-component and will send the best individual as its representative to the master after each evolutionary cycle. Demonstrative results show the effectiveness and superiority of the proposed PCCGWO-based planning technique in terms of several metrics of performance and nonparametric statistical analyses. These results show that the increase in the number of slaves leads to a more efficient result as well as a further improved computational time.

Multi-objective cooperative coevolution algorithm with a Master–Slave mechanism for Seru Production

Seru Production is usually used as a creative mode of production in electronics. It involves two NP-hard subproblems, namely seru formation and seru scheduling. To obtain the optimal global solution of multi-objective Seru Production, we develop a multi-objective cooperative coevolution algorithm with a Master–Slave mechanism. In the proposed algorithm, a cooperative mechanism is used to simultaneously optimize seru formation and seru scheduling. In addition, three usually non-dominated solutions are defined and used in the cooperative mechanism to improve the quality of non-dominated solutions, which takes more computational time. To reduce the computational time, three seru scheduling/seru formation populations evolve in parallel with the assistance of the three corresponding non-dominated seru formations/seru schedulings. To further improve the quality of non-dominated solutions, we propose a Master–Slave​ mechanism. The Master population is designed to store the current non-dominated solutions and communicates with three Slave populations. Extensively tested experiments show that the proposed algorithm outperforms existing algorithms for multi-objective Seru Production.

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.

Bipartite Cooperative Coevolution for Energy-Aware Coverage Path Planning of UAVs

The coverage path planning of unmanned aerial vehicles (UAVs) is a complex optimization problem in practice, especially for those involving multiple target areas. It is challenging to comprehensively plan the inter-area visiting order and the intra-area coverage paths simultaneously. Due to the battery limitation, usually the task can hardly be finished by a single UAV, and instead a fleet of UAVs are required. In this article, we first formulate an energy-aware multi-UAV multi-area coverage path planning (EM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^2$</tex-math></inline-formula> CPP) model, in order to characterize the practical path planning requirements of UAVs in complex conditions. Subsequently, to accomplish the optimization task, we propose a bipartite cooperative coevolution (BiCC) algorithm that coevolves an inter-area path planning and an intra-area path planning components to obtain good solutions. The basic operators in BiCC, such as the initialization and the reproduction operators, are tailored for the task of EM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^2$</tex-math></inline-formula> CPP. Besides, we also develop a fast heuristic algorithm for EM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^2$</tex-math></inline-formula> CPP, which is able to produce approximate solutions in a short time. Simulations on real-world datasets validate the good performance of the proposed methods.

Reducing Tardy Batches by Seru Production: Model, Exact Solution, Cooperative Coevolution Solution, and Insights

Reducing Tardy Batches by Seru Production: Model, Exact Solution, Cooperative Coevolution Solution, and Insights

An Agent-Based Cooperative Co-Evolutionary Approach for the Many-Objective Optimal Production Planning in Energy Supply Chains

An Agent-Based Cooperative Co-Evolutionary Approach for the Many-Objective Optimal Production Planning in Energy Supply Chains

An Agent-Based Cooperative Co-Evolutionary Approach for the Many-Objective Optimal Production Planning in Energy Supply Chains

An Agent-Based Cooperative Co-Evolutionary Approach for the Many-Objective Optimal Production Planning in Energy Supply Chains

Co-evolution of cooperation with resource allocation in spatial multigame using switching control

In reality, complicated situations usually include multiple game scenarios, which cannot be effectively described by a single game model. Hence, how to model and reveal the cooperative behaviors in complex multiple game environments is a meaningful topic. In this article, by using switching control, a spatial multigame model with reciprocal reward and reputation mechanism is proposed, where a specific game scenario at each time step is determined by current individuals’ behaviors and the game type. Besides, the allocation of limited resources is co-evolved with the evolution of cooperation, which can be regarded as the results of the game and meanwhile affect the while game processes. The evolution dynamics of the proposed model is detailly discussed and the mutual influence of reputation mechanism, reward reciprocity and resource allocation on cooperative behaviors is quantitatively studied. Finally, in order to illustrate the robustness of the analyzed results, its impact on the cooperative behaviors in single PD and SD games are comparatively discussed.

An alternative way of evolutionary multimodal optimization: density-based population initialization strategy

Evolutionary algorithms rely on the population initialization strategy to determine a set of candidate solutions, which provide the preliminary knowledge of the problem landscape for the subsequent evolutionary process. However, the distribution of the initial population is rarely concerned in the multimodal evolutionary community. Moreover, a large initial population has not been attractive enough for evolutionary multimodal optimization, because it is difficult and challenging to achieve a balance between diversity and convergence within limited computing resources. As an extended version of our previous conference paper, this paper focuses on the construction of a large initial population that is beneficial for evolutionary multimodal optimization. First, we propose an improved density-based population initialization strategy to generate a uniform initial population with a certain degree of randomness. Then, after acquiring the raw fitness landscape of the problem, a fitness-weighted density-based population initialization strategy is proposed to explore potential global peaks. Finally, we design a multi-species cooperative coevolution algorithm for multimodal optimization, which balances the exploration and exploitation of such a population in the evolutionary process. Experimental results demonstrate that the proposed algorithm is better than the mainstream algorithms on the CEC2013 multimodal optimization benchmark.

A decomposition approach for large-scale non-separable optimization problems

Large-scale optimization is the key to many practical decision processes. To deal with the dimensional issue in such problems, many approaches incorporate a divide-and-conquer strategy. Among them, cooperative coevolution approaches have recently gained popularity. Depending on the problem’s structure, the decomposition of any large problem, into a number of smaller sub-problems, may leave some variables common in more than one sub-problem. Such a decomposition may have a negative effect on the quality of the final solution of an optimization problem. In this paper, we have proposed an algorithm that incorporates a novel decomposition method, where the objective of decomposition is to minimize the number of common variables between sub-problems, achieved by exploiting a variable interaction matrix developed from the problem. So the algorithm works as a two-stage approach, where the first stage is the problem decomposition, and the second stage is to find the solutions of the problem. The performance of our proposed algorithm is assessed by solving different sets of large-scale non-separable benchmark functions with up to 2,905 variables. The experimental results provide important insights into the efficiency of the proposed decomposition method, which in turn improves the performance of the optimization process.