Cooperative Coevolutionary Bare-Bones Particle Swarm Optimization With Function Independent Decomposition for Large-Scale Supply Chain Network Design With Uncertainties

Neural Net-Enhanced Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization

The competitive swarm optimizer (CSO) classifies swarm particles into loser and winner particles and then uses the winner particles to efficiently guide the search of the loser particles. This approach has very promising performance in solving large-scale multiobjective optimization problems (LMOPs). However, most studies of CSOs ignore the evolution of the winner particles, although their quality is very important for the final optimization performance. Aiming to fill this research gap, this article proposes a new neural net-enhanced CSO for solving LMOPs, called NN-CSO, which not only guides the loser particles via the original CSO strategy, but also applies our trained neural network (NN) model to evolve winner particles. First, the swarm particles are classified into winner and loser particles by the pairwise competition. Then, the loser particles and winner particles are, respectively, treated as the input and desired output to train the NN model, which tries to learn promising evolutionary dynamics by driving the loser particles toward the winners. Finally, when model training is complete, the winner particles are evolved by the well-trained NN model, while the loser particles are still guided by the winner particles to maintain the search pattern of CSOs. To evaluate the performance of our designed NN-CSO, several LMOPs with up to ten objectives and 1000 decision variables are adopted, and the experimental results show that our designed NN model can significantly improve the performance of CSOs and shows some advantages over several state-of-the-art large-scale multiobjective evolutionary algorithms as well as over model-based evolutionary algorithms.

A deep memory bare-bones particle swarm optimization algorithm for single-objective optimization problems

A deep memory bare-bones particle swarm optimization algorithm (DMBBPSO) for single-objective optimization problems is proposed in this paper. The DMBBPSO is able to perform high-precision local search while maintaining a large global search, thus providing a reliable solution to high-dimensional complex optimization problems. Normally, maintaining high accuracy while conducting global searches is an important challenge for single-objective optimizers. Traditional particle swarms optimizers can rapidly lose the diversity during iterations and are unable to perform global searches efficiently, and thus are more likely to be trapped by local optima. To address this problem, the DMBBPSO combines multiple memory storage mechanism (MMSM) and a layer-by-layer activation strategy (LAS). The MMSM catalyzes a set of deep memories to increase the diversity of the particle swarm. For every single particle, both of the personal best position and deep memories will be used in the evaluation process. The LAS enables the particle swarm to avoid premature convergence while enhancing local search capabilities. The collaboration between MMSM and LAS enhances the diversity of the particle swarm, which in turn enhances the robustness of the DMBBPSO. To investigate the optimization ability of the DMBBPSO for single-objective optimization problems, The CEC2017 benchmark functions are used in experiments. Five state-of-the-art evolutionary algorithms are used in the control group. Finally, experimental results demonstrate that the DMBBPSO can provide high precision results for single-objective optimization problems.

Distributed Differential Evolution With Adaptive Resource Allocation

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.

Optimizing Niche Center for Multimodal Optimization Problems

Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.

Appropriate noise addition to metaheuristic algorithms can enhance their performance

Nature-inspired swarm-based algorithms are increasingly applied to tackle high-dimensional and complex optimization problems across disciplines. They are general purpose optimization algorithms, easy to implement and assumption-free. Some common drawbacks of these algorithms are their premature convergence and the solution found may not be a global optimum. We propose a general, simple and effective strategy, called heterogeneous Perturbation-Projection (HPP), to enhance an algorithm's exploration capability so that our sufficient convergence conditions are guaranteed to hold and the algorithm converges almost surely to a global optimum. In summary, HPP applies stochastic perturbation on half of the swarm agents and then project all agents onto the set of feasible solutions. We illustrate this approach using three widely used nature-inspired swarm-based optimization algorithms: particle swarm optimization (PSO), bat algorithm (BAT) and Ant Colony Optimization for continuous domains (ACO). Extensive numerical experiments show that the three algorithms with the HPP strategy outperform the original versions with 60-80% the times with significant margins.

Many-Objective Job-Shop Scheduling: A Multiple Populations for Multiple Objectives-Based Genetic Algorithm Approach

The job-shop scheduling problem (JSSP) is a challenging scheduling and optimization problem in the industry and engineering, which relates to the work efficiency and operational costs of factories. The completion time of all jobs is the most commonly considered optimization objective in the existing work. However, factories focus on both time and cost objectives, including completion time, total tardiness, advance time, production cost, and machine loss. Therefore, this article first time proposes a many-objective JSSP that considers all these five objectives to make the model more practical to reflect the various demands of factories. To optimize these five objectives simultaneously, a novel multiple populations for multiple objectives (MPMO) framework-based genetic algorithm (GA) approach, called MPMOGA, is proposed. First, MPMOGA employs five populations to optimize the five objectives, respectively. Second, to avoid each population only focusing on its corresponding single objective, an archive sharing technique (AST) is proposed to store the elite solutions collected from the five populations so that the populations can obtain optimization information about the other objectives from the archive. This way, MPMOGA can approximate different parts of the entire Pareto front (PF). Third, an archive update strategy (AUS) is proposed to further improve the quality of the solutions in the archive. The test instances in the widely used test sets are adopted to evaluate the performance of MPMOGA. The experimental results show that MPMOGA outperforms the compared state-of-the-art algorithms on most of the test instances.

Developing Nonlinear Customer Preferences Models for Product Design Using Opining Mining and Multiobjective PSO-Based ANFIS Approach

Online customer reviews can clearly show the customer experience, and the improvement suggestions based on the experience, which are helpful to product optimization and design. However, the research on establishing a customer preference model based on online customer reviews is not ideal, and the following research problems are found in previous studies. Firstly, the product attribute is not involved in the modelling if the corresponding setting cannot be found in the product description. Secondly, the fuzziness of customers' emotions in online reviews and nonlinearity in the models were not appropriately considered. Thirdly, the adaptive neuro-fuzzy inference system (ANFIS) is an effective way to model customer preferences. However, if the number of inputs is large, the modelling process will be failed due to the complex structure and long computational time. To solve the above-given problems, this paper proposed multiobjective particle swarm optimization (PSO) based ANFIS and opinion mining, to build customer preference model by analyzing the content of online customer reviews. In the process of online review analysis, the opinion mining technology is used to conduct comprehensive analysis on customer preference and product information. According to the analysis of information, a new method for establishing customer preference model is proposed, that is, a multiobjective PSO based ANFIS. The results show that the introducing of multiobjective PSO method into ANFIS can effectively solve the defects of ANFIS itself. Taking hair dryer as a case study, it is found that the proposed approach performs better than fuzzy regression, fuzzy least-squares regression, and genetic programming based fuzzy regression in modelling customer preference.

A Promotive Particle Swarm Optimizer With Double Hierarchical Structures

In this study, a novel promotive particle swarm optimizer with double hierarchical structures is proposed. It is inspired by successful mechanisms present in social and biological systems to make particles compete fairly. In the proposed method, the swarm is first divided into multiple independent subpopulations organized in a hierarchical promotion structure, which protects subpopulation at each hierarchy to search for the optima in parallel. A unidirectional communication strategy and a promotion operator are further implemented to allow excellent particles to be promoted from low-hierarchy subpopulations to high-hierarchy subpopulations. Furthermore, for the internal competition within each subpopulation of the hierarchical promotion structure, a hierarchical multiscale optimum controlled by a tiered architecture of particles is constructed for particles, in which each particle can synthesize a set of optima of its different scales. The hierarchical promotion structure can protect particles that just fly to promising regions and have low fitness from competing with the entire swarm. Also, the double hierarchical structures increase the diversity of searching. Numerical experiments and statistical analysis of results reported on 30 benchmark problems show that the proposed method improves the accuracy and convergence speed especially in solving complex problems when compared with several variations of particle swarm optimization.

A survey on binary metaheuristic algorithms and their engineering applications

This article presents a comprehensively state-of-the-art investigation of the engineering applications utilized by binary metaheuristic algorithms. Surveyed work is categorized based on application scenarios and solution encoding, and describes these algorithms in detail to help researchers choose appropriate methods to solve related applications. It is seen that transfer function is the main binary coding of metaheuristic algorithms, which usually adopts Sigmoid function. Among the contributions presented, there were different implementations and applications of metaheuristic algorithms, or the study of engineering applications by different objective functions such as the single- and multi-objective problems of feature selection, scheduling, layout and engineering structure optimization. The article identifies current troubles and challenges by the conducted review, and discusses that novel binary algorithm, transfer function, benchmark function, time-consuming problem and application integration are need to be resolved in future.

Elite Directed Particle Swarm Optimization with Historical Information for High-Dimensional Problems

High-dimensional optimization problems are ubiquitous in every field nowadays, which seriously challenge the optimization ability of existing optimizers. To solve this kind of optimization problems effectively, this paper proposes an elite-directed particle swarm optimization (EDPSO) with historical information to explore and exploit the high-dimensional solution space efficiently. Specifically, in EDPSO, the swarm is first separated into two exclusive sets based on the Pareto principle (80-20 rule), namely the elite set containing the top best 20% of particles and the non-elite set consisting of the remaining 80% of particles. Then, the non-elite set is further separated into two layers with the same size from the best to the worst. As a result, the swarm is divided into three layers. Subsequently, particles in the third layer learn from those in the first two layers, while particles in the second layer learn from those in the first layer, on the condition that particles in the first layer remain unchanged. In this way, the learning effectiveness and the learning diversity of particles could be largely promoted. To further enhance the learning diversity of particles, we maintain an additional archive to store obsolete elites, and use the predominant elites in the archive along with particles in the first two layers to direct the update of particles in the third layer. With these two mechanisms, the proposed EDPSO is expected to compromise search intensification and diversification well at the swarm level and the particle level, to explore and exploit the solution space. Extensive experiments are conducted on the widely used CEC’2010 and CEC’2013 high-dimensional benchmark problem sets to validate the effectiveness of the proposed EDPSO. Compared with several state-of-the-art large-scale algorithms, EDPSO is demonstrated to achieve highly competitive or even much better performance in tackling high-dimensional problems.

A genetic algorithm with two-step rank-based encoding for closed-loop supply chain network design

The closed-loop supply chain (CLSC) plays an important role in sustainable development and can help to increase the economic benefits of enterprises. The optimization for the CLSC network is a complicated problem, since it often has a large problem scale and involves multiple constraints. This paper proposes a general CLSC model to maximize the profits of enterprises by determining the transportation route and delivery volume. Due to the complexity of the multi-constrained and large-scale model, a genetic algorithm with two-step rank-based encoding (GA-TRE) is developed to solve the problem. Firstly, a two-step rank-based encoding is designed to handle the constraints and increase the algorithm efficiency, and the encoding scheme is also used to improve the genetic operators, including crossover and mutation. The first step of encoding is to plan the routes and predict their feasibility according to relevant constraints, and the second step is to set the delivery volume based on the feasible routes using a rank-based method to achieve greedy solutions. Besides, a new mutation operator and an adaptive population disturbance mechanism are designed to increase the diversity of the population. To validate the efficiency of the proposed algorithm, six heuristic algorithms are compared with GA-TRE by using different instances with three problem scales. The results show that GA-TRE can obtain better solutions than the competitors, especially on large-scale instances.

Performance optimization of support vector machine with oppositional grasshopper optimization for acute appendicitis diagnosis

Preoperative differentiation of complicated and uncomplicated appendicitis is challenging. The research goal was to construct a new intelligent diagnostic rule that is accurate, fast, noninvasive, and cost-effective, distinguishing between complicated and uncomplicated appendicitis. Overall, 298 patients with acute appendicitis from the Wenzhou Central Hospital were recruited, and information on their demographic characteristics, clinical findings, and laboratory data was retrospectively reviewed and applied in this study. First, the most significant variables, including C-reactive protein (CRP), heart rate, body temperature, and neutrophils discriminating complicated from uncomplicated appendicitis, were identified using random forest analysis. Second, an improved grasshopper optimization algorithm-based support vector machine was used to construct the diagnostic model to discriminate complicated appendicitis (CAP) from uncomplicated appendicitis (UAP). The resultant optimal model can produce an average of 83.56% accuracy, 81.71% sensitivity, 85.33% specificity, and 0.6732 Matthews correlation coefficients. Based on existing routinely available markers, the proposed intelligent diagnosis model is highly reliable. Thus, the model can potentially be used to assist doctors in making correct clinical decisions.

Stochastic Triad Topology Based Particle Swarm Optimization for Global Numerical Optimization

Particle swarm optimization (PSO) has exhibited well-known feasibility in problem optimization. However, its optimization performance still encounters challenges when confronted with complicated optimization problems with many local areas. In PSO, the interaction among particles and utilization of the communication information play crucial roles in improving the learning effectiveness and learning diversity of particles. To promote the communication effectiveness among particles, this paper proposes a stochastic triad topology to allow each particle to communicate with two random ones in the swarm via their personal best positions. Then, unlike existing studies that employ the personal best positions of the updated particle and the neighboring best position of the topology to direct its update, this paper adopts the best one and the mean position of the three personal best positions in the associated triad topology as the two guiding exemplars to direct the update of each particle. To further promote the interaction diversity among particles, an archive is maintained to store the obsolete personal best positions of particles and is then used to interact with particles in the triad topology. To enhance the chance of escaping from local regions, a random restart strategy is probabilistically triggered to introduce initialized solutions to the archive. To alleviate sensitivity to parameters, dynamic adjustment strategies are designed to dynamically adjust the associated parameter settings during the evolution. Integrating the above mechanism, a stochastic triad topology-based PSO (STTPSO) is developed to effectively search complex solution space. With the above techniques, the learning diversity and learning effectiveness of particles are largely promoted and thus the developed STTPSO is expected to explore and exploit the solution space appropriately to find high-quality solutions. Extensive experiments conducted on the commonly used CEC 2017 benchmark problem set with different dimension sizes substantiate that the proposed STTPSO achieves highly competitive or even much better performance than state-of-the-art and representative PSO variants.

Stochastic Cognitive Dominance Leading Particle Swarm Optimization for Multimodal Problems

Optimization problems become increasingly complicated in the era of big data and Internet of Things, which significantly challenges the effectiveness and efficiency of existing optimization methods. To effectively solve this kind of problems, this paper puts forward a stochastic cognitive dominance leading particle swarm optimization algorithm (SCDLPSO). Specifically, for each particle, two personal cognitive best positions are first randomly selected from those of all particles. Then, only when the cognitive best position of the particle is dominated by at least one of the two selected ones, this particle is updated by cognitively learning from the better personal positions; otherwise, this particle is not updated and directly enters the next generation. With this stochastic cognitive dominance leading mechanism, it is expected that the learning diversity and the learning efficiency of particles in the proposed optimizer could be promoted, and thus the optimizer is expected to explore and exploit the solution space properly. At last, extensive experiments are conducted on a widely acknowledged benchmark problem set with different dimension sizes to evaluate the effectiveness of the proposed SCDLPSO. Experimental results demonstrate that the devised optimizer achieves highly competitive or even much better performance than several state-of-the-art PSO variants.

Multi-objective multi-criteria evolutionary algorithm for multi-objective multi-task optimization

Evolutionary multi-objective multi-task optimization is an emerging paradigm for solving multi-objective multi-task optimization problem (MO-MTOP) using evolutionary computation. However, most existing methods tend to directly treat the multiple multi-objective tasks as different problems and optimize them by different populations, which face the difficulty in designing good knowledge transferring strategy among the tasks/populations. Different from existing methods that suffer from the difficult knowledge transfer, this paper proposes to treat the MO-MTOP as a multi-objective multi-criteria optimization problem (MO-MCOP), so that the knowledge of all the tasks can be inherited in a same population to be fully utilized for solving the MO-MTOP more efficiently. To be specific, the fitness evaluation function of each task in the MO-MTOP is treated as an evaluation criterion in the corresponding MO-MCOP, and therefore, the MO-MCOP has multiple relevant evaluation criteria to help the individual selection and evolution in different evolutionary stages. Furthermore, a probability-based criterion selection strategy and an adaptive parameter learning method are also proposed to better select the fitness evaluation function as the criterion. By doing so, the algorithm can use suitable evaluation criteria from different tasks at different evolutionary stages to guide the individual selection and population evolution, so as to find out the Pareto optimal solutions of all tasks. By integrating the above, this paper develops a multi-objective multi-criteria evolutionary algorithm framework for solving MO-MTOP. To investigate the proposed algorithm, extensive experiments are conducted on widely used MO-MTOPs to compare with some state-of-the-art and well-performing algorithms, which have verified the great effectiveness and efficiency of the proposed algorithm. Therefore, treating MO-MTOP as MO-MCOP is a potential and promising direction for solving MO-MTOP.

Evolutionary Computation for Expensive Optimization: A Survey

Expensive optimization problem (EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation (EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.

Multi-Population Enhanced Slime Mould Algorithm and with Application to Postgraduate Employment Stability Prediction

In this study, the authors aimed to study an effective intelligent method for employment stability prediction in order to provide a reasonable reference for postgraduate employment decision and for policy formulation in related departments. First, this paper introduces an enhanced slime mould algorithm (MSMA) with a multi-population strategy. Moreover, this paper proposes a prediction model based on the modified algorithm and the support vector machine (SVM) algorithm called MSMA-SVM. Among them, the multi-population strategy balances the exploitation and exploration ability of the algorithm and improves the solution accuracy of the algorithm. Additionally, the proposed model enhances the ability to optimize the support vector machine for parameter tuning and for identifying compact feature subsets to obtain more appropriate parameters and feature subsets. Then, the proposed modified slime mould algorithm is compared against various other famous algorithms in experiments on the 30 IEEE CEC2017 benchmark functions. The experimental results indicate that the established modified slime mould algorithm has an observably better performance compared to the algorithms on most functions. Meanwhile, a comparison between the optimal support vector machine model and other several machine learning methods on their ability to predict employment stability was conducted, and the results showed that the suggested the optimal support vector machine model has better classification ability and more stable performance. Therefore, it is possible to infer that the optimal support vector machine model is likely to be an effective tool that can be used to predict employment stability.

A coevolutionary algorithm based on the auxiliary population for constrained large-scale multi-objective supply chain network

Supply chain network is important for the enterprise to improve the operation and management, but has become more complicated to optimize in reality. With the consideration of multiple objectives and constraints, this paper proposes a constrained large-scale multi-objective supply chain network (CLMSCN) optimization model. This model is to minimize the total operation cost (including the costs of production, transportation, and inventory) and to maximize the customer satisfaction under the capacity constraints. Besides, a coevolutionary algorithm based on the auxiliary population (CAAP) is proposed, which uses two populations to solve the CLMSCN problem. One population is to solve the original complex problem, and the other population is to solve the problem without any constraints. If the infeasible solutions are generated in the first population, a linear repair operator will be used to improve the feasibility of these solutions. To validate the effectivity of the CAAP algorithm, the experiment is conducted on the randomly generated instances with three different problem scales. The results show that the CAAP algorithm can outperform other compared algorithms, especially on the large-scale instances.

Generation-Level Parallelism for Evolutionary Computation: A Pipeline-Based Parallel Particle Swarm Optimization

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P³SO). Due to the generation-level parallelism in P³SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P³SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems.

A survey on evolutionary computation for complex continuous optimization

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

Particle Swarm Optimization Based on a Novel Evaluation of Diversity

In this paper, we propose a particle swarm optimization variant based on a novel evaluation of diversity (PSO-ED). By a novel encoding of the sub-space of the search space and the hash table technique, the diversity of the swarm can be evaluated efficiently without any information compression. This paper proposes a notion of exploration degree based on the diversity of the swarm in the exploration, exploitation, and convergence states to characterize the degree of demand for the dispersion of the swarm. Further, a disturbance update mode is proposed to help the particles jump to the promising regions while reducing the cost of function evaluations for poor particles. The effectiveness of PSO-ED is validated on the CEC2015 test suite by comparison with seven popular PSO variants out of 12 benchmark functions; PSO-ED achieves six best results for both 10-D and 30-D.