ADAPTIVE MULTI-OBJECTIVE OPTIMIZATION BASED ON NONDOMINATED SOLUTIONS

An adaptive hybrid model (AHM) based on nondominated solutions is presented in this study for multi-objective optimization problems (MOPs). In this model, three search phases are devised according to the number of nondominated solutions in the current population: 1) emphasizing the dominated solutions when the population contains very few nondominated solutions; 2) maintaining the balance between nondominated and dominated solutions when nondominated ones become more; 3) when the population consists of adequate nondominated solutions, dominated ones could be ignored and the isolated nondominated ones are allocated more computational budget by their crowding distance values for heuristic search. To exploit local information efficiently, a local incremental search algorithm, LISA, is proposed and merged into the model. This model maintains the adaptive mechanism between the optimization process by the online discovered nondominated solutions. The proposed model is validated using five ZDT and five DTLZ problems. Compared with three other state-of-the-art multi-objective algorithms, namely NSGA-II, SPEA2, and PESA-II, AHM achieves comparable results in terms of convergence and diversity metrics. Finally, the sensitivity of introduced parameters and scalability to the number of objectives are investigated.     

A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems

This paper proposes a self-organized speciation based multi-objective particle swarm optimizer (SS-MOPSO) to locate multiple Pareto optimal solutions for solving multimodal multi-objective problems. In the proposed method, the speciation strategy is used to form stable niches and these niches/subpopulations are optimized to search and maintain Pareto-optimal solutions in parallel. Moreover, a self-organized mechanism is proposed to improve the efficiency of the species formulation as well as the performance of the algorithm. To maintain the diversity of the solutions in both the decision and objective spaces, SS-MOPSO is incorporated with the non-dominated sorting scheme and special crowding distance techniques. The performance of SS-MOPSO is compared with a number of the state-of-the-art multi-objective optimization algorithms on fourteen test problems. Moreover, the proposed SS-MOSPO is also employed to solve a real-life problem. The experimental results suggest that the proposed algorithm is able to solve the multimodal multi-objective problems effectively and shows superior performance by finding more and better distributed Pareto solutions.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

基于决策者偏好区域的多目标粒子群算法研究*

多目标优化问题中,决策者往往只对目标空间的某一区域感兴趣,因此需要在这一特定的区域能够得到比较稠密的Pareto解,但传统的方法却找出全部的Pareto前沿,决策效率不高。针对该问题,给出了基于决策者偏好区域的多目标粒子群优化算法。它只求出与决策者偏好区域相关的部分Pareto最优集,从而减少了进化代数,加快收敛速度,有利于决策者进行更有效的决策。算法把解与偏好区域的距离作为影响引导者选择和剪枝策略的一个因素,运用格栅方法实现解在Pareto边界分布的均匀性。仿真结果表明该算法是有效的。     

一种基于相角映射的改进多目标粒子群优化算法

提出一种相角粒子群优化算法求解多目标优化问题。该算法采用相角映射实现了粒子在相角空间上仅依赖于归一化多目标函数的快速搜索,在粒子飞行信息共享机制上引入共享池概念,提出基于关联支配排序和相似度排序的共享池更新策略,提高了Pareto解的多样性。采用Sigma领导策略和混沌变异操作,平衡了算法的快速搜索能力和全局寻优能力。标准多目标测试函数和电力系统广域阻尼控制多目标优化算例表明了所提出算法的可行性和有效性。     

基于病毒进化遗传算法的复杂产品设计任务规划

为提高复杂决策环境下产品设计任务规划的科学性,针对设计项目中资源以知识型员工为主的特点,综合考虑项目时间最短、完成质量最高及设计人员负载均衡等问题建立多目标优化的数学模型.在此基础上,为提高横向搜索能力以获得多样性解,提出了基于病毒进化机制的求解算法,其中引入多种群思想以使算法适用于多目标问题,并采用非支配排序保证算法全局搜索能力.最后通过仿真分析对文中算法进行了验证.     

Multi-objective optimization using teaching-learning-based optimization algorithm

Two major goals in multi-objective optimization are to obtain a set of nondominated solutions as closely as possible to the true Pareto front (PF) and maintain a well-distributed solution set along the Pareto front. In this paper, we propose a teaching-learning-based optimization (TLBO) algorithm for multi-objective optimization problems (MOPs). In our algorithm, we adopt the nondominated sorting concept and the mechanism of crowding distance computation. The teacher of the learners is selected from among current nondominated solutions with the highest crowding distance values and the centroid of the nondominated solutions from current archive is selected as the Mean of the learners. The performance of proposed algorithm is investigated on a set of some benchmark problems and real life application problems and the results show that the proposed algorithm is a challenging method for multi-objective algorithms.     

基于物理规划的航空保障多目标优化模型

根据作战需求确定优化权衡目标,以使用保障需求和技术可行性为约束条件,以保障能力指标集合,以备件储备量的组合为决策变量,建立多个单目标优化模型和多目标优化模型,提出了基于物理规划的航空保障能力多目标优化方法,结合粒子群算法得到了满足设计者偏好的最佳航材备件方案.设计了航空保障能力系数的满意等级,构造了各优化目标的偏好函数和综合偏好函数,使整个设计过程更加灵活地反映决策者偏好,减轻大规模多目标设计问题的计算负担,使军用机群的保障能力更适合实际作战要求,同时通过对比单目标优化的结果,验证了算法的有效性.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

Automatic calibration of a rapid flood spreading model using multiobjective optimisations

In order to successfully calibrate a numerical model, multiple criteria should be considered. Multi-objective differential evolution (MODE) and multi-objective particle swarm optimisation (MOPSO) have proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of two population based search algorithms [nondominated sorting particle swarm optimisation (NSPSO), and nondominated sorting differential evolution (NSDE)] when applied to calibration of a rapid flood spreading model (RFSM). Formulation of an automatic calibration strategy for the RFSM is outline. The simulations show that the both methods possess the ability to find the optimal Pareto front.     

一种优化模糊神经网络的多目标微粒群算法

模糊神经网络优化是一个多目标优化问题．通过对模糊神经网络和微粒群算法的深入分析，提出了一种多目标微粒群算法．在算法中将网络的精确性和复杂性分别作为目标进行优化，再用一种启发性分量加权均值法来选取个体极值和全局极值．算法能够引导粒子较快地向非劣最优解区域移动并最终获得多个非劣最优解，为模糊神经网络的精确性和复杂性的折中寻优问题提供了一种解决方法．茶味觉信号识别的仿真实验验证了该算法的有效性．     

基于局部搜索与混合多样性策略的多目标粒子群算法

为了提高算法的收敛性与非支配解集的多样性,提出一种基于局部搜索与混合多样性策略的多目标粒子群算法（LH-MOPSO）.该算法使用增广Lagrange乘子法对非支配解进行局部搜索以快速接近Pareto最优解;利用基于改进的Maximin适应值函数与拥挤距离的混合多样性策略对非支配解集进行维护以保留解的多样性,同时引入高斯变异算子以避免算法早熟收敛;最后针对多目标约束优化问题,给出一种有效的约束处理方法.实验研究表明该算法具有良好的优化性能.     

融合分区和局部搜索的多模态多目标优化

为解决多模态多目标优化中种群多样性维持难和所得等价解数量不足问题,基于分区搜索和局部搜索,本研究提出一种融合分区和局部搜索的多模态多目标粒子群算法(multimodal multi-objective particle swarm optimization combing zoning search and local search,ZLS-SMPSO-MM)。在所提算法中,整个搜索空间被分割成多个子空间以维持种群多样性和降低搜索难度;然后,使用已有的自组织多模态多目标粒子群算法在每个子空间搜索等价解和挖掘邻域信息,并利用局部搜索能力较强的协方差矩阵自适应算法对有潜力的区域进行精细搜索。通过14个多模态多目标优化问题测试,并与其他5种知名算法进行比较;实验结果表明ZLS-SMPSO-MM在决策空间能够找到更多的等价解,且整体性能要好于所比较算法。     

Handling multiple objectives with biogeography-based optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization (BBMO) is introduced, which uses the cluster attribute of islands to naturally decompose the problem. The proposed algorithm makes use of nondominated sorting approach to improve the convergence ability effciently. It also combines the crowding distance to guarantee the diversity of Pareto optimal solutions. We compare the BBMO with two representative state-of-the-art evolutionary multi-objective optimization methods, non-dominated sorting genetic algorithm-II (NSGA-II) and archive-based micro genetic algorithm (AMGA) in terms of three metrics. Simulation results indicate that in most cases, the proposed BBMO is able to find much better spread of solutions and converge faster to true Pareto optimal fronts than NSGA-II and AMGA do.     

Multi-objective differential evolution with performance-metric-based self-adaptive mutation operator for chemical and biochemical dynamic optimization problems

Each mutation operator of differential evolution (DE) algorithm is generally suitable for certain specific types of multi-objective optimization problems (MOPs) or particular stages of the evolution. To automatically select an appropriate mutation operator for solving MOPs in different phases of the evolution, a multi-objective differential evolution with performance-metric-based self-adaptive mutation operator (MODE-PMSMO) is proposed in this study. In MODE-PMSMO, a modified inverted generational distance (IGD) is utilized to evaluate the performance of each mutation operator and guide the evolution of mutation operators. The proposed MODE-PMSMO is then compared with seven multi-objective evolutionary algorithms (MOEAs) on five bi-objective and five tri-objective optimization problems. Generally, MODE-PMSMO exhibits the best average performance among all compared algorithms on ten MOPs. Additionally, MODE-PMSMO is employed to solve four typical multi-objective dynamic optimization problems in chemical and biochemical processes. Experimental results indicate that MODE-PMSMO is suitable for solving these actual problems and can provide a set of nondominated solutions for references of decision makers.     

目标空间映射策略的高维多目标粒子群优化算法

为了平衡优化算法在高维多目标优化问题中收敛性和多样性之间的关系,增加算法的选择压力,本文提出了一种基于目标空间映射策略的高维多目标粒子群优化算法(many-objective particle swarm optimization algorithm based on objective space mapping strategy,MOPSO-OSM)。在求解高维多目标优化问题时,Pareto准则难以从众多的非支配解中确定最优“折中”解,因此将高维多目标空间映射为以收敛性和多样性评价指标的2维空间,再将上述2维空间根据性能指标的优劣划分为4个不同区域。同时,使用反向学习策略提高算法跳出局部最优的能力。实验表明,MOPSO-OSM算法可以有效平衡收敛性和多样性之间的关系,达到求解复杂多目标优化问题的目的。     

A particle swarm approach for optimizing a multi-stage closed loop supply chain for the solar cell industry

In order to implement sustainable strategies in a supply chain, enterprises should provide highly favorable and effective solutions for reducing carbon dioxide emissions, which brings out the issues of designing and managing a closed-loop supply chain (CLSC). This paper studies an integrated CLSC network design problem with cost and environmental concerns in the solar energy industry from sustainability perspectives. A multi-objective closed-loop supply chain design (MCSCD) model has been proposed, in consideration of many practical characteristics including flow conservation at each production/recycling unit of forward/reverse logistics (FL/RL), capacity expansion, and recycled components. A deterministic multi-objective mixed integer linear programming (MILP) model capturing the tradeoffs between the total cost and total CO₂ emissions was developed to address the multistage CSLC design problem. Subsequently, a multi-objective PSO (MOPSO) algorithm with crowding distance-based nondominated sorting approach is developed to search the near-optimal solution of the MCSCD model. The computational study shows that the proposed MOPSO algorithm is suitable and effective for solving large-scale complicated CLSC structure than the conventional branch-and-bound optimization approach. Analysis results show that an enterprise needs to apply an adequate recycling strategy or energy saving technology to achieve a better economic effectiveness if the carbon emission regulation is applied. Consequently, the Pareto optimal solution obtained from MOPSO algorithm may give the superior suggestions of CLSC design, such as factory location options, capacity expansion, technology selection, purchasing, and order fulfillment decisions in practice.     

An augmented multi-objective particle swarm optimizer for building cluster operation decisions

It is envisioned that other than the grid-building communication, the smart buildings could potentially treat connected neighborhood buildings as a local buffer thus forming a local area energy network through the smart grid. As the hardware technology is in place, what is needed is an intelligent algorithm that coordinates a cluster of buildings to obtain Pareto decisions on short time scale operations. Research has proposed a memetic algorithm (MA) based framework for building cluster operation decisions and it demonstrated the framework is capable of deriving the Pareto solutions on an 8-h operation horizon and reducing overall energy costs. While successful, the memetic algorithm is computational expensive which limits its application to building operation decisions on an hourly time scale. To address this challenge, we propose a particle swarm framework, termed augmented multi-objective particle swarm optimization (AMOPSO). The performance of the proposed AMOPSO in terms of solution quality and convergence speed is improved via the fusion of multiple search methods. Extensive experiments are conducted to compare the proposed AMOPSO with nine multi-objective PSO algorithms (MOPSOs) and multi-objective evolutionary algorithms (MOEAs) collected from the literature. Results demonstrate that AMOPSO outperforms the nine state-of-the-art MOPSOs and MOEAs in terms of epsilon, spread, and hypervolume indicator. A building cluster case is then studied to show that the AMOPSO based decision framework is able to make hourly based operation decisions which could significantly improve energy efficiency and achieve more energy cost savings for the smart buildings.     

多目标粒子群和人工蜂群混合优化的阈值图像分割算法

在图像分割中,为了准确地把目标和背景分离出来,提出了一种基于多目标粒子群和人工蜂群混合优化的阈值图像分割算法。在多目标优化的框架下,将改进的类间方差准则和最大熵准则作为适应度函数,通过粒子群和蜂群混合优化这2个适应度函数来获得1组非支配解。同时,为了提高全局和局部搜索能力,在蜂群进化时,将粒子群的全局最优解引入到人工蜂群算法的雇佣蜂阶段蜜源的更新中,并对搜索方程进行改进。最后通过类间差异和改进的类内差异的加权比值,从一组非支配解中选取最优阈值。实验结果表明,该算法能够取得理想的分割结果。     

Multi-objective optimal scheduling of reconfigurable assembly line for cloud manufacturing

We propose a multi-objective optimization scheduling model to improve the production efficiency of a reconfigurable assembly line. We aim to minimize the costs of assembly line reconstruction, achieve the production load equalization, and minimize the delayed workload using this model. However, the proposed multi-objective optimization model is significantly complex for conventional mathematical optimization methods. Thus, we present an efficient solution approach based on a distance sorting particle swarm optimization. Finally, a case study is conducted to illustrate the feasibility and efficiency of the proposed method. Experimental results indicate that our proposed approach can significantly improve the production efficiency (i.e. increased production load balance, minimized reconstruction cost, and minimized delayed workload).