Coevolutionary Algorithm Research Articles

Multi-strategy competitive-cooperative co-evolutionary algorithm and its application

In order to effectively solve multi-objective optimization problems (MOPs) and fully balance uniformity and convergence, a multi-strategy competitive-cooperative co-evolutionary algorithm based on adaptive random competition and neighborhood crossover, namely MSCOEA is developed in this paper. In the MSCOEA, a new adaptive random competition strategy is designed to determine whether one sub-population loses diversity through the performance. A random competition process is executed to increase the sub-population diversity in order to compete for participation opportunities in the next iteration. And the extra population is employed to store the found non-dominated solutions. A new neighborhood crossover strategy is designed to enhance the local search ability. Finally, three different types of multi-objective benchmark functions are selected to verify the effectiveness of the MSCOEA. The experiment results show that the MSCOEA can effectively balance convergence and uniformity, and obtains better optimization performance and robustness by comparing with other algorithms. The convergence performance of the adaptive random competition and the neighborhood crossover strategies are also analyzed in detail.

Co-evolutionary algorithm based on problem analysis for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) vary over time, requiring an optimization algorithm to track the position of Pareto-optimal front (PF) in a dynamic environment. To achieve that, a novel co-evolutionary algorithm based on problem analysis (CAPA) is proposed in this paper. CAPA is designed to solve DMOPs from decision space and objective space simultaneously, which is achieved by the combination of adjustable prediction (AP) and precise mapping strategy (PM). In decision space, the proposed multi-model prediction can estimate the location of new population based on the historical median points. In objective space, a novel sampling method is developed to search for sample points with better convergence or diversity. Then, mapping these sample points back to decision space based on inverse model. Through the problem analysis mechanism, the proportion of the new solutions produced by each strategy changes adaptively. CAPA is incorporated into the dynamic multiobjective evolutionary algorithm (DMOEA) based on decomposition (MOEA/D) to construct a novel algorithm. The efficacy of CAPA is validated by comparison with five state-of-the-art algorithms on 28 benchmarks. Experimental results show that CAPA has the ability to generate high quality population uniformly along PF.

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 co-evolutionary algorithm with elite archive strategy for generating diverse high-quality satellite range schedules

AbstractSatellite range scheduling, a multi-constrained combinatorial optimization problem, is crucial to guaranteeing the normal operation and application of onboard satellites. Traditional methods are dedicated to finding one optimal schedule, having ignored the problem may process multiple high-quality schedules. To provide a set of alternative schedules while maintaining the solution quality, we propose a co-evolutionary algorithm with elite archive strategy (COEAS) in this article. In COEAS, two populations are evolved to solve the original and relaxed problem in terms of schedule quality and diversity, respectively. During the evolution, the populations maintain a weak cooperation and only share the information in offspring combination phase. Further, an elite archive strategy is derived to identify and preserve potential stagnated and optimal individuals. In this strategy, the promising individuals would further participate in parent mating and offspring replacement for the dual purpose of maintaining potential optima recovery and fine-tuning the population. The experimental results show that the proposed algorithm is better than comparison algorithms in terms of efficacy (obtaining higher quality schedule), diversity (locating more optimal schedules) and flexibility (providing better alternatives).

Optimization of digital multi-beamforming for space-based ADS-B using distributed cooperative coevolution with an adaptive grouping strategy

Space-based Automatic Dependent Surveillance-Broadcast (ADS-B) technology can eliminate the blind spots of terrestrial ADS-B systems because of its global coverage capability. However, the space-based ADS-B system faces new problems such as extremely low Signal-to-Noise Ratio (SNR) and serious co-channel interference, which result in long update intervals. To minimize the position message update interval at an update probability of 95% with full coverage constraint, this paper presents an optimization model of digital multi-beamforming for space-based ADS-B. Then, a coevolution method DECCG_A&A is proposed to enhance the optimization efficiency by using an improved adaptive grouping strategy. The strategy is based on the locations of uncovered areas and the aircraft density under the coverage of each beam. Simulation results show that the update interval can be effectively controlled to be below 8 seconds compared with other existing methods, and DECCG_A&A is superior in convergence to the Genetic Algorithm (GA) as well as the coevolution algorithms using other grouping strategies. Overall, the proposed optimization model and method can significantly reduce the update interval, thus improving the surveillance performance of space-based ADS-B for air traffic control.

A coevolutionary algorithm based on reference line guided archive for constrained multiobjective optimization

The objective space of the constrained multiobjective optimization problem (CMOP) is constantly torn by the applied constraints. This makes evolutionary algorithms, which are driven by objectives, face greater difficulties in feasibility, convergence, and diversity. Most evolutionary algorithms will be trapped in local optimums such as a fake Pareto-optimal front or a mutilated Pareto-optimal front. To address this issue, this paper proposes an archive-assisted evolutionary framework with a novel archive structure and cooperative mechanism. A reference line guided archive (RA) is established to record the evolution of the unconstrained solutions. The updated criteria of RA are based on the distance from the individual to the reference line and the unconstrained dominance relation. A specially designed adaptive mating selection operator will select mating parents from RA and the main population according to the convergence of the main population and RA, respectively. The participation of RA in offspring reproduction is conducive to skipping infeasible regions for extensive searches. The performance of the archive-assisted nondominated sorting genetic algorithm (AA-NSGA), which embeds the proposed archive strategy into the nondominated sorting genetic algorithm II, is compared with four state-of-the-art constrained multiobjective evolutionary algorithms (MOEAs). The experimental results on 38 benchmark CMOPs and a reactor network design problem show that the proposed AA-NSGA has a high performance among the existing MOEAs in terms of feasibility, convergence, and diversity.

A Coevolutionary Algorithm for Many-Objective Optimization Problems with Independent and Harmonious Objectives

Evolutionary algorithm is an effective strategy for solving many-objective optimization problems. At present, most evolutionary many-objective algorithms are designed for solving many-objective optimization problems where the objectives conflict with each other. In some cases, however, the objectives are not always in conflict. It consists of multiple independent objective subsets and the relationship between objectives is unknown in advance. The classical evolutionary many-objective algorithms may not be able to effectively solve such problems. Accordingly, we propose an objective set decomposition strategy based on the partial set covering model. It decomposes the objectives into a collection of objective subsets to preserve the nondominance relationship as much as possible. An optimization subproblem is defined on each objective subset. A coevolutionary algorithm is presented to optimize all subproblems simultaneously, in which a nondominance ranking is presented to interact information among these sub-populations. The proposed algorithm is compared with five popular many-objective evolutionary algorithms and four objective set decomposition based evolutionary algorithms on a series of test problems. Numerical experiments demonstrate that the proposed algorithm can achieve promising results for the many-objective optimization problems with independent and harmonious objectives.

Development of an Algorithm for Multicriteria Optimization of Deep Learning Neural Networks

Nowadays, machine learning methods are actively used to process big data. A promising direction is neural networks, in which structure optimization occurs on the principles of self-configuration. Genetic algorithms are applied to solve this nontrivial problem. Most multicriteria evolutionary algorithms use a procedure known as non-dominant sorting to rank decisions. However, the efficiency of procedures for adding points and updating rank values in non-dominated sorting (incremental non-dominated sorting) remains low. In this regard, this research improves the performance of these algorithms, including the condition of an asynchronous calculation of the fitness of individuals. The relevance of the research is determined by the fact that although many scholars and specialists have studied the self-tuning of neural networks, they have not yet proposed a comprehensive solution to this problem. In particular, algorithms for efficient non-dominated sorting under conditions of incremental and asynchronous updates when using evolutionary methods of multicriteria optimization have not been fully developed to date. To achieve this goal, a hybrid co-evolutionary algorithm was developed that significantly outperforms all algorithms included in it, including error-back propagation and genetic algorithms that operate separately. The novelty of the obtained results lies in the fact that the developed algorithms have minimal asymptotic complexity. The practical value of the developed algorithms is associated with the fact that they make it possible to solve applied problems of increased complexity in a practically acceptable time. Doi: 10.28991/HIJ-2023-04-01-011 Full Text: PDF

BRCE: bi-roles co-evolution for energy-efficient distributed heterogeneous permutation flow shop scheduling with flexible machine speed

Distributed manufacturing is the mainstream model to accelerate production. However, the heterogeneous production environment makes engineer hard to find the optimal scheduling. This work investigates the energy-efficient distributed heterogeneous permutation flow scheduling problem with flexible machine speed (DHPFSP-FMS) with minimizing makespan and energy consumption simultaneously. In DHPFSP-FMS, the local search misleads the population falling into local optima which reduces the convergence and diversity. To solve this problem, a bi-roles co-evolutionary algorithm is proposed which contains the following improvements: First, the global search and local search is divided into two swarms producer and consumer to balance computation. Second, three heuristic rules are designed to get a high-quality initialization population. Next, five problem-based local search strategies are designed to accelerate converging. Then, an efficient energy-saving strategy is presented to save energy. Finally, to verify the performance of the proposed algorithm, 22 instances are generated based on the Taillard benchmark, and a number of numerical experiments are adopted. The experiment results state that our algorithm is superior to the state-of-arts and more efficient for DHPFSP-FMS.

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.

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.

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.

Two-Stage Multi-Objective Stochastic Model on Patient Transfer and Relief Distribution in Lockdown Area of COVID-19.

The outbreak of an epidemic disease may cause a large number of infections and a slightly higher death rate. In response to epidemic disease, both patient transfer and relief distribution are significant to reduce corresponding damage. This study proposes a two-stage multi-objective stochastic model (TMS-PTRD) considering pre-pandemic preparedness measures and post-pandemic relief operations. The proposed model considers the following four objectives: the total number of untreated infected patients, the total transfer time, the overall cost, and the equity distribution of relief supplies. Before an outbreak, the locations of temporary relief distribution centers (TRDCs) and the inventory levels of established TRDCs should be determined. After an outbreak, the locations of temporary hospitals (THs), the locations of designated hospitals (DHs), the transfer plans for patients, and the relief distribution should be determined. To solve the TMS-PTRD model, we address an improved preference-inspired co-evolutionary algorithm named the PICEA-g-AKNN algorithm, which is embedded with a novel similarity distance and three different tailored evolutionary strategies. A real-world case study of Hunan of China and 18 test instances are randomly generated to evaluate the TMS-PTRD model. The finding shows that the PICEA-g-AKNN algorithm is better than some most widely used multi-objective algorithms.

A co-evolutionary genetic algorithm for robust and balanced controller placement in software-defined networks

The controller placement problem (CPP) is one of the main issues that need to be addressed in the context of Software Defined Networking (SDN), especially when different aspects are being considered, such as latency, capacity, reliability, and load balancing. Most of the solutions in the literature address these aspects by considering a fixed load for each controller and attempting to equally distribute the traffic demand of the switches among the controllers, which also have a fixed common capacity. On the contrary, in this work, the CPP is studied by considering load, controller capacity, and the failure probability of controllers and links as varying over time. The CPP is formulated in terms of a robust optimization problem, which, by introducing the concept of scenario, takes into account changes in the network status due to failures, load variations, and changes in switches’ demand and controllers’ capacity. The provided solution is robust, that is, neither controllers’ re-placement nor switches’ re-assignment is required as network conditions change. Besides, a co-evolutionary algorithm is provided to solve the aforementioned optimization problem. Two populations coevolve based on the concept of complementary evolution of allied species in nature. Experimental results on a set of real-world network topologies and comparisons with the state-of-the-art have proven the superiority of the proposal, in terms of better latency, load balancing and resilience, in solving the CPP under different network status changes that might occur over time.

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.

Multidisciplinary Modeling and Optimization Method of Remote Sensing Satellite Parameters Based on SysML-CEA

To enhance the efficiency of system modeling and optimization in the conceptual design stage of satellite parameters, a system modeling and optimization method based on System Modeling Language and Co-evolutionary Algorithm is proposed. At first, the objectives of satellite mission and optimization problems are clarified, and a design matrix of discipline structure is constructed to process the coupling relationship of design variables and constraints of the orbit, payload, power and quality disciplines. In order to solve the problem of increasing non-linearity and coupling between these disciplines while using a standard collaborative optimization algorithm, an improved genetic algorithm is proposed and applied to system-level and discipline-level models. Finally, the CO model of satellite parameters is solved through the collaborative simulation of Cameo Systems Modeler (CSM) and MATLAB. The result obtained shows that the method proposed in this paper for the conceptual design phase of satellite parameters is efficient and feasible. It can shorten the project cycle effectively and additionally provide a reference for the optimal design of other complex projects.

An annealing based approach to informed mode choice in agent-based transport simulations

Modeling and simulating travelers mode choice is of great importance when evaluating novel transportation modes, policy measures or other changes to the overall transport system. The agent-based transportation framework MATSim has been widely used to study such scenarios and evaluate potential changes in the modal split. The default mode choice behavior in MATSim lets agents explore all their mode options randomly. A scoring-based co-evolutionary algorithm is applied to maximize the utility over a large number of iterations and arrive at consistent modes shares.In this paper, we present a new mode choice approach, that resembles a more rational decision-making process. First, the utilities of all available modes are estimated and used as costs to build a graph with all trips of the day. A k-shortest-path algorithm is applied to compute the most promising k combinations of modes for the day. Additionally, we formulate a pruning methodology that allows to remove unpromising modes. Finally, a selection model based on a multinomial logit is used to choose one of the plan candidates. The scale parameter of the selection model is annealed over the course of iterations to predict deterministically to the candidate with the highest estimate utility. Our simulation experiments show that convergence speed compared to random mode choice is significantly increased and only 25% of iterations are required to achieve overall better scores.

Evolution-by-Coevolution of Neural Networks for Audio Classification

Neural networks are increasingly used in recognition problems, including static and moving images, sounds, etc. Unfortunately, the selection of optimal neural network architecture for a specific recognition problem is a difficult task, which often has an experimental nature. In this paper we present the use of evolutionary algorithms to obtain optimal architectures of neural networks used for audio sample classification. We extend the Pytorch DNN Evolution tool implementing co-evolutionary algorithms which create groups of neural networks that solve a given problem with a certain accuracy, with the support for problems in which training data consists of audio samples. In this paper we use the co-evolutionary approach to solve a sample sound classification problem. We describe how the sound data was prepared for processing with the use of the Mel Frequency Cepstral Coefficients (MFCC). Next we present the results of experiments conducted with the AudioMnist dataset. The obtained neural network architectures, whose classification accuracy is comparable to the classification accuracy attained by the AlexNet neural network, and their implications are discussed.

Energy-Efficient Hybrid Flowshop Scheduling with Consistent Sublots Using an Improved Cooperative Coevolutionary Algorithm

Energy conservation, emission reduction, and green and low carbon are of great significance to sustainable development, and are also the theme of the transformation and upgrading of the manufacturing industry. This paper concentrates on studying the energy-efficient hybrid flowshop scheduling problem with consistent sublots (HFSP_ECS) with the objective of minimizing the energy consumption. To solve the problem, the HFSP_ECS is decomposed by the idea of “divide-and-conquer”, resulting in three coupled subproblems, i.e., lot sequence, machine assignment, and lot split, which can be solved by using a cooperative methodology. Thus, an improved cooperative coevolutionary algorithm (vCCEA) is proposed by integrating the variable neighborhood descent (VND) strategy. In the vCCEA, considering the problem-specific characteristics, a two-layer encoding strategy is designed to represent the essential information, and a novel collaborative model is proposed to realize the interaction between subproblems. In addition, special neighborhood structures are designed for different subproblems, and two kinds of enhanced neighborhood structures are proposed to search for potential promising solutions. A collaborative population restart mechanism is established to ensure the population diversity. The computational results show that vCCEA can coordinate and solve each subproblem of HFSP_ECS effectively, and outperform the mathematical programming and the other state-of-the-art algorithms.

A Coevolutionary Algorithm for Cooperative Platoon Formation of Connected and Automated Vehicles

This paper proposes a coevolutionary algorithm to optimize longitudinal trajectories of multiple vehicles with an energy-aware non-linear objective during the cooperative platoon formation process. In this work, an adaptive encoding scheme is adopted to represent trajectories as knot vectors of parametric cubic splines, and therefore the original problem is reformulated into a constrained numerical optimization version. The number of knots can be adjusted to trade-off between the shape flexibility and computation efficiency. Further, the proposed coevolutionary algorithm decomposes the initially high-dimensional problem into smaller subproblems, significantly reducing the complexity. A hybrid evolutionary algorithm is developed as an optimizer for subproblems. Additionally, a branch-and-bound strategy and a Tabu search component are integrated into the steepest ascent hill-climbing algorithm to speed up convergences within the local exploitation phase. Numerical experiments are conducted on extensive scenarios with different platooning sizes and initial separations. Experimental results indicate the superiority of the proposed approach in optimality and stability with reasonable sub-second computation time for real-life applications.