A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

基于改进NSGA-Ⅱ算法的电-气-热综合能源系统多目标优化

随着电力、天然气和热力网络耦合紧密程度不断加深,综合能源系统协同优化成为了新的研究热点。提出一种适用于含非凸约束条件的综合能源系统多目标优化问题的改进NSGA-Ⅱ算法,通过维护全局的帕累托最优解集提升解的搜索效率,同时采用动态调整法,提高在高维等式约束下找到可行解的概率。算例分析验证了该方法的有效性。     

Archery Algorithm: A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge. Therefore, these must be addressed utilizing proper approaches. Based on a random search space, optimization algorithms can find acceptable solutions to problems. Archery Algorithm (AA) is a new stochastic approach for addressing optimization problems that is discussed in this study. The fundamental idea of developing the suggested AA is to imitate the archer's shooting behavior toward the target panel. The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer. The AA is mathematically described, and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions. Furthermore, the proposed algorithm's performance is compared vs. eight approaches, including teaching-learning based optimization, marine predators algorithm, genetic algorithm, grey wolf optimization, particle swarm optimization, whale optimization algorithm, gravitational search algorithm, and tunicate swarm algorithm. According to the simulation findings, the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios, and it can give adequate quasi-optimal solutions to these problems. The analysis and comparison of competing algorithms’ performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.     

An efficient multi-objective optimization approach based on the micro genetic algorithm and its application

In this paper, an efficient multi-objective optimization approach based on the micro genetic algorithm is suggested to solving the multi-objective optimization problems. An external elite archive is used to store Pareto-optimal solutions found in the evolutionary process. A non-dominated sorting is employed to classify the combinational population of the evolutionary population and the external elite population into several different non-dominated levels. Once the evolutionary population converges, an exploratory operator will be performed to explore more non-dominated solutions, and a restart strategy will be subsequently adopted. Simulation results for several difficult test functions indicate that the present method has higher efficiency and better convergence near the globally Pareto-optimal set for all test functions, and a better spread of solutions for some test functions compared to NSGAII. Eventually, this approach is applied to the structural optimization of a composite laminated plate for maximum stiffness in thickness direction and minimum mass.     

Optimal power system generation scheduling by multi-objective genetic algorithms with preferences

Power system generation scheduling is an important issue both from the economical and environmental safety viewpoints. The scheduling involves decisions with regards to the units start-up and shut-down times and to the assignment of the load demands to the committed generating units for minimizing the system operation costs and the emission of atmospheric pollutants.As many other real-world engineering problems, power system generation scheduling involves multiple, conflicting optimization criteria for which there exists no single best solution with respect to all criteria considered. Multi-objective optimization algorithms, based on the principle of Pareto optimality, can then be designed to search for the set of nondominated scheduling solutions from which the decision-maker (DM) must a posteriori choose the preferred alternative. On the other hand, often, information is available a priori regarding the preference values of the DM with respect to the objectives. When possible, it is important to exploit this information during the search so as to focus it on the region of preference of the Pareto-optimal set.In this paper, ways are explored to use this preference information for driving a multi-objective genetic algorithm towards the preferential region of the Pareto-optimal front. Two methods are considered: the first one extends the concept of Pareto dominance by biasing the chromosome replacement step of the algorithm by means of numerical weights that express the DM’ s preferences; the second one drives the search algorithm by changing the shape of the dominance region according to linear trade-off functions specified by the DM.The effectiveness of the proposed approaches is first compared on a case study of literature. Then, a nonlinear, constrained, two-objective power generation scheduling problem is effectively tackled.     

The benefits of adaptive parametrization in multi-objective Tabu Search optimization

In real-world optimization problems, large design spaces and conflicting objectives are often combined with a large number of constraints, resulting in a highly multi-modal, challenging, fragmented landscape. The local search at the heart of Tabu Search, while being one of its strengths in highly constrained optimization problems, requires a large number of evaluations per optimization step. In this work, a modification of the pattern search algorithm is proposed: this modification, based on a Principal Components’ Analysis of the approximation set, allows both a re-alignment of the search directions, thereby creating a more effective parametrization, and also an informed reduction of the size of the design space itself. These changes make the optimization process more computationally efficient and more effective – higher quality solutions are identified in fewer iterations. These advantages are demonstrated on a number of standard analytical test functions (from the ZDT and DTLZ families) and on a real-world problem (the optimization of an axial compressor preliminary design).     

A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling

This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-front. In the second phase, to improve the Pareto-front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over a genetic algorithm in the first phase and three hybrid metaheuristics in the second and third phases. Experiments on the test problems with different structures show that the multi-phase method is a better tool to approximate the efficient set than the global archive sub-population genetic algorithm presented previously.     

Hybrid evolutionary multi-objective algorithms for integrating assembly sequence planning and assembly line balancing

Assembly sequence planning (ASP) and assembly line balancing (ALB) play critical roles in designing product assembly systems. In view of the trend of concurrent engineering, pondering simultaneously over these two problems in the development of assembly systems is significant for establishing a manufacturing system. This paper contemplates the assembly tool change and the assembly direction as measurements in ASP; and further, Equal Piles assembly line strategy is adopted and the imbalanced status of the system employed as criteria for the evaluation concerning ALB. Focus of the paper is principally on proposing hybrid evolutionary multiple-objective algorithms (HEMOAs) for solutions with regard to integrate the evolutionary multi-objective optimization and grouping genetic algorithms. The results provide a set of objectives and amend Pareto-optimal solutions to benefit decision makers in the assembly plan. In addition, an implemented decision analytic model supports the preference selection from the Pareto-optimal ones. Finally, the exemplifications demonstrate the effectiveness and performance of the proposed algorithm. The consequences definitely illustrate that HEMOAs search out Pareto-optimal solutions effectively and contribute to references for the flexible change of assembly system design.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.     

AMGA2: improving the performance of the archive-based micro-genetic algorithm for multi-objective optimization

In this article, an improved Archive-based Micro Genetic Algorithm (referred to as AMGA2) for constrained multi-objective optimization is proposed. AMGA2 is designed to obtain fast and reliable convergence on a wide variety of optimization problems. AMGA2 benefits from the existing literature in that it borrows and improves upon several concepts from existing multi-objective optimization algorithms. Improvements and modifications to the existing diversity assessment techniques and genetic variation operators are also proposed. AMGA2 employs a new kind of selection strategy that attempts to reduce the probability of exploring less desirable search regions. The proposed AMGA2 is a steady-state genetic algorithm that maintains an external archive of best and diverse solutions and a very small working population. AMGA2 has been designed to facilitate the decoupling of the working population, the external archive, and the number of solutions desired as the outcome of the optimization process. Comprehensive benchmarking and comparison of AMGA2 with the current state-of-the-art multi-objective optimization algorithms demonstrate its improved search capability.     

A hybrid multi-objective particle swarm algorithm for a mixed-model assembly line sequencing problem

Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management where diversified customers' demands exist. In this article, three major goals are considered: (i) total utility work, (ii) total production rate variation and (iii) total setup cost. Due to the complexity of the problem, a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) is devised to obtain the locally Pareto-optimal frontier where simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed algorithm in terms of solution quality and diversity level, the algorithm is applied to various test problems and its reliability, based on different comparison metrics, is compared with three prominent multi-objective genetic algorithms, PS-NC GA, NSGA-II and SPEA-II. The computational results show that the proposed hybrid algorithm significantly outperforms existing genetic algorithms in large-sized problems.     

SSABA: Search Step Adjustment Based Algorithm

Finding the suitable solution to optimization problems is a fundamental challenge in various sciences. Optimization algorithms are one of the effective stochastic methods in solving optimization problems. In this paper, a new stochastic optimization algorithm called Search Step Adjustment Based Algorithm (SSABA) is presented to provide quasi-optimal solutions to various optimization problems. In the initial iterations of the algorithm, the step index is set to the highest value for a comprehensive search of the search space. Then, with increasing repetitions in order to focus the search of the algorithm in achieving the optimal solution closer to the global optimal, the step index is reduced to reach the minimum value at the end of the algorithm implementation. SSABA is mathematically modeled and its performance in optimization is evaluated on twenty-three different standard objective functions of unimodal and multimodal types. The results of optimization of unimodal functions show that the proposed algorithm SSABA has high exploitation power and the results of optimization of multimodal functions show the appropriate exploration power of the proposed algorithm. In addition, the performance of the proposed SSABA is compared with the performance of eight well-known algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), and Tunicate Swarm Algorithm (TSA). The simulation results show that the proposed SSABA is better and more competitive than the eight compared algorithms with better performance.     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

An improved imperialist competitive algorithm for multi-objective optimization

This article proposes an improved imperialistic competitive algorithm to solve multi-objective optimization problems. The proposed multi-objective imperialistic competitive algorithm (MOICA) uses the elitist strategy, based on the mutation and crossover as in genetic algorithms, and the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Three performance metrics are used to evaluate the performance of the new algorithm: convergence to the true Pareto-optimal set, solution diversity and robustness, characterized by the variance over 10 runs. To validate the efficiency of the proposed algorithm, several multi-objective standard test functions with true solutions are used. The obtained results show that the MOICA outperforms most of the methods available in the literature. The proposed algorithm can also handle multi-objective engineering design problems with high dimensions.     

Combining mutual information and stable matching strategy for dynamic evolutionary multi-objective optimization

It is reasonable to assume that the changing of the optimization environment is smooth when considering a dynamic multi-objective optimization problem. Learning techniques are widely used to explore the dependence structure to facilitate population re-initialization in evolutionary search paradigms. The aim of the learning techniques is to discover knowledge from history information, thereby to track the movement of the optimal front quickly through good initialization when a change occurs. In this article, a new learning strategy is proposed, where the main ideas are (1) to use mutual information to identify the relationship between previously found approximated solutions; (2) to use a stable matching mechanism strategy to associate previously found optimal solutions bijectively; and (3) to re-initialize the new population based on a kinematics model. Controlled experiments were carried out systematically on some widely used test problems. Comparison against several state-of-the-art dynamic multi-objective evolutionary algorithms showed comparable performance in favour of the developed algorithm.     

基于分级免疫萤火虫算法的桥梁振动传感器优化布置研究

针对结构健康监测系统设计的振动传感器优化布置问题,在基本萤火虫算法的基础上引入等级划分策略和免疫机制,提出了一种分级免疫萤火虫算法。采用二重结构编码,弥补了基本萤火虫算法只能用于连续优化问题的不足;建立等级划分制度,使不同等级种群内部形成独立的搜索空间,维持了种群多样性,并让优质个体得以保留;引进免疫机制,进行萤火虫的选择、记忆、交叉和变异,增强了算法的全局搜索能力和局部寻优能力;文末利用足尺Benchmark桥梁模型,对算法参数进行了敏感性分析,并开展了振动传感器优化布置方案的选择。结果表明,与基本离散型萤火虫算法相比,分级免疫萤火虫算法的计算效率和寻优结果均有显著提升,能够很好地解决振动传感器优化布置问题。     

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.     

A hybrid Jaya algorithm for reliability–redundancy allocation problems

This article proposes an efficient improved hybrid Jaya algorithm based on time-varying acceleration coefficients (TVACs) and the learning phase introduced in teaching–learning-based optimization (TLBO), named the LJaya-TVAC algorithm, for solving various types of nonlinear mixed-integer reliability–redundancy allocation problems (RRAPs) and standard real-parameter test functions. RRAPs include series, series–parallel, complex (bridge) and overspeed protection systems. The search power of the proposed LJaya-TVAC algorithm for finding the optimal solutions is first tested on the standard real-parameter unimodal and multi-modal functions with dimensions of 30–100, and then tested on various types of nonlinear mixed-integer RRAPs. The results are compared with the original Jaya algorithm and the best results reported in the recent literature. The optimal results obtained with the proposed LJaya-TVAC algorithm provide evidence for its better and acceptable optimization performance compared to the original Jaya algorithm and other reported optimal results.     

Stress‐enhanced clonal selection algorithm for structural topology optimization

Recently, numerous modified versions of immune algorithms (IAs) have been adopted in both theoretical and practical applications. However, few have been proposed for solving structural topology optimization problems. In addition, the design connectivity handling and one‐node connected hinge prevention, which are vital in the application of population‐based methods with binary representation for structural topology optimization, have not been applied to IAs in the literature. A stress‐enhanced clonal selection algorithm (SECSA) incorporating an IA with a dominance‐based constraint‐handling technique and a new stress‐enhanced hypermutation operator is proposed to rectify those deficiencies. To demonstrate the high viability of the presented method, comparisons between the presented SECSA and genetic algorithm‐based methods were made on minimum compliance and minimum weight benchmark structural topology design problems in two‐dimensional, three‐dimensional, and multiloading cases. In each case, SECSA was shown to be competitive in terms of convergence speed and solution quality. The main goal of this study is not only to further explore the capabilities of IAs, but also to show that an IA with appropriate enhancements can lead to the development of attractive computational tools for global search in structural topology optimization. Copyright © 2011 John Wiley & Sons, Ltd.