Scheduling a Constrained Hybrid Flowshop Using a Variable Representation Cooperative Co-Evolutionary Algorithm

Cooperative coevolutionary algorithm with resource allocation strategies to minimize unnecessary computations

This paper presents the Constructive Cooperative Coevolutionary (mathrm {C}^3) algorithm, applied to continuous large-scale global optimisation problems. The novelty of mathrm {C}^3 is that it utilises a multi-start architecture and incorporates the Cooperative Coevolutionary algorithm. The considered optimisation problem is decomposed into subproblems. An embedded optimisation algorithm optimises the subproblems separately while exchanging information to co-adapt the solutions for the subproblems. Further, mathrm {C}^3 includes a novel constructive heuristic that generates different feasible solutions for the entire problem and thereby expedites the search. In this work, two different versions of mathrm {C}^3 are evaluated on high-dimensional benchmark problems, including the CEC’2013 test suite for large-scale global optimisation. mathrm {C}^3 is compared with several state-of-the-art algorithms, which shows that mathrm {C}^3 is among the most competitive algorithms. mathrm {C}^3 outperforms the other algorithms for most partially separable functions and overlapping functions. This shows that mathrm {C}^3 is an effective algorithm for large-scale global optimisation. This paper demonstrates the enhanced performance by using constructive heuristics for generating initial feasible solutions for Cooperative Coevolutionary algorithms in a multi-start framework.

Conflict resolution becomes a worldwide urgent problem to guarantee the airspace safety. The existing approaches are mostly short-term or middle-term which obtain solutions by local adjustment. 4D-Trajectory conflict resolution (4DTCR), as a long-term method, can give better solutions to all flights in a global view. 4DTCR involved with China air route network and thousands of flight plans is a large and complex problem which is hard to be solved by classical approaches. In this paper, the cooperative coevolution (CC) algorithm with random grouping strategy is presented for its advantage in dealing with large and complex problem. Moreover, a fast Genetic Algorithm (GA) is designed for each subcomponent optimization which is effective and efficient to obtain optimal solution. Experimental studies are conducted to compare it to the genetic algorithm in previous approach and CC algorithm with classic grouping strategy. The results show that our algorithm has a better performance.Keywords4D-TrjactoryConflict resolutionCooperative coevolutionEvolutionary computation

The scalability performance of the traditional evolutionary algorithms (EAs) deteriorates rapidly as the dimensionality of the optimization problems increases. Therefore, cooperative coevolutionary (CC) framework is proposed to overcome the defect. Different from existing CC algorithms, a novel self-adaptive based cooperative coevolutionary (SaCC) algorithm is presented in this paper. The SaCC employs three algorithms which with self-adaptive mechanism as sub-algorithms. The focus of this paper is on investigating two different cooperative coevolutionary manners. In the first manner, SaCC executes its sub-algorithms in parallel during evolve process and the corresponding algorithm is termed as SaCC-M1. In the second manner, SaCC executes its sub-algorithms in serial and the corresponding algorithm is termed as SaCC-M2. 26 test functions with 1000 dimensionalities are employed to verify the validity of SaCC-M1 and SaCC-M2. Experiment results demonstrate that SaCC-M2 outperforms its sub-algorithms and SaCC-M1. Besides, the results indicate that serial manner is another simple yet efficient manner for CC algorithms to solve large-scale global optimization problems.

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.

Cooperative Coevolution (CC) framework has become a powerful approach to solve large-scale global optimization problems effectively. Although a number of significant modifications of CC algorithms have been introduced in recent years, the theoretical studies of population initialization strategies in the CC framework are quite limited so far. The population initialization strategies can help a population-based algorithm to start with better candidate solutions for achieving better results. In this paper, we propose a CC algorithm with population initialization strategies based on the center region to improve its performance. Three population initialization strategies, namely, center-based normal distribution sampling, central golden region, and hybrid random-center normal distribution sampling are utilized in the CC framework. These population initialization strategies attempt to generate points around center-point with different schemes. The performance of the proposed algorithm is evaluated on CEC-2013 LSGO benchmark functions. Simulation results confirm that the proposed algorithm obtains a promising performance on the majority of the nonseparable high dimension benchmark functions.

Coevolutionary algorithms offer great promise as adaptive problem solvers but suffer from several known pathologies. Historically, spatially embedded coevolutionary algorithms seem to have succeeded where other coevolutionary approaches fail; however, explanations for this have been largely unexplored. We examine this idea more closely by looking at spatial models in the context of a particular coevolutionary pathology: loss of gradient. We believe that loss of gradient in cooperative coevolution is caused by asymmetries in the problem or initial conditions between populations, driving one population to convergence before another. Spatial models seem to lock populations together in terms of evolutionary change, helping establish a type of dynamic balance to thwart loss of gradient. We construct a tunably asymmetric function optimization problem domain and conduct an empirical study to justify this assertion. We find that spatial restrictions for collaboration and selection can help keep population changes balanced when presented with severe asymmetries in the problem.

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.

Morphologically heterogeneous multirobot teams have shown significant potential in many applications. While cooperative coevolutionary algorithms can be used for synthesising controllers for heterogeneous multirobot systems, they have been almost exclusively applied to morphologically homogeneous systems. In this paper, we investigate if and how cooperative coevolutionary algorithms can be used to evolve behavioural control for a morphologically heterogeneous multirobot system. Our experiments rely on a simulated task, where a ground robot with a simple sensor-actuator configuration must cooperate tightly with a more complex aerial robot to find and collect items in the environment. We first show how differences in the number and complexity of skills each robot has to learn can impair the effectiveness of cooperative coevolution. We then show how coevolution’s effectiveness can be improved using incremental evolution or novelty-driven coevolution. Despite its limitations, we show that coevolution is a viable approach for synthesising control for morphologically heterogeneous systems.

Morphologically heterogeneous multirobot teams have
\nshown significant potential in many applications. While cooperative coevolutionary algorithms can be used for synthesising controllers for heterogeneous multirobot systems, they
\nhave been almost exclusively applied to morphologically homogeneous systems. In this paper, we investigate if and
\nhow cooperative coevolutionary algorithms can be used to
\nevolve behavioural control for a morphologically heterogeneous multirobot system. Our experiments rely on a simulated task, where a ground robot with a simple sensor-actuator
\nconfiguration must cooperate tightly with a more complex
\naerial robot to find and collect items in the environment. We
\nfirst show how differences in the number and complexity of
\nskills each robot has to learn can impair the effectiveness of
\ncooperative coevolution. We then show how coevolution’s
\neffectiveness can be improved using incremental evolution or
\nnovelty-driven coevolution. Despite its limitations, we show
\nthat coevolution is a viable approach for synthesising control
\nfor morphologically heterogeneous systems.

The rapid progress of modern technologies generates a massive amount of high-throughput data, called Big Data, which provides opportunities to find new insights using machine learning (ML) algorithms. Big Data consist of many features (also called attributes); however, not all these are necessary or relevant, and they may degrade the performance of ML algorithms. Feature selection (FS) is an essential preprocessing step to reduce the dimensionality of a dataset. Evolutionary algorithms (EAs) are widely used search algorithms for FS. Using classification accuracy as the objective function for FS, EAs, such as the cooperative co-evolutionary algorithm (CCEA), achieve higher accuracy, even with a higher number of features. Feature selection has two purposes: reducing the number of features to decrease computations and improving classification accuracy, which are contradictory but can be achieved using a single objective function. For this very purpose, this paper proposes a penalty-based wrapper objective function. This function can be used to evaluate the FS process using CCEA, hence called Cooperative Co-Evolutionary Algorithm-Based Feature Selection (CCEAFS). An experiment was performed using six widely used classifiers on six different datasets from the UCI ML repository with FS and without FS. The experimental results indicate that the proposed objective function is efficient at reducing the number of features in the final feature subset without significantly reducing classification accuracy. Based on different performance measures, in most cases, naïve Bayes outperforms other classifiers when using CCEAFS.

In this paper, we discuss a curious relationship between Cooperative Coevolutionary Algorithms (CCEAs) and univariate Estimation of Distribution Algorithms (EDAs). Specifically, the distribution model for univariate EDAs is equivalent to the infinite population EGT model common in the analysis of CCEAs. This relationship may permit cross-pollination between these two disparate fields. As an example, we derive a new EDA based on a known CCEA from the literature, and provide some preliminary experimental analysis of the algorithm.

This paper proposes total optimization of energy networks in a smart city (SC) by cooperative coevolution using global-best brain storm optimization (CCGBSO). The smart city problem is one of mixed integer nonlinear programming (MINLP) problems. Therefore, various evolutionary computation methods such as differential evolutionary particle swarm optimization (DEEPSO), Brain Storm Optimization (BSO), Modified BSO (MBSO), Global-best BSO (GBSO) have been applied to the problem. However, quality of solution is still required to be improved. Cooperative Cooperation has a possibility to improve solution quality of large scale optimization problems such as the SC problem and this paper proposes a new cooperative coevolution algorithm, CCGBSO. The results of the proposed CCGBSO based method are verified to be the most improved comparing with those of the conventional DEEPSO, BSO, MBSO, and GBSO based methods.

We present an analysis of the behaviour of Cooperative Co-evolution algorithms (CCEAs) on a simple test problem, that is the optimal placement of a set of lamps in a square room, for various problems sizes. Cooperative Co-evolution makes it possible to exploit more efficiently the artificial Darwinism scheme, as soon as it is possible to turn the optimisation problem into a co-evolution of interdependent sub-parts of the searched solution. We show here how two cooperative strategies, Group Evolution (GE) and Parisian Evolution (PE) can be built for the lamps problem. An experimental analysis then compares a classical evolution to GE and PE, and analyses their behaviour with respect to scale.

Cooperative co-evolutionary algorithms, especially those able to uncover interaction structure between variables, have a great potential in optimizing large-scale problems. Nevertheless, they are expensive in terms of number of function evaluations and this issue can be quite problematic when dealing with computationally expensive optimization problems. An effective approach to deal with such problems lies in the exploitation of surrogate models. The latter ones work as cheap-to-evaluate alternatives to the expensive function reducing the computational cost, while still providing improved designs. This process, called surrogate-assisted optimization, is very effective on small-dimensional problems but is not suitable to solve large-scale problems due to the curse of dimensionality. In this paper, a new algorithm, taking benefit from cooperative coevolution and surrogate models, is introduced to efficiently solve high-dimensional, expensive and black-box problems. The proposed algorithm uses recursive differential grouping to perform an accurate problem decomposition. Experimental results are provided on a set of 1000-dimensional problems and show promising results.