基于SQP和自适应搜索的混沌粒子群算法

针对基本粒子群优化算法（PSO）算法易陷入局部最优的缺点,提出混沌自适应粒子群-序列二次规划算法（CAPSO-SQP）。在基本PSO算法的基础上,加入混沌搜索和自适应惯性权重提高全局收敛能力,并在PSO算法每一代的迭代过程中,引入SQP策略,加快局部搜索并提高对约束优化问题的计算可靠性。测试函数仿真结果表明,CAPSO-SQP算法计算精度高,稳定性好,收敛速度快。将所提出算法应用于悬臂梁结构优化设计,求解结果表明算法在结构优化计算方面的可行性,而且相对于CPSO算法求解更加准确,具有较高的计算可靠性和实用价值。     

求解约束优化问题的动态邻域粒子群算法*

粒子群算法(PSO)求解约束优化问题存在较严重的早熟收敛现象,为了有效抑制早熟收敛,提出了基于改进的约束自适应方法的动态邻域粒子群算法(IPSO)。算法采用动态邻域策略提高算法的全局搜索能力,设计了一种改进的自适应约束处理方法,根据迭代代数线性增加搜索偏向系数,在早期偏向于搜索可行解,在后期偏向于搜索最优解,并引入序列二次规划增强算法的局部搜索能力。通过基准测试函数实验对比分析,表明该算法对于约束优化问题具有较好的全局收敛性。     

直接搜索模拟退火算法的自适应改进

针对直接搜索模拟退火算法求解高维优化问题存在稳定性差、收敛成功率低现象,提出一种自适应的直接搜索模拟退火算法。该算法通过构造基于迭代温度动态调整搜索范围的新点产生方式和自适应寻优模块,增强了算法跳出局部极值和加快邻域搜索的能力,利用柯西分布状态发生函数的大范围遍历特点,弥补了直接搜索模拟退火算法求解高维多峰值问题易陷入局部解和计算效率低的不足。结合可行规则法处理约束问题,典型高维函数和工程优化设计实例的测试结果表明,该算法能够有效求解高维优化问题,整体性能较直接搜索模拟退火算法有显著提高。     

基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度和经济排放联合调度问题

电力生产装置运行中各种燃料的成本逐步增加,需要最小化成本函数以求解此类复杂经济负荷调度问题.鉴于此,提出一种基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度(economic load dispatch, ELD)问题和经济排放联合调度(combined economic emission dispatch, CEED)问题.为了提高蚱蜢算法(grasshopper optimization algorithm, GOA)性能,提出一种改进的混合蚱蜢算法(hybrid grasshopper optimization algorithm, HGOA),将重力搜索算子和鸽群搜索算子-地标算子加入GOA中,增强算法的搜索能力,平衡算法的勘探和开发.同时,为了更好地解决ELD和CEED问题中的约束问题,提出6个惩罚函数,包括2个V型函数、反正切函数、反正弦函数、线性函数和二次函数,并使用动态惩罚策略代替传统的固定值惩罚策略.选取3个ELD问题案例和4个CEED问题案例验证所提出方法的有效性,实验结果表明, HGOA相较于其他元启发式算法在求解质量上表现更好,且动态惩罚策略比固定值惩罚策略效果更...     

一种求解多维函数优化问题的改进组搜索优化算法

为提高组搜索优化算法求解多维函数优化问题的性能,提出一种结合逐维搜索、Metropolis准则、反方向视角和禁忌表策略的改进组搜索优化算法.逐维搜索策略逐维更新并评价成员位置,在每一维,更新的值与其他维组成候选位置,使用模拟退火的Metropolis准则来决定是否接受候选位置.反方向视角策略使成员按一定的概率做反方向搜索,禁忌表策略避免生产者始终保持不变.这些策略能更好地平衡算法的集中性和多样性.在典型测试函数上进行了仿真,结果表明改进策略是有效的,提高了组搜索算法求解多维函数优化问题的全局寻优能力和收敛速度.     

带局部搜索的NSGA Ⅱ算法在负荷分配中的应用

为了改善NSGAⅡ算法的收敛性能,将局部搜索的思想融入到NSGAⅡ中,提出一种带局部搜索的NSGAⅡ算法(NSGAⅡ-LS).该算法采用基于惩罚的边界插入法(PBI)产生局部搜索的优化函数,并使用序列二次规划方法(SQP)进行求解.通过在3个多目标标准测试函数上的仿真实验,结果表明相对于NSGAⅡ,NSGAⅡ-LS具有更好的收敛性能.最后将NSGAⅡ-LS应用到带钢热连轧负荷分配优化计算中,给出了兼顾轧制力平衡、最低轧制功率和优良板形的目标函数表达式,对多目标进化算法在热轧负荷分配优化计算中的应用进行研究,指出了目标之间的冲突关系.     

双种群灰狼优化算法的物流配送中心选址策略

针对物流配送中心选址模型具有多约束和非线性的特点,导致难以求解的问题.提出一种改进灰狼优化算法的求解策略.文章通过引入交叉变异策略,改进了传统灰狼算法在迭代后期易早熟收敛的问题;通过加入双种群寻优策略,丰富了灰狼算法的种群多样性,提高了算法的收敛速度.将改进后的灰狼算法针对物流配送中心选址模型进行求解,实验结果表明,该改进灰狼优化算法具有较高的全局搜索能力,针对物流配送中心选址模型具有较高的搜索精度,很大程度的提高了物流配送效率.     

基于线性搜索的混沌优化及其在非线性约束优化问题中的应用

提出基于线性搜索的混沌优化方法,利用混沌变量的特定内在随机性和遍历性来跳出局部最优点,而线性搜索可以提高局部空间的搜索速度和精度。结合精确不可微罚函数求解非线性约束优化问题。仿真结果表明,该算法简单易行,求解精度、收敛速度和可靠性较高,是解决优化问题一种有效方法。     

求解带约束优化问题的混合式多策略萤火虫算法

目前多目标优化算法主要针对如何处理多个目标之间的冲突,对于如何处理约束考虑较少,鉴于此,提出一种求解带约束优化问题的混合式多策略萤火虫算法(HMSFA-PC).首先,提出一种改进的动态罚函数策略对约束优化问题进行预处理,将其转换为非约束优化问题;其次,对萤火虫算法本身进行改进,采用Lévy flights搜索机制有效地增大搜索范围;接着,引入随机扩张因子改进算法吸引模型,使种群突破束缚,有效避免早熟收敛,提出自适应维度重组机制,根据不同迭代时期选择差异性较大的个体进行信息交互、相互学习.为检验算法处理无约束优化问题的性能,将其在基准测试函数上与部分典型算法进行比较;为检验算法处理约束优化问题的性能,将其在实际约束测试问题中与一些顶尖约束求解算法进行比较.结果表明,HMSFA-PC在处理无约束优化问题时具有收敛速度快、收敛精度高等优势,并且在动态罚函数的协作下求解实际约束优化问题时仍具有良好的优化性能.     

一种基于混沌搜索的文化算法及其应用*

针对文化算法求解函数优化问题存在过早收敛、不稳定等缺陷,基于文化算法框架、嵌入混沌搜索优化,提出了一种混沌文化算法。该算法模型由基于混沌的群体空间和存储知识的信念空间组成,利用标准知识和形势知识分别引导混沌搜索和混沌扰动,有效克服了文化算法过早收敛、混沌搜索优化对初值敏感、搜索效率低等缺陷。实例表明,该方法具有较强的全局搜索能力,在搜索效率、精度和稳定性上有显著表现,并能有效处理高维函数优化问题。     

Multi-fidelity wing aerostructural optimization using a trust region filter-SQP algorithm

A trust region filter-SQP method is used for wing multi-fidelity aerostructural optimization. Filter method eliminates the need for a penalty function, and subsequently a penalty parameter. Besides, it can easily be modified to be used for multi-fidelity optimization. A low fidelity aerostructural analysis tool is presented, that computes the drag, weight and structural deformation of lifting surfaces as well as their sensitivities with respect to the design variables using analytical methods. That tool is used for a mono-fidelity wing aerostructral optimization using a trust region filter-SQP method. In addition to that, a multi-fidelity aerostructural optimization has been performed, using a higher fidelity CFD code to calibrate the results of the lower fidelity model. In that case, the lower fidelity tool is used to compute the objective function, constraints and their derivatives to construct the quadratic programming subproblem. The high fidelity model is used to compute the objective function and the constraints used to generate the filter. The results of the high fidelity analysis are also used to calibrate the results of the lower fidelity tool during the optimization. This method is applied to optimize the wing of an A320 like aircraft for minimum fuel burn. The results showed about 9 % reduction in the aircraft mission fuel burn.     

The second generation of self-organizing adaptive penalty strategy for constrained genetic search

Penalty function approaches have been extensively applied to genetic algorithms for tackling constrained optimization problems. The effectiveness of the genetic searches to locate the global optimum on constrained optimization problems often relies on the proper selections of many parameters involved in the penalty function strategies. A successful genetic search is often completed after a number of genetic searches with varied combinations of penalty function related parameters. In order to provide a robust and effective penalty function strategy with which the design engineers use genetic algorithms to seek the optimum without the time-consuming tuning process, the self-organizing adaptive penalty strategy (SOAPS) for constrained genetic searches was proposed. This paper proposes the second generation of the self-organizing adaptive penalty strategy (SOAPS-II) to further improve the effectiveness and efficiency of the genetic searches on constrained optimization problems, especially when equality constraints are involved. The results of a number of illustrative testing problems show that the SOAPS-II consistently outperforms other penalty function approaches.     

Self-organizing adaptive penalty strategy in constrained genetic search

This research aims to develop an effective and robust self-organizing adaptive penalty strategy for genetic algorithms to handle constrained optimization problems without the need to search for appropriate values of penalty factors for the given optimization problem. The proposed strategy is based on the idea that the constrained optimal design is almost always located at the boundary between feasible and infeasible domains. This adaptive penalty strategy automatically adjusts the value of the penalty parameter used for each of the constraints according to the ratio between the number of designs violating the specific constraint and the number of designs satisfying the constraint. The goal is to maintain equal numbers of designs on each side of the constraint boundary so that the chance of locating their offspring designs around the boundary is maximized. The new penalty function is self-defining and no parameters need to be adjusted for objective and constraint functions in any given problem. This penalty strategy is tested and compared with other known penalty function methods in mathematical and structural optimization problems, with favorable results.     

多目标优化与自适应惩罚的混合约束优化进化算法

提出一种多目标优化与自适应惩罚函数相结合的方法来处理约束优化问题.首先利用多目标优化方法提取当前群体中的主要信息;然后进一步用自适应惩罚函数选出最有价值的信息.将这种约束处理技术与一种基于群的算法生成器模型相结合,即可得到一种新的约束优化进化算法.选取10个标准测试函数对新算法的性能进行数值实验,结果表明了所提出方法的有效性和较强的稳健性,与其他尖端算法相比得到了相似或更优的结果.     

A Runtime Analysis of Evolutionary Algorithms for Constrained Optimization Problems

Although there are many evolutionary algorithms (EAs) for solving constrained optimization problems, there are few rigorous theoretical analyses. This paper presents a time complexity analysis of EAs for solving constrained optimization. It is shown when the penalty coefficient is chosen properly, direct comparison between pairs of solutions using penalty fitness function is equivalent to that using the criteria ldquosuperiority of feasible pointrdquo or ldquosuperiority of objective function value.rdquo This paper analyzes the role of penalty coefficients in EAs in terms of time complexity. The results show that in some examples, EAs benefit greatly from higher penalty coefficients, while in other examples, EAs benefit from lower penalty coefficients. This paper also investigates the runtime of EAs for solving the 0-1 knapsack problem and the results indicate that the mean first hitting times ranges from a polynomial-time to an exponential time when different penalty coefficients are used.     

动态罚函数法求解约束优化问题

针对罚函数法在求解约束优化问题时罚系数不易选取的问题,提出一种基于动态罚函数的差分进化算法.利用罚函数法将约束优化问题转化为无约束优化问题.为平衡种群的目标函数和约束违反程度,结合ε约束法设计了一种动态罚系数策略,其中罚系数随着种群质量和进化代数的改变而改变.采用差分进化算法更新种群直到搜索到最优解.对IEEE CEC...     

改进罚函数法与蝙蝠算法在约束优化中的应用

设计了一种基于自适应罚函数法和改进蝙蝠算法的约束优化问题求解方法。提出了一种自适应罚函数法,该处理方法综合考虑了约束违反的情况和进化过程的特点,如果某个约束违反的次数越多,则证明该约束越强,赋予惩罚系数越大;种群中的不可行解的数量越多,为保持种群的多样性,则约束应该取较小的值,即惩罚系数取较小的值。提出了一种改进的蝙蝠算法,利用混沌的遍历性特点产生初始种群,增强了初始种群的多样性和种群的质量;在考虑了脉冲响度的蝙蝠算法局部搜索中,融入了交叉操作;为防止算法在后期陷入局部最优解,引进了变异操作,保证了群体的多样性。将自适应罚函数法与改进的蝙蝠算法融合起来求解约束优化问题,4个复杂的标准测试函数和2个工程实际问题证明了该约束优化求解方法的可行性和有效性。     

An effective co-evolutionary particle swarm optimization for constrained engineering design problems

Many engineering design problems can be formulated as constrained optimization problems. So far, penalty function methods have been the most popular methods for constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanism. By employing the notion of co-evolution to adapt penalty factors, this paper proposes a co-evolutionary particle swarm optimization approach (CPSO) for constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. The proposed CPSO is population based and easy to implement in parallel. Especially, penalty factors also evolve using PSO in a self-tuning way. Simulation results based on well-known constrained engineering design problems demonstrate the effectiveness, efficiency and robustness on initial populations of the proposed method. Moreover, the CPSO obtains some solutions better than those previously reported in the literature.     

罚函数凸优化迭代算法及在无人机路径规划中的应用

针对无人机路径规划问题,建立了具有定常非线性系统、非仿射等式约束、非凸不等式约束的非凸控制问题模型,并对该模型进行了算法设计和求解。基于迭代寻优的求解思路,提出了凸优化迭代求解方法和罚函数优化策略。前者利用凹凸过程(CCCP)和泰勒公式对模型进行凸化处理,后者将经处理项作为惩罚项施加到目标函数中以解决初始点可行性限制。经证明该方法严格收敛到原问题的Karush-Kuhn-Tucker(KKT)点。仿真实验验证了罚函数凸优化迭代算法的可行性和优越性,表明该算法能够为无人机规划出一条满足条件的飞行路径。     

自适应惩罚策略及其在交通信号优化中的应用

针对约束优化问题的求解,设计了一种处理约束条件的自适应惩罚策略,用于将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题。该策略通过引入约束可行测度、可行度的概念来描述决策变量服从于不等式约束和等式约束的程度,并以此构造处理约束条件的自适应惩罚函数,惩罚值随着约束可行度的变化而动态自适应地改变。为了检验该惩罚策略的有效性,针对单路口交通信号优化问题进行了应用研究,并用三种不同算法进行了大量的仿真计算,结果表明所设计的自适应策略在具有高度约束条件的城市交通信号优化问题中具有良好的效果。