用于结构优化设计的改进多目标群搜索算法

在多目标群搜索算法（multi-objective group search optimization, MGSO）基本原理的基础上,结合Pareto最优解理论,提出了基于约束改进的多目标群搜索算法（IMGSO）,并应用于多目标的结构优化设计．算法的改进主要有3个方面：第一,引入过渡可行域的概念来处理约束条件;第二,利用庄家法来构造非支配解集;最后,结合禁忌搜索算法和拥挤距离机制来选择发现者,以避免解集过早陷入局部最优,并提高收敛精度．采用IMGSO优化算法分别对平面和空间桁架结构进行了离散变量的截面优化设计,并与MGSO优化算法的计算结果进行了比较,结果表明改进的多目标群搜索优化算法IMGSO与MGSO算法相比具有更好的收敛精度.通过算例表明：IMGSO算法得到的解集中的解能大部分支配MGSO算法的解,在复杂高维结构中IMGSO算法的优越性更加明显,且收敛速度也有一定的提高,可有效应用于多目标的实际结构优化设计．     

基于改进NSGA-Ⅱ的仿人机器人上楼梯运动规划方法

针对当前仿人机器人运动优化算法多采用对能耗、稳定性及速度等单目标优化而存在一定的局限性的问题,提出了一种基于多目标优化的仿人机器人上楼梯运动优化方法.针对NSGA-Ⅱ——经典的带精英策略的非支配排序遗传算法(NSGA)的快速非支配排序效率较低的问题,提出了一种基于自调整二叉搜索树的改进NSGA-Ⅱ方法,并采用改进的NSGA-Ⅱ算法实现了仿人机器人上楼梯运动参数优化.通过仿真和实际实验对比了优化前后仿人机器人的能耗和稳定性.实验表明,采用这种方法能克服单目标优化的缺点,在同时满足多个目标需求的同时有效地实现仿人机器人上楼梯.     

基于分布式光伏发电的多目标分时电价优化策略

现有电力定价研究大多为峰谷分时定价,时段划分方式单一且大多采用传统非支配排序遗传算法-II求解多目标问题。针对这个问题,提出一种基于分布式光伏发电的多目标分时电价优化策略。建立用电量与电价响应模型,基于等效负荷进行时段划分,以负荷方差最小,等效负荷的峰谷差最小,用户满意度指数最大为目标,建立多目标非线性分布式光伏分时定价模型,并提出基于邻域搜索的多目标遗传算法求解。数值实验结果表明,供电稳定性提高了37.77%,分布式光伏发电的利用率提高了4.51%,用户满意度为74.3%;且提出的求解算法要优于常用的非支配排序遗传算法-II,表明本文提出的定价策略是有效的。     

一种基于近似模型管理的多目标优化方法

针对实际工程优化问题,为了提高效率和减少近似模型带来的误差,提出一种基于模型管理的多目标优化方法。利用加强径向基插值函数在整个寻优区域内构造目标和约束的近似模型,结合微型多目标遗传算法寻找当前非支配解。通过模型管理方法更新近似模型,并控制由于近似模型带来的误差和更新次数,最后将误差控制在一定范围内的多个非支配解当作实际问题的解。在测试函数中验证了此方法的效率及非支配解的精度和分布的均匀性。最后成功应用于车身薄壁构件的耐撞性优化中,表明了可用于求解复杂的工程优化问题。     

基于MOABCO的多目标测试用例优先级排序

为了提高回归测试的效率,提出了一种基于多目标人工蜂群优化(Multi-Objective Artificial Bee Colony Optimization, MOABCO)算法的多目标测试用例优先级排序(Multi-Objective Test Case Prioritization, MOTCP)方法.针对标准多目标人工蜂群(Multi-Objective Artificial Bee Colony, MOABC)算法容易陷入局部最优解的问题,将差分变异策略融入到新蜜源更新阶段,且基于信息熵改进新蜜源选择方法,以避免算法陷入局部最优并增强了全局搜索能力;然后,将代码覆盖率和测试用例有效执行时间作为优化目标,并用MOABCO算法求Pareto最优解集,以解决MOTCP问题.实验结果表明, MOABCO算法求得的Pareto最优解集在逼近性和分布均匀性上均优于MOABC算法;在解决MOTCP问题上,相对于NSGA-II算法具有更高的收敛速度和更高的缺陷检测率.     

熔融沉积快速成型零件成型方向的多目标优化

为了实现熔融沉积快速成型（FDM）中零件成型精度和成型效率的协同优化,基于零件成型方向对成型精度和成型效率的影响进行分析,以体积误差最小、零件成型方向上高度最低以及所需支撑体积最小为目标,建立了零件成型方向的多目标优化模型。设计了基于非支配排序遗传算法的智能求解算法,通过对模型的优化计算得到零件成型方向的Pareto解集,实现了FDM零件成型方向的智能优化。最后通过实例验证了所建模型的正确性与算法的有效性。     

基于分组策略的多目标三维装箱算法

目的 针对现有三维装箱算法优化目标单一、优化效率低的问题,提出适用于求解大规模货物装载问题的多目标装箱算法,以提高装箱规划效率,确保货物运输安全。方法 考虑5种现实约束条件,以体积利用率和装载垛型重心偏移量为优化目标,建立多目标货物装载优化模型。采用拟人式装箱对货物进行预分组,减小决策空间,然后结合分组信息与装箱算法生成初始解;引入数据驱动的装箱交叉算子提高算法收敛性;设计多策略变异算子提高算法结果的多样性。结果 以公共数据集和真实航空货物数据作为实验数据进行实验。实验结果表明,在满足多种约束条件下,集装箱装载强异构货物平均体积利用率达到92.0%,重心位置空间偏移从20 cm减少到7.5 cm,并且算法运行时间减少了73.5%。结论 本文所提算法应用于求解大规模多目标三维装箱问题,提高了装箱质量和效率,可为三维装箱算法的工程应用提供参考。     

平流层飞艇的多目标优化与决策

该文建立了以平流层飞艇阻力最小、自重最轻、极限承载力最大及刚度最大为优化目标的多目标优化模型;采用强度Pareto进化算法(SPEA)进行了多目标优化设计;基于优化所得的Pareto解集,采用基于信噪比的决策方法选择满足实际需要的最终方案。结果表明:采用的SPEA算法是合理有效的,可以得到非劣解分布较均匀的Pareto曲面;通过基于信噪比的决策方法,可从非劣解集中获得满足实际要求的最稳健设计方案。     

用于约束多目标优化问题的改进蚁群遗传算法

针对多目标蚁群遗传算法(MOAGA)解集边界分布不均的问题,提出改进算法,解决连续空间中带约束条件多目标优化问题.改进算法在基本MOAGA算法的基础上,在选择中引入一定比例的边界决策、单目标最优决策,并提高边界决策的交叉率.实验证明,改进算法解决了基本算法解集分布边界疏中间密的问题,并且能更快的获得散布性较好的Pareto最优解集.     

一种基于“探测"与“开采"的多目标进化算法

针对实践中多目标优化问题(MOPs)的Pareto解集(PS)未知且比较复杂的特性,提出了一种基于"探测"(Exploration)与"开采"(Exploitation)的多目标进化算法(MOEA)——MOEA/2E。该算法在进化过程中采用"探测"与"开采"相结合的方法,用进化操作不断地探测新的搜索区域,用局部搜索充分开采优秀的解区域,并用隐最优个体保留机制保存每一代的最优个体。与目前最流行且有效的多目标进化算法NSGA-Ⅱ及SPEA-Ⅱ进行的比较实验结果表明,MOEA/2E获得的Pareto最优解集具有更好的收敛性与分布性。     

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

An entropy-based three-stage approach for multi-objective system reliability optimization considering uncertainty

This article presents a three-stage approach for solving multi-objective system reliability optimization problems considering uncertainty. The reliability of each component is considered in the formulation as a component reliability estimate in the form of an interval value and discrete values. Component reliability may vary owing to variations in the usage scenarios. Uncertainty is described by defining a set of usage scenarios. To address this problem, an entropy-based approach to the redundancy allocation problem is proposed in this study to identify the deterministic reliability of each component. In the second stage, a multi-objective evolutionary algorithm (MOEA) is applied to produce a Pareto-optimal solution set. A hybrid algorithm based on k-means and silhouettes is performed to select representative solutions in the third stage. Finally, a numerical example is presented to illustrate the performance of the proposed approach.     

Highly reliable optimal solutions to multi-objective problems and their evolution by means of worst-case analysis

In the current article, high reliability in the presence of uncertainty is of interest. Therefore, no violation of constraints by any solution, although uncertainty exists, is mandatory. The article studies uncertainties in which the boundaries of uncertainty are known. To allow a high reliability, the notion of worst-violation set is introduced. Moreover, two possible measures to assess the extent of the violation of the constraints by a solution, which is subjected to uncertainty, are suggested. One of these measures is then introduced into a multi-objective evolutionary algorithm (MOEA) in order to search for optimal reliable solutions. It is shown that the approach applies a search towards solutions with optimal performances while taking into account high reliability. The suggested approach is the only one available so far (to the authors’ best knowledge), which treats reliability through evolutionary multi-objective search, while not assuming any probability distribution of the uncertainty.     

Non-dominated archiving multi-colony ant algorithm for multi-objective optimization: Application to multi-purpose reservoir operation

Multi-objective optimization using heuristic methods has been established as a subdiscipline that combines the fields of heuristic computation and classical multiple criteria decision making. This article presents the Non-dominated Archiving Ant Colony Optimization (NA-ACO), which benefits from the concept of a multi-colony ant algorithm and incorporates a new information-exchange policy. In the proposed information-exchange policy, after a given number of iterations, different colonies exchange information on the assigned objective, resulting in a set of non-dominated solutions. The non-dominated solutions are moved into an offline archive for further pheromone updating. Performance of the NA-ACO is tested employing two well-known mathematical multi-objective benchmark problems. The results are promising and compare well with those of well-known NSGA-II algorithms used in real-world multi-objective-optimization problems. In addition, the optimization of reservoir operating policy with multiple objectives (i.e. flood control, hydropower generation and irrigation water supply) is considered and the associated Pareto front generated.     

Modelling and optimisation of energy-efficient U-shaped robotic assembly line balancing problems

Within U-shaped assembly lines, the increase of labour costs and subsequent utilisation of robots has led to growing energy consumption, which is the current main expense of auto and electronics industries. However, there are limited researches concerning both energy consumption reduction and productivity improvement on U-shaped robotic assembly lines. This paper first develops a nonlinear multi-objective mixed-integer programming model, reformulates it into a linear form by linearising the multiplication of two binary variables, and then refines the weight of multiple objectives so as to achieve a better approximation of true Pareto frontiers. In addition, Pareto artificial bee colony algorithm (PABC) is extended to tackle this new complex problem. This algorithm stores all the non-dominated solutions into a permanent archive set to keep all the good genes, and selects one solution from this set to overcome the strong local minima. Comparative experiments based on a set of newly generated benchmarks verify the superiority of the proposed PABC over four multi-objective algorithms in terms of generation distance, maximum spread, hypervolume ratio and the ratio of non-dominated solution.     

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.     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

A multi-objective simulated annealing approach to reactive power compensation

Reactive power compensation is an important problem in electrical distribution systems, involving the sizing and location of capacitors (sources of reactive power). The installation of capacitors also contributes to releasing system capacity and improving voltage level. A multi-objective simulated annealing approach to provide decision support in this problem is presented. This approach is able to compute a set of well-distributed and diversified solutions underlying distinct trade-offs, even for a challenging network. The characterization of the non-dominated front is relevant information for aiding planning engineers to select satisfactory compromise solutions (compensation schemes) to improve the network operation conditions.