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Community detection of dynamic networks provides more effective information than static network community detection in the real world. The mainstream method for community detection in dynamic networks is evolutionary clustering, which uses temporal smoothness of community structures to connect snapshots of networks in adjacent time intervals. However, the error accumulation issues limit the effectiveness of evolutionary clustering. While the multi-objective evolutionary approach can solve the issue of fixed settings of the two objective function weight parameters in the evolutionary clustering framework, the traditional multi-objective evolutionary approach lacks self-adaptability.

This paper proposes a community detection algorithm that integrates evolutionary clustering and decomposition-based multi-objective optimization methods. In this approach, a benchmark correction procedure is added to the evolutionary clustering framework to prevent the division results from drifting.

Experimental results demonstrate the superior accuracy of this method compared to similar algorithms in both real and synthetic dynamic datasets.

To enhance the clustering results, adaptive variances and crossover probabilities are designed based on the relative change amounts of the subproblems decomposed by MOEA/D (A Multiobjective Optimization Evolutionary Algorithm based on Decomposition) to dynamically adjust the focus of different evolutionary stages.

In this work, the multi-objective optimization shuffled complex evolution is proposed. The algorithm is based on the extension of shuffled complex evolution, by incorporating two classical operators into the original algorithm: the rank ordering and crowding distance. In order to accelerate the convergence process, a Local Search strategy based on the generation of potential candidates by using Latin Hypercube method is also proposed.

The multi-objective optimization shuffled complex evolution is used to accelerate the convergence process and to reduce the number of objective function evaluations.

In general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics. From a statistical point of view, we demonstrated that differences may exist between the proposed methodology and other evolutionary strategies concerning two different metrics (convergence and diversity), for a class of benchmark functions (ZDT functions).

The development of a new numerical method to solve multi-objective optimization problems is the major contribution.

The interval multi-objective optimization problems (IMOPs) are universal and vital uncertain optimization problems. In this study, an interval multi-objective grey wolf optimization algorithm (GWO) based on fuzzy system is proposed to solve IMOPs effectively.

First, the classical genetic operators are embedded into the interval multi-objective GWO as local search strategies, which effectively balanced the global search ability and local development ability. Second, by constructing a fuzzy system, an effective local search activation mechanism is proposed to save computing resources as much as possible while ensuring the performance of the algorithm. The fuzzy system takes hypervolume, imprecision and number of iterations as inputs and outputs the activation index, local population size and maximum number of iterations. Then, the fuzzy inference rules are defined. It uses the activation index to determine whether to activate the local search process and sets the population size and the maximum number of iterations in the process.

The experimental results show that the proposed algorithm achieves optimal hypervolume results on 9 of the 10 benchmark test problems. The imprecision achieved on 8 test problems is significantly better than other algorithms. This means that the proposed algorithm has better performance than the commonly used interval multi-objective evolutionary algorithms. Moreover, through experiments show that the local search activation mechanism based on fuzzy system proposed in this study can effectively ensure that the local search is activated reasonably in the whole algorithm process, and reasonably allocate computing resources by adaptively setting the population size and maximum number of iterations in the local search process.

This study proposes an Interval multi-objective GWO, which could effectively balance the global search ability and local development ability. Then an effective local search activation mechanism is developed by using fuzzy inference system. It closely combines global optimization with local search, which improves the performance of the algorithm and saves computing resources.

The purpose of this paper is to design an improved multi-objective algorithm with better spread and convergence than some current algorithms. The proposed application is for engineering design problems.

This study proposes two novel approaches which focus on faster convergence to the Pareto front (PF) while adopting the advantages of Strength Pareto Evolutionary Algorithm-2 (SPEA2) for better spread. In first method, decision variables corresponding to the optima of individual objective functions (Utopia Point) are strategically used to guide the search toward PF. In second method, boundary points of the PF are calculated and their decision variables are seeded to the initial population.

The proposed methods are tested with a wide range of constrained and unconstrained multi-objective test functions using standard performance metrics. Performance evaluation demonstrates the superiority of proposed algorithms over well-known existing algorithms (such as NSGA-II and SPEA2) and recent ones such as NSLS and E-NSGA-II in most of the benchmark functions. It is also tested on an engineering design problem and compared with a currently used algorithm.

The algorithms are intended to be used for practical engineering design problems which have many variables and conflicting objectives. A complex example of Welded Beam has been shown at the end of the paper.

The algorithm would be useful for many design problems and social/industrial problems with conflicting objectives.

This paper presents two novel hybrid algorithms involving SPEA2 based on: local search; and Utopia point directed search principles. This concept has not been investigated before.

This paper aims to investigate a multi-objective electric vehicle’s (EV’s) synergetic scheduling problem in the automotive industry, where a synergetic delivery mechanism to coordinate multiple EVs is proposed to fulfill part feeding tasks.

A chaotic reference-guided multi-objective evolutionary algorithm based on self-adaptive local search (CRMSL) is constructed to deal with the problem. The proposed CRMSL benefits from the combination of reference vectors guided evolutionary algorithm (RVEA) and chaotic search. A novel directional rank sorting procedure and a self-adaptive energy-efficient local search strategy are then incorporated into the framework of the CRMSL to obtain satisfactory computational performance.

The involvement of the chaotic search and self-adaptive energy-efficient local search strategy contributes to obtaining a stronger global and local search capability. The computational results demonstrate that the CRMSL achieves better performance than the other two well-known benchmark algorithms in terms of four performance metrics, which is inspiring for future researches on energy-efficient co-scheduling topics in manufacturing industries.

This research fully considers the cooperation and coordination of handling devices to reduce energy consumption, and an improved multi-objective evolutionary algorithm is creatively applied to solve the proposed engineering problem.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

The purpose of this paper is to present the application of an efficient genetic algorithm to deal with the problem of computing the trade‐off curves for non‐uniform circular arrays. In order to answer questions related to the performance of the non‐uniform circular phased arrays, two criteria are considered to evaluate the design: the criteria of minimum main beam width and minimum side lobe level (SLL) during scanning.

The design of non‐uniform circular arrays is modeled as a multi‐objective optimization problem. The Non‐dominated Sorting Genetic Algorithm II (NSGA‐II) is employed as the methodology to solve the resulting optimization problem. This algorithm is considered to be one of the best evolutionary optimizer for multi‐objective problems. It is chosen for its ease of implementation and its efficiency for computation of non‐dominated ranks. The method is based on the survival of the fittest paradigm, where each individual in the population represents a feasible solution of the optimization problem being solved. The concept of fitness is adapted to take into account the concept of solution quality in multi‐objective problems. This evolutionary method can be used effectively for computing the trade‐off curves between the SLL and the main beam width.

The NSGA‐II algorithm can effectively compute the trade‐off curve of different non‐uniform circular arrays. The simulation results presented in this paper show design options that maintain a low SLL and main beam width without pattern distortion during beam steering. Moreover, these trade‐off curves provide a more realistic approach to the solution of the design problem.

The design problem is set to determine which are the best design configurations or separations between the antenna elements and the best amplitude excitations when a circular structure is employed. Owing to the complex feasible region and the non‐linear dependence of optimization criteria from the decision variables, simple traditional and more sophisticated mathematical programming approaches will lead us to local optimal solutions in the case we can apply them. To the best of our knowledge, this multi‐objective optimization problem has not dealt with before, when two or more conflicting design criteria are taken into account. Therefore, the solution to this problem constitutes the main contribution of our paper.

In recent decades, development of effective methods for optimizing a set of conflicted objective functions has been absorbing an increasing interest from researchers. This refers to the essence of real-life engineering systems and complex natural mechanisms which are generally multi-modal, non-convex and multi-criterion. Until now, several deterministic and stochastic methods have been proposed to cope with such complex systems. Advanced soft computational methods such as evolutionary games (cooperative and non-cooperative), Pareto-based techniques, fuzzy evolutionary methods, cooperative bio-inspired algorithms and neuro-evolutionary systems have effectively come to the aid of researchers to build up efficient paradigms with application to vector optimization. The paper aims to discuss this issue.

A novel hybrid algorithm called synchronous self-learning Pareto strategy (SSLPS) is presented for the sake of vector optimization. The method is the ensemble of evolutionary algorithms (EA), swarm intelligence (SI), adaptive version of self-organizing map (CSOM) and a data shuffling mechanism. EA are powerful numerical optimization algorithms capable of finding a global extreme point over a wide exploration domain. SI techniques (the swarm of bees in our case) can improve both intensification and robustness of exploration. CSOM network is an unsupervised learning methodology which learns the characteristics of non-dominated solutions and, thus, enhances the quality of the Pareto front.

To prove the effectiveness of the proposed method, the authors engage a set of well-known benchmark functions and some well-known rival optimization methods. Additionally, SSLPS is employed for optimal design of shape memory alloy actuator as a nonlinear multi-modal real-world engineering problem. The experiments show the acceptable potential of SSLPS for handling both numerical and engineering multi-objective problems.

To the author’s best knowledge, the proposed algorithm is among the rare multi-objective methods which fosters the use of automated unsupervised learning for increasing the intensity of Pareto front (while preserving the diversity). Also, the research evaluates the power of hybridization of SI and EA for efficient search.

The goal of this study is to carry out multi‐objective optimization by considering minimization of surface roughness (Ra) and build time (T) in selective laser sintering (SLS) process, which are functions of “build orientation”. Evolutionary algorithms are applied for this purpose. The performance comparison of the optimizers is done based on statistical measures. In order to find truly optimal solutions, local search is proposed. An important task of decision making, i.e. the selection of one solution in the presence of multiple trade‐off solutions, is also addressed. Analysis of optimal solutions is done to gain insight into the problem behavior.

The minimization of Ra and T is done using two popular optimizers – multi‐objective genetic algorithm (non‐dominated sorting genetic algorithm (NSGA‐II)) and multi‐objective particle swarm optimizers (MOPSO). Standard measures from evolutionary computation – “hypervolume measure” and “attainment surface approximator” have been borrowed to compare the optimizers. Decision‐making schemes are proposed in this paper based on decision theory.

The objects are categorized into groups, which bear similarity in optimal solutions. NSGA‐II outperforms MOPSO. The similarity of spread and convergence patterns of NSGA‐II and MOPSO ensures that obtained solutions are (or are close to) Pareto‐optimal set. This is validated by local search. Based on the analysis of obtained solutions, general trends for optimal orientations (depending on the geometrical features) are found.

A novel and systematic way to address multi‐objective optimization decision‐making post‐optimal analysis is shown. Simulations utilize experimentally derived models for roughness and build time. A further step could be the experimental verification of findings provided in this study.

This study provides a thorough methodology to find optimal build orientations in SLS process. A route to decipher valuable problem information through post‐optimal analysis is shown. The principles adopted in this study are general and can be extended to other rapid prototyping (RP) processes and expected to find wide applicability.

This paper is a distinct departure from past studies in RP and demonstrates the concepts of multi‐objective optimization, decision‐making and related issues.

This study aims to solve the problem of job scheduling and multi automated guided vehicle (AGV) cooperation in intelligent manufacturing workshops.

In this study, an algorithm for job scheduling and cooperative work of multiple AGVs is designed. In the first part, with the goal of minimizing the total processing time and the total power consumption, the niche multi-objective evolutionary algorithm is used to determine the processing task arrangement on different machines. In the second part, AGV is called to transport workpieces, and an improved ant colony algorithm is used to generate the initial path of AGV. In the third part, to avoid path conflicts between running AGVs, the authors propose a simple priority-based waiting strategy to avoid collisions.

The experiment shows that the solution can effectively deal with job scheduling and multiple AGV operation problems in the workshop.

In this paper, a collaborative work algorithm is proposed, which combines the job scheduling and AGV running problem to make the research results adapt to the real job environment in the workshop.