An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

混合多目标粒子群优化算法在热精轧负荷分配优化中的应用

通过对热精轧负荷分配过程的分析,选取负荷均衡、板形良好和轧制功率最低为目标,建立了热精轧负荷分配多目标优化模型.为了提高多目标优化算法解集的分布性和收敛性,提出了一种混合多目标粒子群优化算法(HMOPSO),该算法根据Pareto支配关系得到Pareto前沿进而保证种群收敛;采用分解策略维护外部存档,该策略首先根据Pareto前沿求出上界点对目标空间进行归一化处理,然后对种群进行分区处理进而保证种群的分布性能.仿真结果表明,HMOPSO的收敛性和分布性都好于MOPSO和d MOPSO;采用模糊多属性决策的方法从Pareto最优解集中选择一个Pareto最优解,通过与经验负荷分配方法相比,表明该Pareto最优解可以使轧制方案更加合理.     

A new multi objective optimization approach based on TLBO for location of automatic voltage regulators in distribution systems

This paper proposes a new multi-objective optimization algorithm based on modified teaching–learning-based optimization (MTLBO) algorithm in order to solve the optimal location of automatic voltage regulators (AVRs) in distribution systems at presence of distributed generators (DGs). The objective functions including energy generation costs, electrical energy losses and the voltage deviation are considered in this paper. In the proposed MTLBO algorithm, teacher and learner phases are modified. The considered objective functions are energy generation costs, electrical energy losses and the voltage deviations. The proposed algorithm uses an external repository to save founded Pareto optimal solutions during the search process. Since the objective functions are not the same, a fuzzy clustering method is used to control the size of the repository. The proposed technique allows the decision maker to select one of the Pareto optimal solutions (by compromising) for different applications. The performance of the suggested algorithm on a 70-bus distribution network in comparison with other evolutionary methods such as genetic algorithm (GA), particle swarm optimization (PSO) and TLBO is extraordinary.     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

多子群协同进化的多目标微粒群优化算法

微粒群优化(PSO)算法是一种非常有竞争力的求解多目标优化问题的群智能算法,因其容易陷入局部极值,导致非劣解集的收敛性和正确性不理想。为此提出一种基于多目标分解进化策略的多子群协同进化的多目标微粒群优化算法(MOPSO_MC),算法中每个子群对应于一个多目标分解之后的子问题,并构造了一种新的速率更新策略,每个粒子跟踪自身历史最优值、子群最优值和子群邻域最优值,从而在增强算法的局部寻优能力的同时,也能从邻域子群获得进化信息,实现协同进化。最后通过仿真实验,与现在主流的多目标微粒群算法在ZDT基准测试函数上比较,验证了算法的收敛性,解分布的均匀性和正确性。     

高维多目标多方向协同进化算法

提出一种高维多目标多方向协同进化算法(HMMCA).该算法利用目标空间内的一组方向向量将多目标优化问题分解成多个方向进行寻优,并提出一种混合变异策略以加强算法在每个方向上的收敛能力;同时,该算法采用改进的交互式模糊支配和拥挤度估计因子来维护外部归档集的规模,增强种群的收敛性和分布性.将该算法与目前性能最好的3种多目标进化算法在标准测试函数集上进行对比实验,所得结果表明HMMCA与其他算法相比具有更好的收敛性和分布性.     

基于遗传算法的混合流水线车间调度多目标求解*

为了解决传统的多目标优化算法难以很好实现企业的实际决策需要问题,针对混合流水线车间调度（HFSP）的多目标优化调度问题,提出了一种新的多目标遗传算法。根据企业实际需求,采用分模块两层建模的思想,将多目标分为约束性目标和优化性目标。算法根据目标性质的不同分别进行不同的搜索。最后将新算法应用于HFSP多目标优化问题进行实例验证。结果表明,所提出的算法具有很好的可行性,与其他多目标优化方法相比,该算法具有明显的优越性、实用性和可操作性。     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

A single front genetic algorithm for parallel multi-objective optimization in dynamic environments

This paper proposes a new parallel evolutionary procedure to solve multi-objective dynamic optimization problems along with some measures to evaluate multi-objective optimization in dynamic environments. These dynamic optimization problems appear in quite different real-world applications with actual socio-economic relevance. In these applications, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online whilst the size of the changes is unknown. Although parallel processing could be very useful in these problems to meet the solution quality requirements and constraints, to date, not many parallel approaches have been reported in the literature. Taking this into account, we introduce a multi-objective optimization procedure for dynamic problems that are based on PSFGA, a parallel evolutionary algorithm previously proposed by us for multi-objective optimization. It uses an island model where a process divides the population among the remaining processes and allows the communication and coordination among the subpopulations in the different islands. The proposed algorithm makes an exclusive use of non-dominating individuals for the selection and variation operator and applies a crowding mechanism to maintain the diversity and the distribution of the solutions in the Pareto front. We also propose a model to understand the benefits of parallel processing in multi-objective problems and the speedup figures obtained in our experiments.     

基于深度强化学习的电力物资配送多目标路径优化

针对现有电力物资车辆路径问题（EVRP）优化时考虑目标函数较为单一、约束不够全面,并且传统求解算法效率不高的问题,提出一种基于深度强化学习（DRL）的电力物资配送多目标路径优化模型和求解算法。首先,充分考虑了电力物资配送区域的加油站分布情况、物资运输车辆的油耗等约束,建立了以电力物资配送路径总长度最短、成本最低、物资需求点满意度最高为目标的多目标电力物资配送模型;其次,设计了一种基于DRL的电力物资配送路径优化算法DRL-EVRP求解所提模型。DRL-EVRP使用改进的指针网络（Ptr-Net）和Q-学习（Q-learning）算法结合的深度Q-网络（DQN）来将累积增量路径长度的负值与满意度之和作为奖励函数。所提算法在进行训练学习后,可直接用于电力物资配送路径规划。仿真实验结果表明,DRL-EVRP求解得到的电力物资配送路径总长度相较于扩展C-W（ECW）节约算法、模拟退火（SA）算法更短,且运算时间在可接受范围内,因此所提算法能更加高效、快速地进行电力物资配送路径优化。     

可持续闭环供应链网络设计的多目标模糊规划问题

为解决不确定条件下可持续闭环供应链网络设计的问题,以成本和环境影响最小、社会影响最大为目标,建立带有模糊参数的多目标闭环供应链网络规划模型.首先采用Me测度处理相关模糊目标和参数,并运用加权增广Epsilon-约束方法解决多目标问题,在此基础上设计一种基于[0, 1]随机数的双层编码遗传鲸鱼(GA–WOA)混合算法进行求解,然后构造多个不同规模算例,将混合算法求解结果与CPLEX、遗传算法的求解结果进行对比,结果证明该编码方式和混合算法具有合理性.最后针对模型的多个参数变化进行分析,以验证所建模型的可行性.     

环链种群结构的多目标教与学优化算法*

针对教与学算法采用贪婪进化机制,易造成种群多样性较差的问题,将环链拓扑结构引入到多目标教与学算法中,并改进了自我学习机制,提出了一种环链种群结构的多目标教与学优化算法。根据多种群进化方式,通过一种环链结构将种群划分为多个邻域,每个邻域代表一个小种群,且相邻种群之间存在重叠。在教与学进化过程中,在每个小种群中设置一名教师,由每一位教师引导各自的种群独立进化,且彼此之间存在进化信息交流。同时,提出一种改进的学习机制来提升局部寻优能力,由此平衡算法的全局搜索和局部寻优。该算法通过与五种对等算法在ZDT和DTLZ系列组成的12个多目标测试问题进行测试,实验结果表明了新算法在收敛性、多样性和稳定性等方面均优于或部分优于其他的对比算法。     

Voltage and frequency regulation in autonomous microgrids using Hybrid Big Bang-Big Crunch algorithm

This paper proposes an optimal power control strategy for inverter-based Distributed Generation (DG) units in autonomous microgrids. It consists of power, voltage, and current controllers with Proportional-Integral (PI) regulators. The droop concept is used for the power control strategy. Static parameters in PI regulators may not ensure the most optimal solution due to inevitable changes happening in microgrid configuration and loads. In the proposed method, after occurring a load change in a standalone microgrid, parameters of the PI controller are dynamically adjusted to get the most optimal operating point that satisfies objective functions. The optimization problem is formulated as a multi-objective programming with objective functions of minimizing overshoot/undershoot, settling time, rise time, and Integral Time Absolute Error (ITAE) in the output voltage. These objective functions are combined using fuzzy memberships. The Hybrid Big Bang-Big Crunch algorithm (HBB-BC) is used to solve the optimization problem. The proposed methodology is simulated on a case study and according to obtained results, the suggested tuning of PI parameters leads to a better voltage response than previous methods. The case study is also solved using the Particle Swarm Optimization (PSO) and Big Bang-Big Crunch (BB-BC) algorithms and it is found that the HBB-BC gives a better solution than the PSO and BB-BC.     

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。     

基于多点非均匀变异的多目标极值优化算法研究

多目标进化算法因其在解决含有多个矛盾目标函数的多目标优化问题中的强大处理能力,正受到越来越多的关注与研究。极值优化作为一种新型的进化算法,已在各种离散优化、连续优化测试函数以及工程优化问题中得到了较为成功的应用,但有关多目标EO算法的研究却十分有限。本文将采用Pareto优化的基本原理引入到极值优化算法中,提出一种求解连续多目标优化问题的基于多点非均匀变异的多目标极值优化算法。通过对六个国际公认的连续多目标优化测试函数的仿真实验结果表明：本文提出算法相比NSGA-II、 PAES、SPEA和SPEA2等经典多目标优化算法在收敛性和分布性方面均具有优势。     

An efficient evolutionary optimization algorithm for multiobjective distribution feeder reconfiguration

In this paper, a Multi-objective Modified Honey Bee Mating Optimization (MMHBMO) evolutionary algorithm is proposed to solve the multi-objective Distribution Feeder Reconfiguration (DFR). The real power loss, the number of the switching operations and the deviation of the voltage at each node are considered as the objective functions. Conventional algorithms for solving the multiobjective optimization problems convert the multiple objectives into a single objective using a vector of the user-predefined weights. This paper presents a new MHBMO algorithm for the DFR problem. In the proposed algorithm an external repository is utilized to save non-dominated solutions found during the search process. A fuzzy clustering technique is used to control the size of the repository within the limits because of the objective functions are not the same. The proposed algorithm is tested on a distribution test feeder.     

Fuzzy random multi-objective optimization based routing for wireless sensor networks

Wireless sensor networks are deployed in complex and uncertain environments, and multiple objectives of routing algorithms are expected to be optimal. However, routing algorithms based on deterministic single objective optimization may not flexibly meet the above needs of applications. This paper adopts fuzzy random optimization and multi-objective optimization, introduces fuzzy random variables to describe both fuzziness and randomness of link delay, link reliability and nodes’ residual energy, and proposes a routing model based on fuzzy random expected value and standard deviation model. A hybrid routing algorithm based on fuzzy random multi-objective optimization is designed, which embeds fuzzy random simulation into genetic algorithm with Pareto optimal solution. Simulation results show that the presented algorithm, by adjusting the parameters of fuzzy random variables for depicting both fuzziness and randomness, achieves a longer lifetime and wider performances of delay, latency jitter, reliability, communication interference, energy and balanced energy distribution. Therefore, the presented algorithm can meet different application needs of the cluster head network in the two-tiered wireless sensor networks.     

基于模糊控制的权重决策灰狼优化算法

针对灰狼优化算法后期收敛速度慢,求解精度低等问题,提出一种基于模糊控制的权重决策灰狼优化算法.首先,提出一种新的非线性收敛因子,以提高算法的全局搜索能力及收敛速度;其次,提出一种基于模糊控制的权重决策策略,通过模糊控制器对决策层的个体赋予不同权重进行种群位置更新的决策,增强算法的寻优能力.选取23个标准测试函数对该算法及对比算法进行数值实验,实验结果表明,本文提出的改进的灰狼优化算法在求解精度和算法稳定性等指标优于对比算法.