This paper proposes a variable range-based interaction preference multi-objective optimization algorithm through objective decomposition (VR-MOEA-OD). VR-MOEA-OD focuses on finding the preferred solutions of decision maker (DM) and can adjust the size of the preference range based on the DM’s needs. First, the DM is asked to provide a preference direction and the number of needed solutions. Then, the algorithm searches for the DM’s preferred solutions using the multi-objective evolutionary algorithm based on objective decomposition (MOEA-OD). If unsatisfied with the results, the DM needs to provide a range parameter to adjust the size of preference range and respecify the number of desired solutions. Based on the range parameter and the change in the number of solutions required before and after the interaction, VR-MOEA-OD can modulate the size of the preference range, either enlarging or narrowing the preference range. The results indicate that VR-MOEA-OD can fully utilize preference information and satisfy the interaction information provided by the DM to achieve desired results.

In recent years, many dynamic multi-objective optimization algorithms (DMOAs) have been proposed to address dynamic multi-objective optimization problems (DMOPs). Most existing DMOAs treat all decision variables uniformly and respond to them in an identical manner. This paper proposes a dynamic multi-objective optimization algorithm based on the classification response of decision variables (CRDV-DMO). Firstly, CRDV-DMO categorizes the decision variables into convergence variables and diversity variables. Different decision variables adopt distinct response strategies. The response strategy of diversity variable (RSDV) uses Latin hypercube sampling to generate the diversity variables of the new environment. For each dimensional convergence variable, the response strategy of convergence variable (RSCV) first evaluates whether the basic center prediction strategy (CPS) yields positive feedback or negative feedback, further determining the predictability of that dimensional convergence variable. RSCV then decides to either use the basic CPS to generate the convergence variable for that dimension or to retain that dimensional convergence variable from the current environment, based on the predictability of that dimensional convergence variable. The proposed algorithm is extensively studied through comparison with several advanced DMOAs, demonstrating its effectiveness in dealing with the benchmark DMOPs and the parameter-tuning problem of the PID controller on a dynamic system.

Evolutionary multitasking optimization (EMTO) has attracted much attention in the community of evolutionary computation, which solves multiple tasks simultaneously by exchanging information between tasks. Multitasking traveling salesman problem (MTSP) is one of the most important combinatorial optimization problems in EMTO. However, redundant encoding and inefficient probabilistic transfer mechanisms used in most existing works may lead to negative transfer. In this paper, a new multi-population evolutionary algorithm via seed transfer (MPEA-ST) is proposed for MTSP. Firstly, combining heuristics with EMTO, a new seed encoding strategy, and seed growth mechanism are proposed to overcome redundant coding and suppress negative transfer. Moreover, a new seed selection mechanism and transfer strategy are designed to select seeds with knowledge. Finally, a new dataset construction method is developed to address the lack of MTSP benchmarks with different similarities. Experimental results show the superiority of the proposed MPEA-ST compared to other state-of-the-art methods on synthetic datasets and real-world datasets.

The use of containerization technology in microservice architecture has become widespread, owing to its potential to support fast deployment of web applications and improve the resource utilization in cloud data centers. Evolutionary algorithms (EAs) have been performed promising on the deployment of applications created using microservices. However, with the growing demand for microservice application, the existing EAs fail to solve the large-scale container placement problem due to the high time complexity and poor scalability. A multi-factorial evolutionary algorithm (MFEA) is proposed in this article, which can evolve multiple optimization problems simultaneously for the container placement problem in heterogeneous cluster environments. First, a system model integrated the heterogeneous clusters, microservices, containers, and four optimization objectives is presented. Then, embedded with local search strategy, a multi-objective container placement MFEA (MOCP-MFEA) algorithm is developed to address the container placement problem. MOCP-MFEA is applied to a variety of container placement problems with different application sizes in heterogeneous cluster environments. Experimental results show that compared with various conventional and evolutionary-based approaches, MOCP-MFEA could shorten optimization time significantly and offer a competitive placement solution for the container placement problem and show a good elasticity in heterogeneous cluster environments. Moreover, the deployment scheme of container to physical machines is crucial to lowering resources wastage.

With the rapid development of the economy, the increasingly diversified and personalized needs of consumers, the timeliness of logistics distribution has attracted more and more attention of enterprises and customers. However, modern logistics enterprises need to consider the emergence of several dynamic demands in the distribution process to realize the dynamic planning of the routes. This paper puts forward an adaptive genetic algorithm (AGA) with the elastic strategy to solve the dynamic vehicle routing problem with time windows (DVRPTWs), and the proposed algorithm is denoted as AGA-ES-TW. Firstly, AGA designs a population initialization method considering time windows, and designs an adaptive local search strategy that realizes the adaptive local adjustment of different individuals. Meanwhile, AGA develops adaptive crossover and mutation operators, which could adaptively adjust the probability of evolution for different individuals. The experiments prove the better performance of AGA on the traditional vehicle routing problem with time windows (VRPTWs). Then, AGA cooperates with an elastic strategy to deal with DVRPTWs. This paper major considers four types of dynamic demands: the increase of distribution nodes, the decrease of distribution nodes, the change of distribution road conditions, and the change of time windows. The proposed AGA-ES-TW could detect the types of different demands, and adaptively adopt diverse strategies to deal with the corresponding demands, then plan reasonable routes. The experiments on benchmark data sets indicate that AGA-ES-TW performs well on solving DVRPTWs. Furthermore, this paper constructs the distribution information of 100 SF express stations in Xi’an based on actual information, and employs AGA-ES-TW to solve the actual DVRPTWs.

Multi-depot Cumulative Capacited Vehicle Routing Problem (MDCCVRP) is a relatively new research field in Vehicle Routing Problems (VRP), which is composed of several traditional VRP variants. This model is usually applicable to the logistics and transportation problems after the disaster. A decomposition-based Max-Min ant system (DMMAS) algorithm is proposed to solve MDCCVRP in this paper. First of all, a new indicator which measures the nearness between two routes for multi-depot problems is proposed. The original problem is decomposed into a series of smaller subproblems, and then, after the optimization phase, a specific pheromone communication rule between the master problem and subproblems is adopted to guide the search direction of ants. Finally, when the search gets into a halt, a mechanism of perturbation is used to get rid of the local optimality. The algorithm is tested on many benchmark problems and the experimental results show that our algorithm can effectively improve the performance in most cases compared to several state-of-the-art evolutionary algorithms.

Dynamic multiobjective optimization deals with simultaneous optimization of multiple conflicting objectives that change over time. Several response strategies for dynamic optimization have been proposed, which do not work well for all types of environmental changes. In this article, we propose a new dynamic multiobjective evolutionary algorithm based on objective space decomposition, in which the maxi-min fitness function is adopted for selection and a self-adaptive response strategy integrating a number of different response strategies is designed to handle unknown environmental changes. The self-adaptive response strategy can adaptively select one of the strategies according to their contributions to the tracking performance in the previous environments. Experimental results indicate that the proposed algorithm is competitive and promising for solving different DMOPs in the presence of unknown environmental changes. Meanwhile, the proposed algorithm is applied to solve the parameter tuning problem of a proportional integral derivative (PID) controller of a dynamic system, obtaining better control effect.

Decomposition-based evolutionary algorithms have been quite successful in dealing with multiobjective optimization problems. Recently, more and more researchers attempt to apply the decomposition approach to solve many-objective optimization problems. A many-objective evolutionary algorithm based on decomposition with correlative selection mechanism (MOEA/D-CSM) is also proposed to solve many-objective optimization problems in this article. Since MOEA/D-SCM is based on a decomposition approach which adopts penalty boundary intersection (PBI), a set of reference points must be generated in advance. Thus, a new concept related to the set of reference points is introduced first, namely, the correlation between an individual and a reference point. Thereafter, a new selection mechanism based on the correlation is designed and called correlative selection mechanism. The correlative selection mechanism finds its correlative individuals for each reference point as soon as possible so that the diversity among population members is maintained. However, when a reference point has two or more correlative individuals, the worse correlative individuals may be removed from a population so that the solutions can be ensured to move toward the Pareto-optimal front. In a comprehensive experimental study, we apply MOEA/D-CSM to a number of many-objective test problems with 3 to 15 objectives and make a comparison with three state-of-the-art many-objective evolutionary algorithms, namely, NSGA-III, MOEA/D, and RVEA. Experimental results show that the proposed MOEA/D-CSM can produce competitive results on most of the problems considered in this study.

This letter puts forward a new algorithm, ensemble strategy multiobjective fuzzy clustering method (ESMOFCM). To fully combine the gray information and spatial information of neighbor pixels, a new dividing fluctuant parameter is proposed for producing a difference image. Then, we use a frame based on multiobjective fuzzy clustering to alleviate the contradiction between removing noise and preserving details in images. Ensemble strategy is adopted to integrate all Pareto optimal solutions. The experimental results show that the proposed algorithm is superior to comparison algorithms.

In this paper, two multi-objective clustering ensemble algorithms are proposed named MOCLED and MOCNCD. MOCLED is different from MOCLE on three points. First, different clustering algorithms are used to produce some new individuals in evolutionary process. Second, a new screening mechanism is added. In each generation, the worst individual is replaced by the best individual. Third, a new objective function is added to ensure a diverse population. MOCNCD is the same as MOCLED except the crossover operator. We replace it with a new proposed cluster ensemble algorithm, IDICLENS. Experimental results reveal the advantages of our method on finding good partitions.

Quantum-behaved particle swarm optimization (QPSO) algorithm simulates quantum mechanics among individuals. For improving the local search ability of QPSO and guiding the search, an improved QPSO algorithm based on combining the dynamic mutation and cooperative background (MCQPSO) is proposed in this paper. The dynamic Cauchy mutation strategy is introduced to enhance the global search ability. The cooperative background strategy is used to change the updating mode of the particles in order to guarantee the effectiveness and simplification. The MCQPSO algorithm keeps the diversity of the population, and increasing convergence rates. Results compared with some previous study show that the MCQPSO algorithm performs much better than the Sun Jun's Cooperative Quantum-Behaved Particle Swarm Optimization (sunCQPSO) and WQPSO algorithm in terms of the image segmentation accuracy and the computation efficiency.

Due to the specificity and complexity of the dynamic optimization problems (DOPs), those excellent static optimization algorithms cannot be applied in these problems directly. So some special algorithms only for DOPs are needed. There is a multi-swarm algorithm with a better performance than others in DOPs, which utilizes a parent swarm to explore the search space and some child swarms to exploit promising areas found by the parent swarm. In addition, a static optimization algorithm OLPSO is so attractive, which utilize an orthogonal learning (OL) strategy to utilize previous search information (experience) more efficiently to predict the positions of particles and improve the convergence speed. In this paper, we bring the essence of OLPSO called OL strategy to the multi-swarm algorithm to improve its performance further. The experimental results conducted on different dynamic environments modeled by moving peaks benchmark show that the efficiency of this algorithm for locating and tracking multiple optima in dynamic environments is outstanding in comparison with other particle swarm optimization models, including MPSO, a similar particle swarm algorithm for dynamic environments.

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job scheduling which is concerned with the determination of a sequence of jobs, consisting of many operations, on different machines, satisfying parallel goals. This paper addresses the FJSP with two objectives: Minimize makespan, Minimize total operation cost. We introduce a memetic algorithm based on the Nondominated Neighbor Immune Algorithm (NNIA), to tackle this problem. The proposed algorithm adds, to NNIA, local search procedures including a rational combination of undirected simulated annealing (UDSA) operator, directed cost simulated annealing (DCSA) operator and directed makespan simulated annealing (DMSA) operator. We have validated its efficiency by evaluating the algorithm on multiple instances of the FJSPs. Experimental results show that the proposed algorithm is an efficient and effective algorithm for the FJSPs, and the combination of UDSA operator, DCSA operator and DMSA operator with NNIA is rational.

Community detection has received a great deal of attention in recent years. Modularity is the most used and best known quality function for measuring the quality of a partition of a network. Based on the optimization of modularity, we proposed a memetic algorithm with a local search operator to detect community structure. The local search operator uses a quality function of local community tightness based on structural similarity. In addition, the tactics of vertex mover is used for reassigning vertices to neighboring communities to improve the partition result. Experiments on real-world networks and computer-generated networks show the effectiveness of our algorithm.

Data processing in high-dimensional spaces is a challenging task. In order to effectively classify the data in a high-dimensional space, a quantum particle swarm optimization classification algorithm (QPSOCA) for high-dimensional datasets is proposed in this paper. In QPSOCA, an uncorrelated discriminant analysis algorithm is utilized to reduce the dimension of the data, which is implemented automatically and no extra parameters are needed. In addition, to avoid the randomness of the swarm and improve the convergence speed, quantum computation is introduced into particle swarm optimization (PSO). In the experimental section, a detailed comparison of three different combinatorial optimization methods is given to demonstrate the efficiency of the proposed algorithm. Comparative experiments show that the proposed algorithm can improve the classification accuracy.

A number of studies has focused on the community detection in complex networks in recent years. Single-objective approaches which have only one optimization function (e.g., modularity or modularity density) may have weaknesses such as just a single community structure can be obtained or resolution limit. In this paper, a spectral clustering-based adaptive hybrid multi-objective harmony search algorithm (SCAH-MOHSA) combined with a local search strategy is proposed to detect the community structure in complex networks. At first, an improved spectral method is employed to convert the community detection problem into a data clustering issue while the length of the representation of a harmony in the harmony memory can be determined. Then, an adaptive hybrid multi-objective harmony search algorithm is used to solve the multi-objective optimization problem so as to resolve the community structure. The experiments on both synthetic and real world networks demonstrate our method achieves partition results which fit the real situation in an even better fashion.

In this paper, we present a cluster algorithm which is an improvement of the multi-objective clustering ensemble algorithm (MOCLE), which is denoted as IMOCLE for short. First, we introduce a new clustering objective function to measure the individual difference in the optimization process so as to remain the diversity of the population. Then, a clustering ensemble technique is applied to MOCLE to obtain more competitive individual. The proposed algorithm can also ensure good partitions not be eliminated. The performance of the proposed algorithm has been compared with MOCLE over a suit of gene datasets. The experimental results show that, the superiority of the proposed method in terms of capability found the optimum number of clusters, and accuracy.

In this paper, we proposed a new approach to solve the clustering problem in which the cluster number is uncertainty. It utilizes IWO (Invasive Weed Optimization) algorithm to optimize two fuzzy clustering objective function simultaneously, and a variable-length real-coded scheme has been adopted, the variable length weed encodes the cluster centers with variable numbers. In order to keep the diversity of the weeds, we introduce a new mechanism called feedback update mechanism to update the individuals which the corresponding number of cluster centers has been eliminated in one generation. Finally, the Silhouette index is used to select the best solution. The algorithm is used to cluster 15 artificial data sets and 4 real life data sets and shows good performance.

Recently, one of the main tools of decision maker (DM) preference incorporation in the multiobjective optimization (MOO) has been using reference points and achievement scalarizing functions (ASF). The core idea of these methods is converting the original multiobjective problem (MOP) into single objective problem by using ASF to find a single preferred point. However, many DMs not only interest in a single point but also a set of efficient points in their preferred region. In this paper, we introduce a hybrid multiobjective immune algorithm (HMIA) for DM. It combines the immune inspired algorithm and region preference based on a novel dominance concept called region-dominance without ASF. The new algorithm can let DMs flexibly decide the number of reference points and accurately determine the preferred region with its simple and effective interactive methods. To exemplify its advantages, simulated results of HMIA are shown with some well-known problems.

Vector Quantization (VQ) is a useful tool for data compression and can be applied to compress the data vectors in the database. The quality of the recovered data vector depends on a good codebook. Mean/residual vector quantization (M/RVQ) has been shown to be efficient in the encoding time and it only needs a little storage. In this paper, Clonal Selection Algorithm for Image Compression (CSAIC) is proposed. In CSAIC, Based on M/RVQ algorithm, an improved clonal selection algorithm is used to cluster the data of compressed images in order to obtain the optimal codebook. The proposed method has been extensively compared with Linde-Buzo-Gray(LBG), Self-Organizing Mapping (SOM) and Modified K-means(Mod-KM) over a test suit of seven natural images. The experimental results show that CSAIC outperforms other three algorithms in terms of image compression performance.

Based on clonal selection principle and the immunodominance theory, a new immune clustering algorithm, Immunodomaince based Clonal Selection Clustering Algorithm (ICSCA) is proposed in this paper. An immunodomaince operator is introduced to the clonal selection algorithm, which can realize on-line gaining prior knowledge and sharing information among different antibodies. The proposed method has been extensively compared with Fuzzy C-means (FCM), Genetic Algorithm based FCM (GAFCM) and Clonal Selection Algorithm based FCM (CSAFCM) over a test suit of several real life datasets and synthetic datasets. The result of experiment indicates the superiority of the ICSCA over FCM, GAFCM and CSAFCM on stability and reliability for its ability to avoid trapping in local optimum.

A clonal selection clustering algorithm using point symmetry-based distance measure (CSCAPS) is proposed in this paper, a point symmetry-based similarity measure is used to evaluate the similarity between two samples in order to cluster data sets with the character of symmetry. Both Kd-trees based nearest neighbor search and k-nearest-neighbor consistency strategy are used to reduce the computation complexity and improve the clustering accuracy. The proposed method has been extensively compared with four well-known clustering algorithms over a test suit of real life data sets and synthetic data sets. The results of experiments indicate the superiority of the CSCAPS on accuracy.

Real-world optimization involving multiple objectives in changing environment known as dynamic multi-objective optimization (DMO) is a challenging task, especially special regions are preferred by decision maker (DM). Based on a novel preference dominance concept called sphere-dominance and the theory of artificial immune system (AIS), a sphere-dominance preference immune-inspired algorithm (SPIA) is proposed for DMO in this paper. The main contributions of SPIA are its preference mechanism and its sampling study, which are based on the novel sphere-dominance and probability statistics, respectively. Besides, SPIA introduces two hypermutation strategies based on history information and Gaussian mutation, respectively. In each generation, which way to do hypermutation is automatically determined by a sampling study for accelerating the search process. Furthermore, The interactive scheme of SPIA enables DM to include his/her preference without modifying the main structure of the algorithm. The results show that SPIA can obtain a well distributed solution set efficiently converging into the DM's preferred region for DMO.

Inspired by the principle of gene transposon proposed by Barbara McClintock, a new immune computing algorithm for clustering multi-class data sets named as Gene Transposition based Clone Selection Algorithm (GTCSA) is proposed in this paper, The proposed algorithm does not require a prior knowledge of the numbers of clustering; an improved variant of the clonal selection algorithm has been used to determine the number of clusters as well as to refine the cluster center. a novel operator called antibody transposon is introduced to the framework of clonal selection algorithm which can realize to find the optimal number of cluster automatically. The proposed method has been extensively compared with Variable-string-length Genetic Algorithm(VGA)based clustering techniques over a test suit of several real life data sets and synthetic data sets. The results of experiments indicate the superiority of the GTCSA over VGA on stability and convergence rate, when clustering multi-class data sets.