Cooperative Coevolutionary Algorithm Research Articles

Mathematical model and enhanced cooperative co-evolutionary algorithm for scheduling energy-efficient manufacturing cell

Owing to the rapid exhaustion of energy in the manufacturing sector, energy-efficient scheduling has become a research hotspot. This work addresses an energy-efficient manufacturing cell scheduling problem, in which three major energy-saving strategies, machine off/on criterion, speed-scaling policy and transportation optimization strategy, are simultaneously utilized to save energy comprehensively. A mixed-integer linear programming model is hereafter developed to reduce the transportation energy, processing energy and standby energy via cell formation, cell scheduling and machine off/on decision respectively. To solve this problem efficiently, an enhanced cooperative co-evolutionary algorithm (ECCA) with two improvements is developed. Specifically, four energy-oriented heuristic rules are designed to create initial sub-swarms with lower energy consumption; a Q-learning-based sub-swarm size adjustment mechanism is developed to maximize the exploration efficiency across all sub-problem domains and escape from local optima. Experimental results indicate that the two improvements in ECCA are effective, and the proposed ECCA significantly outperforms six state-of-the-art algorithms with a p-value much less than 0.0001. More importantly, by simultaneously employing the three major energy-saving strategies in manufacturing cells, the resulted energy-saving ratio is above 5%.

Cooperative coevolutionary instance selection for multilabel problems

Multilabel classification as a data mining task has recently attracted greater research interest. Many current data mining applications address problems having instances that belong to more than one class, which requires the development of new efficient methods. Advantageously using the correlation among different labels can provide better performance than methods that deal with each label separately. Instance-based classification models, such as k-nearest neighbors for multilabel datasets, ML-kNN, are among the best performing methods on any classification task and have also shown very goog performance in multilabel problems. Despite their simplicity, they achieve comparable performance to considerably more complex methods. One of the challenges associated with instance-based classification models is their requirement for storing all the training instances in memory. To ameliorate this problem, instance selection methods have been proposed. However, their application to multilabel problems is problematic because the adaptation of most of their concepts to multilabel problems is difficult. In this paper, we propose a cooperative coevolutionary algorithm for instance selection for multilabel problems. Two different populations evolve together cooperatively. One of the populations is devoted to obtaining solutions for each label, whereas the other population combines these results into solutions for the instance selection for multilabel dataset tasks. On a large set of 70 real-world problems, our approach improves the results of both the ML-kNN method with the whole dataset and an instance selection method using a standard evolutionary algorithm.

A Nash bargaining solution for a multi period competitive portfolio optimization problem: Co-evolutionary approach

This study focuses on proposing a Nash bargaining model to solve a novel multi-period competitive portfolio optimization problem for large investors in the stock market who want to maximize their terminal wealth while taking into account competitors' profits. In this study, a Competitive Portfolio Model (CPM) is developed in accordance with the Cournot competition principle for a static, non-cooperative, and non-zero-sum game with complete information. Transaction costs, risk-free assets and cash are also included to match real-world conditions. Also, three criteria including the average value at risk, the mean absolute semi-deviation, and entropy are considered to control the investment risk in the model. Moreover, due to common constraints between players (free floating shares of risky assets) in stock markets, this study falls into the category of Generalized Nash Equilibrium Problems (GNEP). Therefore, to overcome the problem, a Cooperative Co-evolutionary Algorithm (CCA) based on Particle Swarm Optimization (PSO) is customized and used. A few experimental tests and a numerical example with descriptive analytics (using real data from two large mutual funds who invest in the Iranian Stock Exchange market) are used to evaluate the feasibility of the proposed model and the efficiency of the design algorithm. After solving the model, for each time period, investors' trading strategies (trading signals and stock volume in their portfolio) are determined. The results show that the volume of transactions due to the market power of an investor has a significant effect on the terminal wealth of competitors. Also, the results of sensitivity analysis show that profit-making is inversely related to the degree of risk aversion of investors.

A cooperative coevolution algorithm for complex hybrid seru-system scheduling optimization

Under the current volatile business environment, the requirement of flexible production is becoming increasingly urgent. As an innovative production mode, seru-system with reconfigurability can overcome the lack of flexibility in traditional flow lines. Compared with pure seru-system, the hybrid seru-system composed of both serus and production lines is more practical for adapting to many production processes. This paper addresses a specific hybrid seru-system scheduling optimization problem (HSSOP), which includes three strongly coupled sub-problems, i.e., hybrid seru formation, seru scheduling and flow line scheduling. To minimize the makespan of the whole hybrid seru-system, we propose an efficient cooperative coevolution algorithm (CCA). To tackle three sub-problems, specific sub-algorithms are designed based on the characteristic of each sub-problem, i.e., a sub-space exploitation algorithm for hybrid seru formation, an estimation of distribution algorithm for seru scheduling, and a first-arrive-first-process heuristic for flow line scheduling. Since three sub-problems are coupled, a cooperation coevolution mechanism is proposed for the integrated algorithm by information sharing. Moreover, a batch reassign rule is designed to overcome the mismatch of partial solutions during cooperative coevolution. To enhance the exploitation ability, problem-specific local search methods are designed and embedded in the CCA. In addition to the investigation about the effect of parameter setting, extensive computational tests and comparisons are carried out which demonstrate the effectiveness and efficiency of the CCA in solving the HSSOP.

A model and algorithm for identifying driver pathways based on weighted non-binary mutation matrix

It is generally acknowledged that driver pathway plays a decisive role in the occurrence and progress of tumors, and the identification of driver pathways has become imperative for precision medicine or personalized medicine. Due to the inevitable sequencing error, the noise contained in single omics cancer data usually plays a negative effect on identification. It is a feasible approach to take advantage of multi-omics cancer data rather than a single one now that large amounts of multi-omics cancer data have become available. The identification of driver pathways by integrating multi-omics cancer data has attracted attention of researchers in bioinformatics recently. In this paper, a weighted non-binary mutation matrix is constructed by integrating copy number variations, somatic mutations and gene expressions. Based on the weighted non-binary mutation matrix, a new identification model is proposed through defining new measurements of coverage and exclusivity. Then, a cooperative coevolutionary algorithm CGA-MWS is put forward for solving the presented model. Both real cancer data and simulated one were used to conduct comparisons among methods Dendrix, GA, iMCMC, MOGA, PGA-MWS and CGA-MWS. Compared with the pathways identified by the other five methods, more genes, belonging to the pathway identified by the CGA-MWS method, are enriched in a known signaling pathway in most cases. Simultaneously, the high efficiency of method CGA-MWS makes it practical in realistic applications. All of which have been verified through a number of experiments.

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 Dual-Population-Based Evolutionary Algorithm for Constrained Multiobjective Optimization

The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> . In c-DPEA, a novel self-adaptive penalty function, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">saPF</i> , is designed to preserve competitive infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> . On the other hand, infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bCAD</i> , is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.

CDE-GAN: Cooperative Dual Evolution-Based Generative Adversarial Network

Generative adversarial networks (GANs) have been a popular deep generative model for real-world applications. Despite many recent efforts on GANs that have been contributed, mode collapse and instability of GANs are still open problems caused by their adversarial optimization difficulties. In this article, motivated by the cooperative co-evolutionary algorithm, we propose a cooperative dual evolution-based GAN (CDE-GAN) to circumvent these drawbacks. In essence, CDE-GAN incorporates dual evolution with respect to the generator(s) and discriminators into a unified evolutionary adversarial framework to conduct effective adversarial multiobjective optimization. Thus, it exploits the complementary properties and injects dual mutation diversity into the training, to steadily diversify the estimated density in capturing multimodes and improve generative performance. Specifically, CDE-GAN decomposes the complex adversarial optimization problem into two subproblems (generation and discrimination), and each subproblem is solved with a separated subpopulation (<i>E-Generators</i> and <i>E-Discriminators</i>), evolved by its own evolutionary algorithm. Additionally, we further propose a <i>Soft Mechanism</i> to balance the tradeoff between E-Generators and E-Discriminators to conduct steady training for CDE-GAN. Extensive experiments on one synthetic dataset and three real-world benchmark image datasets demonstrate that the proposed CDE-GAN achieves a competitive and superior performance in generating good quality and diverse samples over baselines. The code and more generated results are available at our project homepage <i><uri>https://shiming-chen.github.io/CDE-GAN-website/CDE-GAN.html</uri></i>.

MLFS-CCDE: multi-objective large-scale feature selection by cooperative coevolutionary differential evolution

Feature selection is a pre-processing procedure of choosing the optimal feature subsets for constructing model, yet it is difficult to satisfy the requirements of reducing number of features and maintaining classification accuracy. Towards this problem, we propose novel multi-objectives large-scale cooperative coevolutionary algorithm for three-objectives feature selection, termed MLFS-CCDE. Firstly, a cooperative searching framework is designed for efficiently and effectively seeking for the optimal feature subset. Secondly, in the framework, three objectives, feature’s number, classification accuracy and total information gain are established for guiding the evolution of features’ combination. Thirdly, in framework’s decomposition process, cluster-based decomposition strategy is elaborated for reducing the computation; in framework’s coevolution process, dual indicator-based representatives are elaborated for balancing the representative solution’ convergence and diversity. Finally, to verify framework’s practicability, a heart disease diagnosis system based on MLFS-CCDE framework is constructed in cardiology. Numerical experiments demonstrate that the proposed MLFS-CCDE outperforms its competitors in terms of both classification accuracy and metrics of features’ number.

A decision variable classification-based cooperative coevolutionary algorithm for dynamic multiobjective optimization

This paper proposes a new decision variable classification-based cooperative coevolutionary algorithm, which uses the information of decision variable classification to guide the search process, for handling dynamic multiobjective problems. In particular, the decision variables are divided into two groups: convergence variables (CS) and diversity variables (DS), and different strategies are introduced to optimize these groups. Two kinds of subpopulations are used in the proposed algorithm, i.e., the subpopulations that represent DS and the subpopulations that represent CS. In the evolution process, the coevolution of DS and CS is carried out through genetic operators, and subpopulations of CS are gradually merged into DS, which is optimized in the global search space, based on an indicator to avoid becoming trapped in local optimum. Once a change is detected, a prediction method and a diversity introduction approach are adopted for these two kinds of variables to get a promising population with good diversity and convergence in the new environment. The proposed algorithm is tested on 16 benchmark dynamic multiobjective optimization problems, in comparison with state-of-the-art algorithms. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization.

An improved quantum-inspired cooperative co-evolution algorithm with muli-strategy and its application

In order to overcome the slow convergence speed, poor global search ability and difficult designing rotation angle of quantum-inspired evolutionary algorithm (QEA), an improved quantum-inspired cooperative co-evolution algorithm based on combining the strategies of cooperative co-evolution, random rotation direction and Hamming adaptive rotation angle, namely MSQCCEA is proposed, which is employed to propose a new airport gate allocation optimization method in this paper. In the proposed MSQCCEA, the cooperative co-evolution strategy is used to improve the global search capability. The random rotation direction strategy is developed to change the quantum evolution direction from one to two in order to avoid local optimal solution and realize the full search of the solution space. A new Hamming adaptive rotation angle strategy is designed to enable individuals to adaptively adjust the rotation angle according to the difference degree between the individual and the target individual, so as to improve the global search ability and convergence speed. A new airport gate allocation optimization method using MSQCCEA is realized to effectively allocate airport gates to the flights. Finally, the knapsack problem and the actual airport gate allocation problem are used to verify the effectiveness of the proposed MSQCCEA and gate allocation optimization method, respectively. The comparison experiment results demonstrate that the proposed MSQCCEA has faster convergence speed and higher convergence accuracy, and the proposed gate allocation optimization method takes on great potential to make decisions for actual airport management.

Cooperative Co-Evolution and MapReduce

Real-word large-scale optimisation problems often result in local optima due to their large search space and complex objective function. Hence, traditional evolutionary algorithms (EAs) are not suitable for these problems. Distributed EA, such as a cooperative co-evolutionary algorithm (CCEA), can solve these problems efficiently. It can decompose a large-scale problem into smaller sub-problems and evolve them independently. Further, the CCEA population diversity avoids local optima. Besides, MapReduce, an open-source platform, provides a ready-to-use distributed, scalable, and fault-tolerant infrastructure to parallelise the developed algorithm using the map and reduce features. The CCEA can be distributed and executed in parallel using the MapReduce model to solve large-scale optimisations in less computing time. The effectiveness of CCEA, together with the MapReduce, has been proven in the literature for large-scale optimisations. This article presents the cooperative co-evolution, MapReduce model, and associated techniques suitable for large-scale optimisation problems.

Contribution-Based Cooperative Co-Evolution for Nonseparable Large-Scale Problems With Overlapping Subcomponents.

Cooperative co-evolutionary algorithms have addressed many large-scale problems successfully, but the nonseparable large-scale problems with overlapping subcomponents are still a serious difficulty that has not been conquered yet. First, the existence of shared variables makes the problem hard to be decomposed. Second, existing cooperative co-evolutionary frameworks usually cannot maintain the two crucial factors: high cooperation frequency and effective computing resource allocation, simultaneously when optimizing the overlapping subcomponents. Aiming at these two issues, this article proposes a new contribution-based cooperative co-evolutionary algorithm to decompose and optimize nonseparable large-scale problems with overlapping subcomponents effectively and efficiently: 1) a contribution-based decomposition method is proposed to assign the shared variables. Among all the subcomponents containing a shared variable, the one that contributes the most to the entire problem will include the shared variable and 2) to achieve the two crucial factors at the same time, a new contribution-based optimization framework is designed to award the important subcomponents based on the round-robin structure. Experimental studies show that the proposed algorithm performs significantly better than the state-of-the-art algorithms due to the effective grouping structure generated by the proposed decomposition method and the fast optimizing speed provided by the new optimization framework.

Bi-space Interactive Cooperative Coevolutionary algorithm for large scale black-box optimization

Large scale black-box optimization problems arise in many fields of science and engineering, and many of existing algorithms for these problems still suffer from the “curse of dimensionality”. This paper proposes a generalized framework of Bi-space Interactive Cooperative Coevolutionary Algorithm (BICCA) with evolutions in two spaces. In the pattern space, the interacting patterns of variables are continuously excavated for the evolution of the groups for cooperative coevolution. In the search space, cooperative coevolution and global search are carried out adaptively to get better fitness. By adopting evolutions and interactions within two spaces, patterns evolve to provide better groupings while individuals evolve to reach better fitness. The problem decomposition is conducted along the optimization process, and no extra fitness evaluations are needed for problem decomposition. Experiments on widely-used benchmarks show that BICCA obtains competitive performance on high-dimensional optimization problems with different levels of dimensionality up to 10000.

Joint Customer/Provider Evolutionary Multi-objective Utility Maximization in Cloud Data Center Networks

Cloud computing has found an important role in cost-effective and elastic network resource allocation community. Most researchers and practitioners have focused on cloud provider side for efficient resource allocation to end-users and to warrant their service-level agreements (SLAs). Due to heterogeneous user demands which request services from cloud data center networks, simultaneous satisfaction of all users to their pre-defined SLA level while making the cloud provider and all of the data centers to be cost-effective in terms of the financial income and energy-efficiency is a challenging issue. To address this problem, in the current work, the efficient joint provider/customer efficient resource allocation has been first formulated as a multi-objective optimization problem with convex constraint set in terms of virtual machine (VM) parameters (e.g., storage, CPU core, memory, etc.). Then, an evolutionary solution based on cooperative co-evolution algorithm has been proposed that can conduct a divide-and-conquer methodology for solving the complex optimization problem. Numerical results show the prominent feature of the method in terms of VM usage effectiveness and overall joint network cost/user SLA satisfaction.

Automatic sound synthesis using the fly algorithm

Our study is demonstrated a new type of evolutionary sound synthesis method. This work based on the fly algorithm, a cooperative co-evolution algorithm; it is derived from the Parisian evolution approach. The algorithm has relatively amended the position of individuals (the Flies) represented by 3-D points. The fly algorithm has successfully investigated in different applications, starting with a real-time stereo vision for robotics. Also, the algorithm shows promising results in tomography to reconstruct 3-D images. The final application of the fly algorithm was generating artistic images, such as digital mosaics. In all these applications, the flies’representation started for simple, 3-D points, to complex one, the structure of 9-elements. Our method follows evolutionary digital art with the fly algorithm in representing the pattern of the flies. They represented in a way of having their structure. This structure includes position, colour, rotation angle, and size. Our algorithm has the benefit of graphics processing units (GPUs) to generate the sound waveform using the modern OpenGL shading language.

Cooperative coevolutionary algorithms for optimalPSStuning based onMonte‐Carloprobabilistic small‐signal stability assessment

Cooperative coevolutionary algorithms for optimal<scp>PSS</scp>tuning based on<scp>Monte‐Carlo</scp>probabilistic small‐signal stability assessment

A Formation Reconfiguration Algorithm for Multi‐UAVs Based on Distributed Cooperative Coevolutionary with an Adaptive Grouping Strategy

The Formation reconfiguration problem plays a crucial role in the implementation of complex tasks for multiple unmanned aerial vehicles, which attracted increasing attention in the past decade. Taking into consideration the control parameters and time discretization of the multi-UAVs in the 3 Dimensional (3-D) space, the formation reconfiguration problem can be formulated as a large-scale combinatorial optimization problem with complex constraints and tight couplings between variables. The problem results in the reduction in efficiency and effectiveness using classic bio-inspired algorithms. In this paper, a formation reconfiguration method based on cooperative coevolutionary algorithm is proposed along with a new decomposition strategy to improve the optimization capability and prevent premature convergence. In the proposed approach, variables of multi-UAV are divided into several sub-groups based on an adaptive grouping strategy. The proposed strategy groups the variables in order to better deal with the tight coupling among them, taking into account the variables' variance and multi-UAVs characteristics of the formation reconfiguration problem. Therefore, each subgroup can adopt the Self-adaptive differential evolution strategy with neighborhood search (SaNSDE) with the aim to optimize the UAV's control inputs using multithreaded programming. SaNSDE contributes to calculating the results in a fully distributed and paralleled manner. Optimal solution is then obtained through cooperation and coordination with all subcomponents. Simulation results based on extreme scenarios adopted by previous researches demonstrate that the proposed algorithm outperformed the existing approaches including Particle swarm optimization (PSO), Differential evolution (DE), and the cooperative coevolution algorithms with different well-known grouping strategies.

A Cooperative Coevolutionary Approach to Discretization-Based Feature Selection for High-Dimensional Data.

Recent discretization-based feature selection methods show great advantages by introducing the entropy-based cut-points for features to integrate discretization and feature selection into one stage for high-dimensional data. However, current methods usually consider the individual features independently, ignoring the interaction between features with cut-points and those without cut-points, which results in information loss. In this paper, we propose a cooperative coevolutionary algorithm based on the genetic algorithm (GA) and particle swarm optimization (PSO), which searches for the feature subsets with and without entropy-based cut-points simultaneously. For the features with cut-points, a ranking mechanism is used to control the probability of mutation and crossover in GA. In addition, a binary-coded PSO is applied to update the indices of the selected features without cut-points. Experimental results on 10 real datasets verify the effectiveness of our algorithm in classification accuracy compared with several state-of-the-art competitors.

A hybrid cooperative co-evolution algorithm framework for optimising power take off and placements of wave energy converters

Wave energy technologies have the potential to play a significant role in the supply of renewable energy on a world scale. One of the most promising designs for wave energy converters (WECs) are fully submerged buoys. In this work, we explore the optimisation of WEC arrays consisting of three-tether buoys. Such arrays can be optimised for total energy output by adjusting both the relative positions of buoys and also the power-take-off (PTO) parameters for each buoy. The search space for these parameters is complex and multi-modal. Moreover, the evaluation of each parameter setting is computationally expensive and thus limits the number of full model evaluations that can be made. To handle this problem, we propose a new hybrid cooperative co-evolution algorithm (HCCA). HCCA consists of a symmetric local search plus Nelder-Mead and a cooperative co-evolution algorithm (CC) with a backtracking strategy for optimising the positions and PTO settings of WECs, respectively. For assessing the effectiveness of the proposed approach five popular Evolutionary Algorithms (EAs), four alternating optimisation methods and two recent hybrid ideas (LS-NM and SLS-NM-B) are compared in four real wave situations (Adelaide, Tasmania, Sydney and Perth) with two wave farm sizes (4 and 16). The experimental study shows that the hybrid cooperative framework performs best in terms of both runtime and quality of obtained solutions.