Cooperative Coevolutionary Algorithm Research Articles

A Knowledge-Based Cooperative Co-Evolutionary Algorithm for Non-Contact Voltage Measurement

A Knowledge-Based Cooperative Co-Evolutionary Algorithm for Non-Contact Voltage Measurement

Configuration Optimization of a Skippable Anti-Ship Missile Considering Initial Kinematic Parameters

Skimming the sea at ultralow altitudes can be achieved by repeatedly touching and bouncing off water surface (commonly referred to as skipping), thus giving birth to skippable anti-ship missiles. However, the high impact load during skipping poses a safety hazard to the structure. Whether a missile can rebound primarily depends on the initial kinematic parameters, which also influence the impact load along with the configuration parameters. Therefore, it is important to optimize both of them. Due to the differences in types and complicated coupling of these parameters, the optimization problem becomes highly complex. In this paper, the grouped sequential quadratic programming (GSQP) algorithm is proposed to reduce the nonlinearity and nonconvexity of the problem. By bringing together the global search capability of cooperative co-evolutionary algorithm and the local search strength of GSQP, a combined optimization framework using decomposition strategies is constructed. With the support of fluid–structure interaction models, the optimization is performed to reduce impact load for the missile. The results demonstrate that simultaneously optimizing the configuration and initial kinematic parameters yields a reduction of 12.2% in the impact load on the premise of successful skipping. This research provides a valuable reference for the design of future skippable anti-ship missiles.

Surrogate-Assisted Cooperative Co-evolutionary Reservoir Architecture Search for Liquid State Machines

Liquid state machines (LSMs) are biologically more plausible than feedforward spiking neural networks for brain-inspired computing and neuromorphic engineering. However, optimizing and training complex recurrent network architectures in the reservoir of LSMs remains challenging. Most existing algorithms aim to adjust the synaptic strength only, without fundamentally modifying the reservoir architecture of LSMs. Recently, it has become popular to simultaneously optimize the architecture and parameters of the reservoir in LSMs. However, most existing architecture representation schemes are too restricted to discover more powerful architectures of LSMs. To address the above issue, this paper proposes a generative liquid state machine, whose reservoir architecture is evolved using a cooperative co-evolutionary algorithm whose weights are tuned by synaptic plasticity rules. To reduce the computation time for evolving the reservoir, random forest is adopted to assist the cooperative co-evolutionary algorithm, together with a data parallelism strategy. The proposed algorithm is assessed on three sequence classification benchmarks and our experimental results show that the proposed algorithm outperforms the state-of-the-art on the benchmark problems. Meanwhile, our analysis shows that the data parallelism strategy is effective in speeding up the evaluation process.

A Large-Scale Sensor Layout Optimization Algorithm for Improving the Accuracy of Inverse Finite Element Method.

The inverse finite element method (iFEM) based on fiber grating sensors has been demonstrated as a shape sensing method for health monitoring of large and complex engineering structures. However, the existing optimization algorithms cause the local optima and low computational efficiency for high-dimensional strain sensor layout optimization problems of complex antenna truss models. This paper proposes the improved adaptive large-scale cooperative coevolution (IALSCC) algorithm to obtain the strain sensors deployment on iFEM, and the method includes the initialization strategy, adaptive region partitioning strategy, and gbest selection and particle updating strategies, enhancing the reconstruction accuracy of iFEM for antenna truss structure and algorithm efficiency. The strain sensors optimization deployment on the antenna truss model for different postures is achieved, and the numerical results show that the optimization algorithm IALSCC proposed in this paper can well handle the high-dimensional sensor layout optimization problem.

High-Dimensional Data Global Sensitivity Analysis Based on Deep Soft Sensor Model.

This article investigates the sensitivity analysis (SA) of high-dimensional data to identify the effects of process variables on output quantity of interest (QoI) in industrial soft sensor modeling. The computational cost of analyzing the SA of high-dimensional data is high, and models available for SA techniques usually have limited generalization capacity. Therefore, we propose a novel high-dimensional data global SA (GSA) approach based on a deep soft sensor model to address these issues. We first develop an approximately incremental grouping (AIG) algorithm and a region-based cooperative co-evolution (RBCC) algorithm to decompose the high-dimensional data into independent regions for the GSA. Subsequently, a multihead deep soft sensor model with generalization performance is designed to determine the GSA indices of each decomposed region. Specifically, the region of interest (RoI) align algorithm provides the multihead with precisely located decomposed region features. Finally, based on the uncertainty analysis of each model head, we present a joint loss function with the Monte Carlo dropout (MC-dropout) algorithm to measure the GSA indices of each decomposed region on QoIs. Experimental evaluation results on a benchmark dataset and a real-world one demonstrate the effectiveness of the proposed approach in addressing the GSA of high-dimensional data in industrial processes.

A surrogate-assisted highly cooperative coevolutionary algorithm for hyperparameter optimization in deep convolutional neural networks

Hyperparameter optimization in convolutional neural networks (CNNs) plays a vital role in ensuring the effectiveness of the models. However, with the depth of the existing CNN expanding, this task becomes very challenging due to the high-dimensional and computationally expensive characteristics. Given these difficulties, this study proposes a surrogate-assisted highly cooperative hyperparameter optimization (SHCHO) algorithm for large-scale chain-styled CNNs. SHCHO tackles the original hyperparameter optimization problem by cooperatively optimizing its subproblems. Specifically, it first decomposes the whole CNN into several overlapping sub-CNNs, which conforms to the inherent overlapping interaction structure among hyperparameters and significantly reduces the search space. The resulting hyperparameter optimization subproblems on these sub-CNNs are then coevolved collaboratively and competitively, facilitating a proper hyperparameter configuration for the whole CNN. Besides, SHCHO also employs the computationally efficient surrogate technique to assist in each subproblem optimization. As a result, the expensive computational cost can be greatly reduced. Extensive experimental results on three widely-used image classification datasets indicate that SHCHO shows competitive performance when compared with several state-of-the-art algorithms in terms of both hyperparameter superiority and computational cost.

A Local Parameterization-Based Probabilistic Cooperative Coevolutionary Algorithm for History Matching

A Local Parameterization-Based Probabilistic Cooperative Coevolutionary Algorithm for History Matching

A cooperative population-based iterated greedy algorithm for distributed permutation flowshop group scheduling problem

This paper studies the distributed permutation flowshop group scheduling problem (DPFGSP) with the consideration of minimizing total flowtime (TF), which has important applications in the modern manufacturing process. Based on the characteristics of the problem, a cooperative population-based iterated greedy (CPIG) algorithm is proposed by combining the advantages of the divide-and-rule policy, population-based evolution and iterated greedy algorithm. The CPIG divides the DPFGSP into two coupled sub-problems of group scheduling sub-problem and job scheduling sub-problem, and starts with a single population for simplicity. Unlike in the traditional cooperative co-evolutionary algorithms, the two-coupled sub-problems are addressed with a certain probability that can be determined in favor of solving the whole scheduling problem. Some advanced technologies are used, including the constructive heuristics based initialization, the critical factories based destruction and construction, the new best solution based population updating mechanism. The comprehensive experimental evaluation of 810 instances shows that the CPIG algorithm performs much better than the five state-of-the-art metaheuristics in the literature which are closely related to the considered scheduling problem.

A Cluster-Based Cooperative Co-Evolutionary Algorithm for Multiobjective Workflow Scheduling in a Cloud Environment

A Cluster-Based Cooperative Co-Evolutionary Algorithm for Multiobjective Workflow Scheduling in a Cloud Environment

Cooperative Coevolutionary CMA-ES With Landscape-Aware Grouping in Noisy Environments

Many real-world optimization tasks suffer from noise. So far, the research on noise-tolerant optimization algorithms is still restricted to low-dimensional problems with less than 100 decision variables. In reality, many problems are high-dimensional. Cooperative coevolutionary (CC) algorithms based on a divide-and-conquer strategy are promising in solving complex high-dimensional problems. However, noisy fitness evaluations pose a challenge in problem decomposition for CC. The state-of-the-art grouping methods, such as differential grouping and recursive differential grouping, are unable to work properly in noisy environments. Because it is impossible to distinguish whether the change of one variable’s difference value is caused by noise or the perturbation of its interacting variables. As a result, every pair of variables will be identified as nonseparable in these methods. In this paper, we study how to group decision variables with covariance matrix adaptation evolution strategy (CMA-ES) in noisy environments and subsequently propose a landscape-aware grouping (LAG) method. Instead of detecting pairwise interacting variables, we directly identify a nonseparable subcomponent. To this end, we propose to use two convergence features, variable convergence time and accumulative path, to describe variables’ fitness landscapes; then, variables are clustered according to these two features. Numerical experiments show that LAG can more effectively identify interactive decision variables in the presence of multiplicative noise than the differential grouping and some of its variants. Up to 500 dimensions, the performance of cooperative coevolutionary CMA-ES with landscape-aware grouping (CC-CMAES-LAG) is competitive compared with existing CC algorithms and uncertainty-handling CMA-ES (UH-CMA-ES).

Dual Differential Grouping: A More General Decomposition Method for Large-Scale Optimization.

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.

A Greedy Cooperative Co-Evolutionary Algorithm With Problem-Specific Knowledge for Multiobjective Flowshop Group Scheduling Problems

The flowshop sequence-dependent group scheduling problem (FSDGSP) with the production efficiency measures has been extensively studied due to its wide industrial applications. However, energy efficiency indicators are often ignored in the literature. This paper considers the FSDGSP to minimize makespan, total flow time and total energy consumption, simultaneously. After the problem-specific knowledge is extracted, a mixed-integer linear programming model and a critical path-based accelerated evaluation method are proposed. Since the FSDGSP includes multiple coupled sub-problems, a greedy cooperative co-evolutionary algorithm (GCCEA) is designed to explore the solution space in depth. Meanwhile, a random mutation operator and a greedy energy-saving strategy are employed to adjust the processing speeds of machines to obtain a potential non-dominated solution. A large number of experimental results show that the proposed algorithm significantly outperforms the existing classic multi-objective optimization algorithms, which is due to the usage of problem-related knowledge.

A cooperative coevolutionary algorithm with problem-specific knowledge for energy-efficient scheduling in seru system

With the increasingly prominent issues about the global environment, green manufacturing has become a research hotspot. To cope with the turbulent market environment, seru production system (SPS) as an innovative manufacturing mode has attracted much attention, yet energy consumption is still rarely considered in SPS. This paper addresses an energy-efficient scheduling problem in seru system (EESPSS) with the minimization of energy consumption and makespan simultaneously. It contains three coupled subproblems, i.e., worker-seru assignment, batch-seru assignment, and worker-task assignment. To tackle the problem effectively, we build a mathematical model and design a cooperative coevolutionary algorithm (CCA) with three phases: hybrid initialization, multi-population cooperation exploration with feedback, and knowledge-guided greedy search. Firstly, a knowledge-based rule is designed to produce high-quality initial solutions. Secondly, multi-population cooperation is proposed to achieve subproblem co-optimization. Specifically, two populations are constructed for adjusting worker-seru assignment and batch-seru assignment and an elite population is applied for information sharing by individual migration. Moreover, to enhance algorithm search capability, a feedback strategy is designed for operator selection and population size adjustment. Thirdly, to exploit the nondominated solutions effectively, several properties are derived as the problem-specific knowledge to design a greedy search for the batch-seru assignment and worker-task assignment. Numerical tests and statistical comparisons are carried out, which demonstrate the effectiveness of the specific designs of the CCA and its superiority to the existing algorithms in solving the EESPSS.

Incremental particle swarm optimization for large-scale dynamic optimization with changing variable interactions

Cooperative coevolutionary algorithms have been developed for large-scale dynamic optimization problems via divide-and-conquer mechanisms. Interacting decision variables are divided into the same subproblem for optimization. Their performance greatly depends on problem decomposition and response abilities to environmental changes. However, existing algorithms usually adopt offline decomposition and hence are insufficient to adapt to changes in the underlying interaction structure of decision variables. Quick online decomposition then becomes a crucial issue, along with solution reconstruction for new subproblems. This paper proposes incremental particle swarm optimization to address the two issues. In the proposed method, the incremental differential grouping obtains accurate groupings by iteratively performing edge contractions on the interaction graph of historical groups. A recombination-based sampling strategy is developed to generate high-quality solutions from historical solutions for new subproblems. In order to coordinate with the multimodal property of the problem, swarms are restarted after convergence to search for multiple high-quality solutions. Experimental results on problem instances up to 1000-D show the superiority of the proposed method to state-of-the-art algorithms in terms of solution optimality. The incremental differential grouping can obtain accurate groupings using less function evaluations.

Graph-Based Deep Decomposition for Overlapping Large-Scale Optimization Problems

Decomposition methods play a critical role in cooperative co-evolutionary algorithms (CCEAs) for solving large-scale optimization problems. Although some well-performing decomposition methods have been designed based on the interactions among variables (IaV), their grouping accuracy is still limited due to the poor performance on the overlapping problems and the computational roundoff errors of IaV in the implementation. To deal with these limitations, a graph-based deep decomposition (GDD) method is proposed to obtain more accurate grouping results, especially for the overlapping problems. On the one hand, the GDD mines the IaV information and obtains the minimum vertex separator of the interaction graph of variables, so as to group variables deeply and recursively. On the other hand, the GDD has the ability of fault tolerance to deal with the computational roundoff errors of IaV and can improve the grouping accuracy. For better experimental studies of overlapping problems, a novel overlapping function generator is designed with the random and complicate overlap type, and two new metrics are proposed to evaluate the grouping accuracy. Comprehensive experiments show that GDD can greatly improve the grouping accuracy and help CCEAs perform better than other existing algorithms, especially on the overlapping problems. In addition, the GDD is highly fault tolerant and can divide problems accurately even on the inaccurate IaV.

Scheduling a multi-agent flow shop with two scenarios and release dates

Cloud computing is widely applied in modern industrial areas due to its technological advancement, cost reduction, and applicability. Packets (tasks) belonging to different applications (agents) compete to share the common cloud resource through a series of edge nodes (processors) in pursuit of fast transmission. This paper abstracts the cloud computing system as a multi-agent flow-shop scheduling (MAFS) problem. The objective is to minimise the total completion time of several agents with the restriction that the maximum lateness cannot exceed a given bound. Given the complexity of the considered problem, a branch and bound algorithm combined with several pruning rules and lower bounds is proposed to obtain optimal solutions. Furthermore, the considered problem is generalised to a bi-scenario version, and a bi-population cooperative co-evolutionary (BCCE) algorithm is proposed to solve it. A reinforcement learning-based method is presented to generate the initial population. Several problem-specific intensification strategies are constructed to explore promising solutions. Comprehensive experiments verified the effectiveness of the proposed algorithms. The industrial data from the China Earthquake Network Centre further confirmed the superiority of the BCCE algorithm. Overall, the MAFS model and the proposed algorithms effectively enhance the user experience and reasonably guarantee revenue.

A Fast Multipoint Expected Improvement for Parallel Expensive Optimization

The multipoint expected improvement (EI) criterion is a well-defined parallel infill criterion for expensive optimization. However, the exact calculation of the classical multipoint EI involves evaluating a significant amount of multivariate normal cumulative distribution functions, which makes the inner optimization of this infill criterion very time consuming when the number of infill samples is large. To tackle this problem, we propose a novel fast multipoint EI criterion in this work. The proposed infill criterion is calculated using only univariate normal cumulative distributions; thus, it is easier to implement and cheaper to compute than the classical multipoint EI criterion. It is shown that the computational time of the proposed fast multipoint EI is several orders lower than the classical multipoint EI on the benchmark problems. In addition, we propose to use cooperative coevolutionary algorithms (CCEAs) to solve the inner optimization problem of the proposed fast multipoint EI by decomposing the optimization problem into multiple subproblems with each subproblem corresponding to one infill sample and solving these subproblems cooperatively. Numerical experiments show that using CCEAs can improve the performance of the proposed algorithm significantly compared with using standard evolutionary algorithms. This work provides a fast and efficient approach for parallel expensive optimization.

Cooperative Particle Swarm Optimization With a Bilevel Resource Allocation Mechanism for Large-Scale Dynamic Optimization.

Although cooperative coevolutionary algorithms are developed for large-scale dynamic optimization via subspace decomposition, they still face difficulties in reacting to environmental changes, in the presence of multiple peaks in the fitness functions and unevenness of subproblems. The resource allocation mechanisms among subproblems in the existing algorithms rely mainly on the fitness improvements already made but not potential ones. On the one hand, there is a lack of sufficient computing resources to achieve potential fitness improvements for some hard subproblems. On the other hand, the existing algorithms waste computing resources aiming to find most of the local optima of problems. In this article, we propose a cooperative particle swarm optimization algorithm to address these issues by introducing a bilevel balanceable resource allocation mechanism. A search strategy in the lower level is introduced to select some promising solutions from an archive based on solution diversity and quality to identify new peaks in every subproblem. A resource allocation strategy in the upper level is introduced to balance the coevolution of multiple subproblems by referring to their historical improvements and more computing resources are allocated for solving the subproblems that perform poorly but are expected to make great fitness improvements. Experimental results demonstrate that the proposed algorithm is competitive with the state-of-the-art algorithms in terms of objective function values and response efficiency with respect to environmental changes.

Network planning of metro-based underground logistics system against mixed uncertainties: A multi-objective cooperative co-evolutionary optimization approach

Featured with zero-carbon, jam-free, and high-capacity, the utilization of metro systems for collaborative passenger-and-freight transport (i.e., the metro-based underground logistics system, M-ULS) has been recognized as a favorable alternative to realize automated goods movement in future megacities. This paper proposes an equilibrium chance-constrained programming (ECP) approach for the M-ULS network planning problem (MULNP) considering uncertain demand and costs. Based on the ongoing satellite city development project, the layout formation, facility components, and transportation workflows of a two-tier M-ULS network are designed. The joint decisions (i.e., location, allocation, capacity, inventory, spoke pipeline layout, and flow routing) are formulated as an ECP model with conjoint objectives of minimal fixed cost, operating cost, and penalty cost due to low operating load, wherein the chance-based constraints are further reformulated into crisp equivalent form. To yield high-quality solutions for MULNP problem, an improved multi-objective cooperative co-evolutionary algorithm (MoCC) incorporating non-dominated sorting and chromosomal recombination strategy is proposed and then validated via two groups of instances. Results from the Beijing case study suggest that the proposed method has computational advantages over MoPSO and NSGA-II in acquiring Pareto fronts of large-scale MULNP. The best configurations and layout schemes of the M-ULS networks in both uncertain and deterministic scenarios are analyzed. Based on the findings, several insights for real-world M-ULS network decision-making are provided.

DBCC2: an improved difficulty-based cooperative co-evolution for many-modal optimization

Evolutionary multimodal optimization algorithms aim to provide multiple solutions simultaneously. Many studies have been conducted to design effective evolutionary algorithms for solving multimodal optimization problems. However, optimization problems with many global and acceptable local optima have not received much attention. This type of problem is undoubtedly challenging. In this study, we focus on problems with many optima, the so-called many-modal optimization problems, and this study is an extension of our previous conference work. First, a test suite including additively nonseparable many-modal optimization problems and partially additively separable many-modal optimization problems is designed. Second, an improved difficulty-based cooperative co-evolution algorithm (DBCC2) is proposed, which dynamically estimates the difficulties of subproblems and allocates the computational resources during the search. Experimental results show that DBCC2 has competitive performance.