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.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

全局优化的蝴蝶优化算法

针对基本蝴蝶优化算法中存在的易陷入局部最优值、收敛速度慢等问题,提出一种全局优化的蝴蝶算法,引入limit阈值来限定蝴蝶优化算法陷入局部最优解的次数,从而改变算法易陷入早熟的问题,结合单纯形策略优化迭代后期位置较差的蝴蝶使种群能够较快地找到全局最优解;将正弦余弦算法作为局部算子融入BOA中,改善迭代后期种群多样性下降的缺陷,加快算法跳出局部最优。在仿真模拟实验中与多个算法进行对比,结果表明改进算法的寻优性能更好。     

Biogeography-based optimization for constrained optimization problems

Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm and it has so far been successfully applied in a variety of fields, especially for unconstrained optimization problems. The present paper shows how BBO can be applied for constrained optimization problems, where the objective is to find a solution for a given objective function, subject to both inequality and equality constraints.     

Combining Bayesian optimization and Lipschitz optimization

Machine Learning - Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the...     

Blended biogeography-based optimization for constrained optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems.     

Multi-verse optimization algorithm- and salp swarm optimization algorithm-based optimization of multilevel inverters

Neural Computing and Applications - Renewable energy sources are installed into both distribution and transmission grids more and more with the introduction of smart grid concept. Hence, efficient...     

一种改进的约束优化粒子群算法*

提出一种新的约束优化粒子群算法。该算法采用非固定多段映射罚函数法处理约束条件。在进化过程中,利用混沌序列初始化种群,选取最优粒子进行局部一维搜索,增强了在最优点附近的局部搜索能力,以加快算法的收敛速度;引入维变异方法保持种群的多样性。数值实验结果表明了该算法的有效性。     

Benchmarking optimization solvers for structural topology optimization

The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

Variable mesh optimization for continuous optimization problems

Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive algorithm.     

Multi-objective ordinal optimization for simulation optimization problems

Ordinal optimization (OO) has been successfully applied to accelerate the simulation optimization process with single objective by quickly narrowing down the search space. In this paper, we extend the OO techniques to address multi-objective simulation optimization problems by using the concept of Pareto optimality. We call this technique the multi-objective OO (MOO). To define the good enough set and the selected set, we introduce two performance indices based on the non-dominance relationship among the designs. Then we derive several lower bounds for the alignment probability under various scenarios by using a Bayesian approach. Numerical experiments show that the lower bounds of the alignment probability are valid when they are used to estimate the size of the selected set as well as the expected alignment level. Though the lower bounds are conservative, they have great practical value in terms of narrowing down the search space.     

基于一种新的正交优化的群智能优化算法

目前的智能优化算法易陷入本地最优平衡态,并且进化后期的效率低下。为了克服这些缺陷,提出了一种基于正交优化的群智能优化算法。该算法突破了以往正交设计方法仅能用在粒子群初始化和进化前优化搜索过程的局限,基于方差分析和方差比例分析,证实了正交设计方法进一步的搜索方向和范围。使用正交设计的特征在一次阵列计算中寻找包含最优值的间隔,算法可以在优化搜索过程中循环进行方差比例分析。对六峰值驼背函数的仿真分析结果说明,正交智能优化算法相比目前的智能优化算法,计算量更低,搜索时间更短,运行速度更快,且优化搜索过程的精度更高。     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

基于粒子群算法的WSN覆盖优化

为了提高无线传感器网络性能,针对节点的分布与覆盖方案进行了研究,将拟物力算法中的拟万有引力和拟库仑力与粒子群算法相结合,提出了一种基于惯性权重的拟物粒子群算法。增强了算法全局搜索能力,更快地收敛至全局最优解,减少算法时耗和重复覆盖。仿真结果证明新的算法比基本粒子群和基于惯性权重的标准粒子群算法的全局收敛速度更快,覆盖率更高,重复覆盖的比率更低。     

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。     

一种求解多峰函数优化问题的量子行为粒子群算法

介绍了一种利用量子行为粒子群算法（QPSO）求解多峰函数优化问题的方法。为此,在QPSO中引进一种物种形成策略,该方法根据群体微粒的相似度并行地分成子群体。每个子群体是围绕一个群体种子而建立的。对每个子群体通过QPSO算法进行最优搜索,从而保证每个峰值都有同等机会被找到,因此该方法具有良好的局部寻优特性。将基于物种形成的QPSO算法与粒子群算法(PSO)对多峰优化问题的结果进行比较。对几个重要的测试函数进行仿真实验结果证明,基于物种形成的QPSO算法可以尽可能多地找到峰值点,峰值收敛性能优于PSO。     

求解约束优化的改进粒子群算法

针对种群初始化时粒子过于集中和基本粒子群算法搜索精度不高的缺陷,提出了一种求解约束优化问题的改进粒子群算法。该算法引入佳点集技术来优化种群的初始粒子,使种群粒子初始化时分布均匀,因而种群具有多样性,不会陷入局部极值;同时使用协同进化技术使双种群之间保持通信,从而提高算法的搜索精度。仿真实验结果表明：将该算法用于5个基准测试函数,该算法均获得了理论最优解,其中有4个函数的测试方差为0。该算法提高了计算精度且鲁棒性强,可以广泛应用于其他约束优化问题中。     

Example-based learning particle swarm optimization for continuous optimization

Particle swarm optimization (PSO) is a heuristic optimization technique based on swarm intelligence that is inspired by the behavior of bird flocking. The canonical PSO has the disadvantage of premature convergence. Several improved PSO versions do well in keeping the diversity of the particles during the searching process, but at the expense of rapid convergence. This paper proposes an example-based learning PSO (ELPSO) to overcome these shortcomings by keeping a balance between swarm diversity and convergence speed. Inspired by a social phenomenon that multiple good examples can guide a crowd towards making progress, ELPSO uses an example set of multiple global best particles to update the positions of the particles. In this study, the particles of the example set were selected from the best particles and updated by the better particles in the first-in-first-out order in each iteration. The particles in the example set are different, and are usually of high quality in terms of the target optimization function. ELPSO has better diversity and convergence speed than single-gbest and non-gbest PSO algorithms, which is proved by mathematical and numerical results. Finally, computational experiments on benchmark problems show that ELPSO outperforms all of the tested PSO algorithms in terms of both solution quality and convergence time.     

求解约束优化问题改进的水波优化算法

为提高约束优化模型的求解精度,提出一种改进的水波优化算法。设计主-从异构种群,结合ε约束处理技术使主群实现探索可行解,从群利用可行解搜寻全局最优解。为加快收敛速度和增强信息交互,主群中个体可以依概率进行个体间学习,设计水波波长函数,使其随着水波的适应度值和违反约束度及时调整。为避免早期收敛,从群采用自适应学习策略以平衡群体的探索和利用。设计随迭代次数变化的放松约束度,提高算法收敛精度。对比实验结果表明,该算法可以获得高质量的可行解。