Particle swarm optimization with query-based learning for multi-objective power contract problem

Particle swarm optimization (PSO) is one of the most important research topics on swarm intelligence. Existing PSO techniques, however, still contain some significant disadvantages. In this paper, we present a new QBL-PSO algorithm that uses QBL (query-based learning) to improve both the exploratory and exploitable capabilities of PSO. Here, we apply a QBL method proposed in our previous research to PSO, and then test this new algorithm on a real case study on problems of power conservation. Our algorithm not only broadens the search diversity of PSO, but also improves its precision. Conventional PSO often snag on local solutions when performing queries, instead of finding better global solutions. To resolve this limitation, when particles converge in nature, we direct some of them into an “ambiguous solution space” defined by our algorithm. This paper introduces two ways to invoke this QBL algorithm. Our experimental results confirm that the proposed method attains better convergence to the global best solution. Finally, we present a new PSO model for solving multi-objective power conservation problems. Overall, this model successfully reduces power consumption, and to our knowledge, this paper represents the first attempt within the literature to apply the QBL concept to PSO.     

一类区间多目标粒子群优化算法

针对区间参数多目标优化问题,提出一种基于模糊支配的多目标粒子群优化算法。首先,定义基于决策者悲观程度的模糊支配关系,用于比较解的优劣;然后,定义一种适于区间目标值的拥挤距离,以更新外部存储器并从中选择领导粒子;最后,对多个区间多目标测试函数进行仿真实验,实验结果验证了所提出算法的有效性。     

求解多目标优化问题的一种多子群体进化算法

提出一种新的多目标粒子群优化（MOPSO）算法,根据多目标优化问题（MOP）的特点,将一个进化群体分成若干个子群体,利用非劣支配的概念构造全局最优区域,用以指导整个粒子群的进化．通过子群体间的信息交换．使整个群体分布更均匀,并且避免了局部最优,保证了解的多样性,通过很少的迭代次数便可得到分布均匀的Pareto有效解集．数值实验表明了该算法的有效性.     

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.     

基于混沌的多目标粒子群优化算法

针对多目标优化问题,提出了一种改进的粒子群算法.该算法为了寻找新解,引入了混沌搜索技术,同时采用了一种新的方法--拥挤距离法定义解的适应度.并采取了精英保留策略,在提高非劣解集多样性的同时,使解集更加趋近于Pareto集.最后,把算法应用到4个典型的多目标测试函数.数值结果表明,该算法能够有效的收敛到Pareto非劣最优目标域,并沿着Pareto非劣目标域有很好的分散性.     

一种多目标粒子群改进算法的研究

针对多目标粒子群优化过程中的粒子飞行偏向性和多样性损失问题,提出一种基于最大最小适应函数的改进算法．该算法在最大最小适应函数的计算中引入了函数相对值算法和ε-支配的概念,并提出了变ε-支配的策略,改进了最大最小适应函数的计算方法,解决了粒子飞行过程中的偏向性和多样性损失问题,加快了算法的收敛速度．将该改进算法应用于直流变频压缩机启动时峰值电流和启动转速的优化问题,应用结果表明该算法收敛速度快且效果良好．     

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.     

基于拥挤度与变异的动态微粒群多目标优化算法

提出一种动态微粒群多目标优化算法(DCMOPSO),算法中的惯性权重和加速因子动态变化以增强算法的全局搜索能力,并采用拥挤度的方法对外部档案进行维护以增加非劣解的多样性.在维护过程中,从外部档案中按拥挤度为每个微粒选择全局最好位置,同时使用变异操作避免算法早熟.通过几个典型的多目标测试函数对DCMOPSO算法的性能进行了测试,并与多目标优化算法MOPSO和NSGA-Ⅱ进行对比.结果表明,DCMOPSO算法具有良好的搜索性能.     

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.     

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.     

一种模糊偏好排序的多目标粒子群算法*

为了将决策者对各目标属性的模糊评判信息转换为目标偏好信息,首先将模糊语义转换为三角模糊数,利用模糊数的广义加法、近似乘法和标量乘法进行计算, 从而将决策者对目标属性的离散意见转换为对各目标的综合意见;然后采用多指标模糊排序法确定决策者权重,通过定义一种模糊综合排序指标来确定各目标偏好权重,依据目标权重构建判断多目标Pareto解的适应度函数,并采用粒子群算法对多目标问题进行求解;最后通过一个算例来说明该算法的实用性和有效性。     

Multi-Objective Particle Swarm Optimization with time variant inertia and acceleration coefficients

In this article we describe a novel Particle Swarm Optimization (PSO) approach to multi-objective optimization (MOO), called Time Variant Multi-Objective Particle Swarm Optimization (TV-MOPSO). TV-MOPSO is made adaptive in nature by allowing its vital parameters (viz., inertia weight and acceleration coefficients) to change with iterations. This adaptiveness helps the algorithm to explore the search space more efficiently. A new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non-dominated fronts, while retaining at the same time the convergence to the Pareto-optimal front. TV-MOPSO has been compared with some recently developed multi-objective PSO techniques and evolutionary algorithms for 11 function optimization problems, using different performance measures.     

一种新的多目标粒子群优化算法

论文提出了一种基于拥挤度和动态惯性权重聚合的多目标粒子群优化算法,该算法采用Pareto支配关系来更新粒子的个体最优值,用外部存档策略保存搜索过程中发现的非支配解;采用适应值拥挤度裁剪归档中的非支配解,并从归档中的稀松区域随机选取精英作为粒子的全局最优位置,以保持解的多样性;采用动态惯性权重聚合的方法以使算法尽可能地逼近各目标的最优解。仿真结果表明,该算法性能较好,能很好地求解多目标优化问题。     

Physical programming for preference driven evolutionary multi-objective optimization

Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designer's point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.     

求解多目标优化问题的自适应粒子群算法

提出了一种基于自适应惯性权重的多目标粒子群优化算法AWMOPSO,采用新的适应值分配机制,在搜索过程中根据粒子的适应值对粒子进行分类,动态调整粒子的惯性权重以控制粒子的开发和探索能力。用外部精英集保存非支配解,并通过拥挤距离维持解的多样性。引入精英迁移和局部扰动策略,提高收敛的速度和精度。典型的测试函数的计算结果表明了算法能够快速逼近Pareto最优前沿,是求解多目标优化问题的有效方法。     

A multi-objective particle swarm optimization for project selection problem

Selecting the most appropriate projects out of a given set of investment proposals is recognized as a critical issue for which the decision maker takes several aspects into consideration. Since many of these aspects may be conflicting, the problem is rendered as a multi-objective one. Consequently, we consider a multi-objective project selection problem in this study where total benefits are to be maximized while total risk and total coat must be minimized, simultaneously. Since solving an NP-hard problem becomes demanding as the number of projects grows, a multi-objective particle swarm with new selection regimes for global best and personal best for swarm members is designed to find the locally Pareto-optimal frontier and is compared with a salient multi-objective genetic algorithm, i.e. SPEAII, based on some comparison metrics with random instances.     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.     

On convergence of the multi-objective particle swarm optimizers

Several variants of the particle swarm optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization (MO) problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that govern the convergence behavior of the algorithm to the optimal Pareto front in the objective function space. Computer simulations over benchmark MO problems have also been provided to substantiate the theoretical derivations.     

一种多目标优化问题的理想灰色粒子群算法*

针对逼近理想解的排序方法对Pareto前端的距离跟踪以及灰色关联度能够很好地分析非劣解集曲线与Pareto最优解集曲线的相似性,提出了一种求解多目标优化问题的理想灰色粒子群算法。该算法利用理想解理论与灰色关联度理论来求解粒子与理想解之间的相对适应度和灰色关联度系数,把两者的和定义为相对理想度,通过相对理想度来判别粒子的优劣,以确定个体极值和全局极值。通过四组不同类型的基准函数测试算法性能,并与目标加权法和灰色粒子群算法比较分析,结果表明该算法能够较好地收敛到Pareto最优解集,不但具有较好的收敛性和分布     

用于约束多目标优化问题的混合粒子群算法

针对约束多目标优化问题,结合Pareto支配思想、锦标赛选择和排挤距离技术,采用双种群搜索策略,引进免疫机制,对传统的粒子更新策略进行改进,提出一种用于求解约束多目标优化问题的混合粒子群算法。通过4个标准约束多目标函数进行测试,测试结果表明,该方法有效可行,相比传统多目标优化算法更优。