基于改进智能水滴算法的多目标供应链最优模型

为了最大限度地降低制造型供应链的销售成本并缩短供货时间,提出了一种基于改进智能水滴算法的多目标供应链优化模型。该模型通过在选项选择期间同时考虑成本和时间来提高供应链效率,并能够将制造型供应链中的销售成本和交货时间最小化。通过使用帕累托最优准则对传统的智能水滴算法进行修改,从而得到一个帕累托集,以实现两个目标的最小化。通过3个实例对所提算法进行了测试,并采用世代距离和超区域比指标将其与蚁群优化算法进行了比较。实验结果显示,所提方法的性能更优,生成的解集更接近真实帕累托集,能够覆盖更大的解区域面积,且计算效率较高。     

基于改进粒子群优化的无标记数据鲁棒聚类算法

已有的聚类算法大多仅考虑单一的目标,导致对某些形状的数据集性能较弱,对此提出一种基于改进粒子群优化的无标记数据鲁棒聚类算法。优化阶段:首先,采用多目标粒子群优化的经典形式生成聚类解集合;然后,使用K-means算法生成随机分布的初始化种群,并为其分配随机初始化的速度;最终,采用MaxiMin策略确定帕累托最优解。决策阶段：测量帕累托解集与理想解的距离,将距离最短的帕累托解作为最终聚类解。对比实验结果表明,本算法对不同形状的数据集均可获得较优的类簇数量,对目标问题的复杂度具有较好的鲁棒性。     

混合分解和强度帕累托多目标进化算法

在多目标进化优化中,使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低,使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略,提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿;然后,利用强度帕累托策略使解集均匀分布在帕累托前沿,利用解集重置分解策略中的权重向量集,使其适配于特定的帕累托前沿;最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准,将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优,在5个基准问题上接近于最优,且无论MOP的帕累托前沿是简单或复杂、连续或不连续的,该算法均能生成分布均匀的解集。     

基于帕累托改进的多机器人动态任务分配算法

针对多机器人系统动态任务分配中存在的优化问题,在使用合同网初始任务分配的基础上提出了一种使用帕累托改进的任务二次分配算法。多机器人系统并行执行救火任务时,首先通过初始化任务分配将多机器人划分为若干子群;然后,每个子群承包某一救火任务,子群在执行任务的同时与就近子群进行帕累托改进确定需要迁移的机器人,实现两子群之间帕累托最优;最后,使用后序二叉树遍历对所有子群进行帕累托改进实现全局帕累托最优。理论分析和仿真结果表明,相较于强化学习算法和蚁群算法,所提算法的救火任务时间分别减少26.18%和37.04%;相较于传统合同网方法,所提算法在时间方面能够高效完成救火任务,在系统收益方面也具有明显优势。     

建筑生命周期碳排放评价函数多目标优化算法

碳排放量一旦超标,会使全球气温升高,导致南北极冰川融化,形成自然灾害.为此提出一种建筑生命周期碳排放评价函数多目标优化算法,通过对建筑物的规划设计、施工阶段、运行维护阶段以及拆除阶段二氧化碳总排放量进行计算,获得排放的碳系数,再找出帕累托最优解集以及帕累托前端,决策者依据实际需求,解决建筑工程内多目标优化问题,最后计算非劣解集到达帕累托最优解集间距离、分散性以及错误率,完成对建筑物的碳排放量多目标优化评价.仿真结果证明,所提方法得到的碳排放量的数据更加准确,可更有效完成评价.     

基于AMFOA考虑主客观因素的配电网多目标规划

针对配电网重构的多目标优化及方案决策问题,提出一种基于自适应多种群果蝇算法(AMFOA)并考虑主客观因素的多目标两级优化方法。第一级优化采用自适应多种群果蝇算法对网络结构进行迭代优化,通过协调不同指标得到一组帕累托非支配解。第二级优化引入AHP-CRITIC算法完成每个非支配解的主客观综合评价,结合TOPSIS法确定最优解。通过对IEEE 33节点系统进行仿真分析,验证了所提方法的有效性与高效性。结果表明运行优化方法能够改善配电网的多个运行指标,并为电网调度人员提供切合实际的决策方案。     

融入差异性的帕累托集成剪枝方法

相比于集成学习,集成剪枝方法是在多个分类器中搜索最优子集从而改善分类器的泛化性能,简化集成过程。帕累托集成剪枝方法同时考虑了分类器的精准度及集成规模两个方面,并将二者均作为优化的目标。然而帕累托集成剪枝算法只考虑了基分类器的精准度与集成规模,忽视了分类器之间的差异性,从而导致了分类器之间的相似度比较大。本文提出了融入差异性的帕累托集成剪枝算法,该算法将分类器的差异性与精准度综合为第1个优化目标,将集成规模作为第2个优化目标,从而实现多目标优化。实验表明,当该改进的集成剪枝算法与帕累托集成剪枝算法在集成规模相当的前提下,由于差异性的融入该改进算法能够获得较好的性能。     

双局部粒子群算法解决环境经济调度问题

提出一种基于双局部最优的多目标粒子群优化算法,与可行解为优的约束处理方法相结合,来求解决非线性带约束的多目标电力系统环境经济调度问题。该算法针对传统多目标粒子群算法多样性低的局限性,通过对搜索空间的分割归类来增加帕累托最优解的多样性;并采用一种新的双局部最优来引导粒子的搜索,从而增强了算法的全局搜索能力。算法加入了可行解为优的约束处理方法对IEEE30节点六发电机电力系统环境经济负荷分配模型分别在几个不同复杂性问题的情况进行仿真测试,并与文献中的其他算法进行了比较。结果表明,改进的算法能够在保持帕累托最优解多样性的同时具有良好的收敛性能,更有效地解决电力系统环境经济调度问题。     

基于知识粒度特征的多目标粗糙集属性约简算法

针对多知识粒度粗糙集在条件属性权重计算及约简过程中易忽略单个属性序列产生的等价划分的问题,引入帕累托最优思想,同时考虑基于等价关系的知识依赖分辨度以及属性的重要性程度,将多粒度粗糙集属性约简问题转化为离散多目标优化问题.针对该问题的结构设计具有集群智能优化思想及复杂网络拓扑结构的优化算法,在算法中引入基于个体的非支配解集以平衡局部最优与全局最优的关系,引入基于“均值-方差”的遗传算子增加种群多样性.以UCI中的测试数据集作为算例构建粗糙集决策表进行优化计算,引入多种智能算法进行性能比较,依据约简结果,利用多层感知机对数据集中的对象进行分类,验证约简方法的有效性.研究结果表明:所提出方法具有更强的多目标属性挖掘性能;基于帕累托最优思想的多目标属性约简方法能较好地综合知识分辨度与知识粒度建模方式的优点,提升数据集的分类精度.     

基于分解法与轨迹搜索的无人机群轨迹多目标优化模型

基于深度学习（DL）的传统多目标求解器存在模型利用率低以及容易陷入局部最优的问题。针对这些问题，提出了基于分解法与轨迹搜索的无人机群轨迹多目标优化模型（DTMO-UT）。所提模型包含编码与解码部分。首先，编码部分由设备编码器（Dencoder）和权重编码器（Wencoder）组成，用于提取物联网（IoT）设备的状态信息与权重向量的特征，其中权重向量代表分解多目标优化问题（MOP）的标量优化子问题，因此解决所有子问题即可解决该MOP。权重编码器可以实现对所有子问题的编码，从而提高了模型的利用率。然后，使用包含轨迹解码器（Tdecoder）的解码部分对编码特征进行解码，以生成帕累托最优解。最后，为了减少贪婪策略陷入局部最优的现象，为轨迹解码器设计轨迹搜索技术，即通过生成多个候选轨迹选标量值最优的轨迹作为帕累托最优解，从而增强了轨迹解码器在轨迹规划时的探索能力，并获得质量更好的帕累托集。仿真实验结果表明，所提模型相较于主流的基于DL的MOP求解器，在模型参数量降低98.93%的情况下，MOP解的分布性提高了0.076%，延展性提高了0.014%，平均综合性提高了1.23%，表现出较强的实用性...     

多目标卫星数传调度蚁群优化算法

卫星数传调度问题具有任务多、资源少、调度约束复杂等特点,为满足多目标优化调度的理论和现实需要,提出了多目标卫星数传调度蚁群优化算法。算法建立了基于任务调度关系的解构造图,提出了用于可行解构造的自适应伪随机概率决策模型,以及基于Pareto解偏离度的全局信息素更新策略。仿真结果表明,算法具有较好的Pareto前沿收敛性,各优化目标都能得到较好的指标评价值,所获得的Pareto解集规模适度,Pareto解的多样性、分布均匀性和散布范围都较好。     

Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure

A self-adaptive differential evolution algorithm incorporate Pareto dominance to solve multi-objective optimization problems is presented. The proposed approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. The experiments were performed using eighteen benchmark test functions. The experiment results show that, compared with three other multi-objective optimization evolutionary algorithms, the proposed MOSADE is able to find better spread of solutions with better convergence to the Pareto front and preserve the diversity of Pareto optimal solutions more efficiently.     

云计算环境中面向DAG任务的多目标调度算法

为了实现任务执行效率与执行代价的同步优化,提出了一种云计算环境中的DAG任务多目标调度优化算法。算法将多目标最优化问题以满足Pareto最优的均衡最优解集合的形式进行建模,以启发式方式对模型进行求解;同时,为了衡量多目标均衡解的质量,设计了基于hypervolume方法的评估机制,从而可以得到相互冲突目标间的均衡调度解。通过配置云环境与三种人工合成工作流和两种现实科学工作流的仿真实验测试,结果表明,比较同类单目标算法和多目标启发式算法,算法不仅求解质量更高,而且解的均衡度更好,更加符合现实云的资源使用特征与工作流调度模式。     

教与同伴学习粒子群算法求解多目标柔性作业车间调度问题

针对多目标柔性作业车间调度问题,提出了带Pareto非支配解集的教与同伴学习粒子群算法。首先,以工件的最大完工时间、最大机器负荷和所有机器总负荷为优化目标建立了多目标柔性作业车间调度模型。然后,该算法结合多目标Pareto方法和教与同伴学习粒子群算法,采用快速非支配排序算法产生初始Pareto非支配解集,用提取Pareto支配层程序更新Pareto非支配解集,同时采用混合分派规则产生初始种群,采用开口向上抛物线递减的惯性权重选择策略提高算法的收敛速度。最后,对3个Benchmark算例进行仿真实验。理论分析和仿真表明,与带向导性局部搜索的多目标进化算法(MOEA-GLS)和带局部搜索的控制遗传算法(AL-CGA)相比,对于相同的测试实例,该算法能产生更多更好的Pareto非支配解;在计算时间方面,该算法要小于带向导性局部搜索的多目标进化算法。实验结果表明该算法可以有效解决多目标柔性作业车间调度问题。     

基于MOPSO算法的卫星共形阵列天线多波束形成

针对共形阵列天线多波束方向图综合问题,提出一种基于最大方向性系数方法得到初始非劣解的多目标粒子群算法,求解满足多个期望波束和低副瓣要求的Pareto最优解。算法首先采用多目标分解策略,由多个单波束最优解的加权线性组合得到近最优解的非劣解。然后结合该非劣解,基于粒子空间和目标空间同时约束的局部搜寻策略,使用多目标粒子群算法优化多个波束,并降低副瓣。仿真结果表明,该算法有效地实现了卫星共形阵列天线的多波束形成和低副瓣,且能快速得到Pareto最优解分布。     

An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.     

A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem

To better reflect the uncertainty existing in the actual disassembly environment, the multi-objective disassembly line balancing problem with fuzzy disassembly times is investigated in this paper. First, a mathematical model of the multi-objective fuzzy disassembly line balancing problem (MFDLBP) is presented, in which task disassembly times are assumed as triangular fuzzy numbers (TFNs). Then a Pareto improved artificial fish swarm algorithm (IAFSA) is proposed to solve the problem. The proposed algorithm is inspired from the food searching behaviors of fish including prey, swarm and follow behaviors. An order crossover operator of the traditional genetic algorithm is employed in the prey stage. The Pareto optimal solutions filter mechanism is adopted to filter non-inferior solutions. The proposed model after the defuzzification is validated by the LINGO solver. And the validity and the superiority of the proposed algorithm are proved by comparing with a kind of hybrid discrete artificial bee colony (HDABC) algorithm using two test problems. Finally, the proposed algorithm is applied to a printer disassembly instance including 55 disassembly tasks, for which the computational results containing 12 non-inferior solutions further confirm the practicality of the proposed Pareto IAFSA in solving the MFDLBP.     

Multi-objective genetic algorithm and its applications to flowshop scheduling

In this paper, we propose a multi-objective genetic algorithm and apply it to flowshop scheduling. The characteristic features of our algorithm are its selection procedure and elite preserve strategy. The selection procedure in our multi-objective genetic algorithm selects individuals for a crossover operation based on a weighted sum of multiple objective functions with variable weights. The elite preserve strategy in our algorithm uses multiple elite solutions instead of a single elite solution. That is, a certain number of individuals are selected from a tentative set of Pareto optimal solutions and inherited to the next generation as elite individuals. In order to show that our approach can handle multi-objective optimization problems with concave Pareto fronts, we apply the proposed genetic algorithm to a two-objective function optimization problem with a concave Pareto front. Last, the performance of our multi-objective genetic algorithm is examined by applying it to the flowshop scheduling problem with two objectives: to minimize the makespan and to minimize the total tardiness. We also apply our algorithm to the flowshop scheduling problem with three objectives: to minimize the makespan, to minimize the total tardiness, and to minimize the total flowtime.     

Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge

Particle swarm optimisation (PSO) is an evolutionary metaheuristic inspired by the swarming behaviour observed in flocks of birds. The applications of PSO to solve multi-objective discrete optimisation problems are not widespread. This paper presents a PSO algorithm with negative knowledge (PSONK) to solve multi-objective two-sided mixed-model assembly line balancing problems. Instead of modelling the positions of particles in an absolute manner as in traditional PSO, PSONK employs the knowledge of the relative positions of different particles in generating new solutions. The knowledge of the poor solutions is also utilised to avoid the pairs of adjacent tasks appearing in the poor solutions from being selected as part of new solution strings in the next generation. Much of the effective concept of Pareto optimality is exercised to allow the conflicting objectives to be optimised simultaneously. Experimental results clearly show that PSONK is a competitive and promising algorithm. In addition, when a local search scheme (2-Opt) is embedded into PSONK (called M-PSONK), improved Pareto frontiers (compared to those of PSONK) are attained, but longer computation times are required.