旅行商问题(TSP)的一种改进遗传算法

传统的序号编码遗传算法(GA)使用PMX、CX和OX等特殊的交叉算子，这些算子实施起来很麻烦。针对TSP问题的求解，提出了一种新的改进遗传算法：单亲进化遗传算法(PEGA)，PEGA是利用父体所提供的有效边的信息，使用保留最小边的方法进行个体的进化。与传统的遗传算法相比，PEGA算法弥补了它们的不足之处，简化了遗传算法。给出了PEGA算法的数值算例，仿真实验表明了该算法对于对称的TSP和非对称的TSP问题，都具有收敛速度快的特点，证明了该算法的有效性。     

改进差异演化算法求解约束优化问题

在现实生活中许多实际问题都可以转化为约束优化问题,并且实际问题通常都很复杂,其函数形态各具特色,传统基于梯度信息的各种求解策略对于具有不可微、多峰及非凸的非线性函数约束优化问题很难凑效。而最近兴起的智能类算法却对这类问题的求解效果突出,在借鉴国外的差异演化算法研究成果基础上,运用改进差异演化算法来求解约束优化问题。最后通过实例进行仿真实验,结果表明改进差异演化算法在求解约束优化问题时具有一定的优越性。     

求解高维多模优化问题的自适应差分进化算法

在基变量选择方差理论分析的基础上,提出一种自适应差分进化算法(ADE).ADE算法通过设计自适应收敛因子构建自调整的权重质心变异策略,同时在交叉策略中引入发射、收缩两种单纯形操作算子,保证算法全局搜索能力的同时,能钉效提高算法后期的局部增强能力.30个优化问题的数值研究结果表明ADE算法具有比DE、DERL以及DERB三种算法更快的收敛速度和可靠性,尤其适合于高维多模优化问题的求解.     

Measuring instance difficulty for combinatorial optimization problems

Discovering the conditions under which an optimization algorithm or search heuristic will succeed or fail is critical for understanding the strengths and weaknesses of different algorithms, and for automated algorithm selection. Large scale experimental studies - studying the performance of a variety of optimization algorithms across a large collection of diverse problem instances - provide the resources to derive these conditions. Data mining techniques can be used to learn the relationships between the critical features of the instances and the performance of algorithms. This paper discusses how we can adequately characterize the features of a problem instance that have impact on difficulty in terms of algorithmic performance, and how such features can be defined and measured for various optimization problems. We provide a comprehensive survey of the research field with a focus on six combinatorial optimization problems: assignment, traveling salesman, and knapsack problems, bin-packing, graph coloring, and timetabling. For these problems - which are important abstractions of many real-world problems - we review hardness-revealing features as developed over decades of research, and we discuss the suitability of more problem-independent landscape metrics. We discuss how the features developed for one problem may be transferred to study related problems exhibiting similar structures.     

A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

A note on robustness tolerances for combinatorial optimization problems

We consider so-called generic combinatorial optimization problem, where the set of feasible solutions is some family of nonempty subsets of a finite ground set with specified positive initial weights of elements, and the objective function represents the total weight of elements of the feasible solution. We assume that the set of feasible solutions is fixed, but the weights of elements may be perturbed or are given with errors. All possible realizations of weights form the set of scenarios.A feasible solution, which for a given set of scenarios guarantees the minimum value of the worst-case relative regret among all the feasible solutions, is called a robust solution. The maximum percentage perturbation of a single weight, which does not destroy the robustness of a given solution, is called the robustness tolerance of this weight with respect to the solution considered.In this paper we give formulae for computing the robustness tolerances with respect to an optimal solution obtained for some initial weights and we show that this can be done in polynomial time whenever the optimization problem is polynomially solvable itself.     

基于混合编码的差异演化算法解0-1背包问题*

针对典型的一类NP完全问题——背包问题,提出一种混合编码的差异演化求解方法。该方法基于差异演化算法框架,采用混合编码机制,每个决策变量均由一个实数和一个二进制数的组合表示。利用新定义的映射算子,构建混合编码的种群;增加边界约束处理算子,确保变异算子计算结果满足边界约束条件;利用新定义的丢弃算子对于不可行的装包策略进行修正。通过数值仿真实验,将该方法与遗传算法、二进制差异算法的计算结果比较分析,表明该算法求解背包问题的有效性与适用性。     

非线性约束优化问题的自适应差分进化算法

提出了一种非线性约束优化问题改进的自适应差分进化算法。该算法对差分进化算法中固定的加权因子和交叉概率因子进行改进;定义了约束违反度函数,将约束优化问题转化为无约束双目标优化问题,在每次迭代中按照约束违反度的大小保留一部分性能较优不可行粒子,有效地维持了种群的多样性;为了扩大粒子的搜索范围引入变异算子。数值实验表明,新算法具有较快的收敛速度和较好的全局寻优能力。     

差分进化混合粒子群算法求解项目调度问题*

针对求解资源受限项目调度问题（RCPSP）,提出了基于差分进化（DE）的混合粒子群算法（PSODE）。通过在PSO种群和DE种群之间建立一种信息交流机制,使信息能够在两个种群中传递,以避免个体因错误的信息判断而陷入局部最优点。采用标准测试函数和具体算例进行检验,结果表明PSODE算法可以较好地解决RCPS问题。     

Approximation algorithms for combinatorial multicriteria optimization problems

The computational complexity of combinatorial multiple objective programming problems is investigated. NP-completeness and # P -completeness results are presented. Using two definitions of approximability, general results are presented, which outline limits for approximation algorithms. The performance of the well-known tree and Christofides' heuristics for the traveling salesman problem is investigated in the multicriteria case with respect to the two definitions of approximability.     

协同智能的蝙蝠差分混合算法

为解决差分进化算法后期收敛易陷入局部最优和早熟收敛的问题,提出一种群体智能优化算法,即协同智能的蝙蝠差分混合算法。利用蝙蝠个体脉冲回声定位的特点,与差分种群相互协作,在当前最优解gbest附近进行一次详细搜索,有效增加种群的多样性,跳出局部最优。通过蝙蝠种群和差分种群两个种群的相互协作,较好平衡全局搜索和局部开发之间的能力。为验证算法有效性,选用9个常用的基准测试函数和5个0-1背包问题,与标准粒子群算法、带高斯扰动的粒子群算法、蝙蝠算法、差分算法、烟花算法相对比,仿真实验表明,所提算法总体性能优于其它5种算法。     

一种求解高维多模态复杂问题的差分文化算法

针对在求解高维多峰值复杂问题时种群容易陷入局部搜索、求解精度低的问题,提出了一种基于自适应差分进化算法和小生境高斯分布估计的文化算法。将差分进化算法用于种群空间的优化,利用动态小生境识别算法在种群空间中识别小生境群体。信度空间利用高斯分布估计算法在小生境内进行局部优化,并将小生境特征存入进化知识库,进化知识库进一步引导种群空间,有效地保证了种群的多样性,避免了局部的重复搜索。最后,通过仿真实验测试表明,算法具有收敛速度快、求解精度高、稳定性高和全局搜索能力强等优势。     

Shift-and-merge technique for the DP solution of the time-constrained backpacker problem

We formulate the time-constrained backpacker problem as an extension of the classical knapsack problem (KP), where a ‘backpacker’ travels from a origin to a destination on a directed acyclic graph, and collects items en route within the capacity of his knapsack and within a fixed time limit. We present a dynamic programming (DP) algorithm to solve this problem to optimality, and a ‘shift-and-merge’ DP algorithm to solve larger instances. The latter is an extension of the list-type DP, which has been successful for one-dimensional KPs, to the two-dimensional case. Computational experiments on a series of instances demonstrate advantage of the shift-and-merge technique over commercial MIP solvers.     

混合差异演化算法在背包问题中的应用

提出了一种用于求解0-1背包问题的混合差异演化算法,详细阐述了该算法求解背包问题的具体操作过程。算法主要使用了两个思想策略,即启发式贪婪算法和基于二进制编码的差异演化算法。通过对其它文献中仿真实例的计算和结果对比,表明该算法对求解0-1背包问题的有效性,这对差异演化算法解决其它离散问题会有些帮助。     

A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.     

Multi-center variable-scale search algorithm for combinatorial optimization problems with the multimodal property

Combinatorial optimization problems (COPs) are discrete problems arising from aerospace, bioinformatics, manufacturing, and other fields. One of the classic COPs is the scheduling problem. Moreover, these problems are usually multimodal optimization problems with a quantity of global and local optima. As a result, many search algorithms can easily become trapped into local optima. In this article, we propose a multi-center variable-scale search algorithm for solving both single-objective and multi-objective COPs. The algorithm consists of two distinct points. First, the multi-center strategy chooses several individuals with better performance as the only parents of the next generation, which means that there are a number of separate searching areas around the searching center. Second, the next generation of the population is produced by a variable-scale strategy with an exponential equation based on the searching center. The equation is designed to control the neighborhood scale, and adaptively realize the large-scale and small-scale searches at different search stages to balance the maintenance of diversity and convergence speed. In addition, an approach of adjusting centers is proposed concerning the number and distribution of centers for solving multi-objective COPs. Finally, the proposed algorithm is applied to three COPs, including the well-known flexible job shop scheduling problem, the unrelated parallel machine scheduling problem, and the test task scheduling problem. Both the single-objective optimization algorithm and the multi-objective optimization algorithm demonstrate competitive performance compared with existing methods.     

基于代理模型的差分进化约束优化

针对耗时计算目标函数的约束优化问题,提出用代理模型来代替耗时计算目标函数的方法,并结合目标函数的信息对约束个体进行选择,从而提出基于代理模型的差分进化约束优化算法。首先,采用拉丁超立方采样方法建立初始种群,用耗时计算目标函数对初始种群进行评估,并以此为样本数据建立目标函数的神经网络代理模型。然后,用差分进化方法为种群中的每一个亲本产生后代,并对后代使用代理模型进行评估,采用可行性规则来比较后代与其亲本并更新种群,根据替换机制将种群中较劣的个体替换为备用存档中较优的个体。最后,当达到最大适应度评估次数时算法停止,给出最优解。该算法与对比算法在10个测试函数上运行的结果表明,该算法得出的结果更精确。将该算法应用于工字梁优化问题的结果表明,相较于优化前的算法,该算法的适应度评估次数减少了80%;相对于FROFI（Feasibility Rule with the incorporation of Objective Function Information）算法,该算法的适应度评估次数减少了36%。运用所提算法进行优化可以有效减少调用耗时计算目标函数的次数,提升优化效率,节约计算成本。     

An approximation algorithm for interval data minmax regret combinatorial optimization problems

The general problem of minimizing the maximal regret in combinatorial optimization problems with interval data is considered. In many cases, the minmax regret versions of the classical, polynomially solvable, combinatorial optimization problems become NP-hard and no approximation algorithms for them have been known. Our main result is a polynomial time approximation algorithm with a performance ratio of 2 for this class of problems.     

云环境下求解大规模优化问题的协同差分进化算法

差分进化是一种求解连续优化问题的高效算法。然而差分进化算法求解大规模优化问题时,随着问题维数的增加,算法的性能下降,且搜索时间呈指数上升。针对此问题,本文提出了一种新的基于Spark的合作协同差分进化算法（SparkDECC）。SparkDECC采用分治策略,首先通过随机分组方法将高维优化问题分解成多个低维子问题,然后利用Spark的弹性分布式数据模型,对每个子问题并行求解,最后利用协同机制得到高维问题的完整解。通过在13个高维测试函数上进行的对比实验和分析,实验结果表明算法加速明显且可扩展性好,验证了SparkDECC的有效性和适用性。