解灰色非线性规划问题的随机搜索算法

对带约束条件的灰色非线性规划问题进行了探讨,首先将原灰色约束非线性规划问题进行均值白化处理,转化成一个确定型的带约束条件的非线性规划问题,对该确定型的非线性约束规划问题提出一个基于分布估计算法的随机搜索方法,对所提出的求解方法的关键技术作了详细的说明并给出了具体的算法步骤。 初步的数值算例表明所提出的方法是可行有效的     

基于不可行度和内分泌原理的多目标粒子群方法

针对有约束条件的多目标优化问题,提出了一种求解带约束的基于内分泌思想的多目标粒子群算法。利用不可行度方法和约束主导原理指导进化过程中精英种群的选择操作和约束条件的处理,根据生物体激素调节机制中促激素和释放激素间的相互作用原理,考虑当前非劣解集中的个体对其最邻近的一类群体的监督控制,引入当前粒子的类全局最优位置来反映其所属类中最好位置粒子对当前粒子的影响。为验证多目标约束优化算法的有效性,对两个典型的多目标优化问题进行了仿真实验,仿真结果表明该算法能较大概率地获得多目标约束优化问题的可行Pareto最优解。     

一种求解约束优化问题的演化规划算法

提出了一种新的求解约束优化问题的演化算法--基于混合策略求解约束优化问题的演化规划算法（CMSEP）.借鉴了Mezura-Montes的算法中直接比较的约束处理方法,为求解位于边界附近的全局最优解采用多样性保护机制,允许一定比例最好不可行解进入下一代种群,混合策略变异机制用于指导算法快速搜索过程.标准测试函数的实验结果验证了算法的通用性和有效性.     

基于内部罚函数的进化算法求解约束优化问题

为解决现有约束处理方法可行解的适应度函数不包含约束条件的问题,提出了一种内部罚函数候选解筛选规则.该候选解筛选规则分别对可行解和不可行解采用内部罚函数和约束违反度进行筛选,从而达到平衡最小化目标函数和满足约束条件的目的.以进化策略算法为基础,给出了基于内部罚函数候选解筛选规则的进化算法的一个实现.进一步地,从理论和实验角度分别验证了内部罚函数候选解筛选规则的有效性:以(1+1)进化算法为例,从进化成功率方面验证了内部罚函数候选解筛选规则的理论有效性;通过13个测试问题的数值实验,从进化成功率、候选解后代是可行解的比例、进化步长和收敛速度方面验证了内部罚函数候选解筛选规则的实验有效性.     

求解多限制0-1背包问题的混合遗传算法

为求解多限制0-1背包问题,设计一种新的价值密度,提出一种基于贪心法的混合遗传算法,采用二进制编码对适应值进行升序排列,并运用轮盘赌选择方法对背包资源利用不足的可行解进行修正处理,对不可行解进行修复处理,并将其与传统遗传算法进行比较。实验结果表明,该算法能够有效提高问题求解的速度和精度,具有一定优越性。     

约束优化问题的混合遗传算法研究

如何处理约束条件与增强局部搜索能力是遗传算法用于非线性约束优化问题的线性约束优化问题的不足,提出了一种基于模拟退火算法与外点法的混合遗传算法,对于不满足约束条件的解用外点罚函数法来修正,同时把退火选择算子作为一个与选择、交叉和变异平行的算子,嵌入到实数编码的遗传算法中,来增强其的局部搜索能力.算法兼顾了遗传算法、模拟退火算法和外点法三者的长处,既有较快的收敛速度,又能以较大的概率求得非线性约束优化问题的全局最优解.最后以两个测试函数为算例对算法进行测试,验证了该算法搜索能力强、稳健性好,能获得更好的优化结果.实验结果表明引入外点法处理约束条件是可行的.     

混合二进制差异演化算法解0-1背包问题

为了有效求解0-1背包问题,提出一种混合二进制差异演化算法.该算法基于差异演化算法框架,采用二进制编码,通过增加映射操作、S型变换操作和逆映射操作等3种新的操作,将差异演化算法从实数优化领域推广至离散优化领域,成功解决了差异演化算法直接求解离散优化问题时的计算不封闭问题.此外,在每次迭代求解时,利用贪婪变换法对违反约束条件的不可行解进行变换,使其成为可行解.不同规模的背包问题的数值实验结果表明了该算法的有效性与适用性.     

Pareto强度值演化算法求解约束优化问题

提出了一种求解约束函数优化问题的方法.它不使用传统的惩罚函数,也不区分可行解和不可行解.新的演化算法将约束优化问题转换成两个目标优化问题,其中一个为原问题的目标函数,另一个为违反约束条件的程度函数.利用多目标优化问题中的Pareto优于关系,定义个体Pareto强度值指标以便对个体进行排序选优,根据Pareto强度值排序和最小代数代沟模型设计出新的实数编码遗传算法.对常见测试函数的数值实验证实了新方法的有效性、通用性和稳健性,其性能优于现有的一些演化算法.特别是对于一些既有等式约束又有不等式约束的复杂非线性规划问题,该算法获得了更高精度的解.     

最短路径问题的禁忌搜索求解方法

针对网络优化算法中的最短路径（Shortest Path,SP）问题,建立了有约束条件的SP问题模型,并探讨了使用禁忌搜索（Tabu Search,TS）算法对其求解的算法框架及关键步骤。该求解方法寻优能力强,结构简明,能方便处理问题约束,具有智能计算方法的优点。最后,通过实例进行测试和比较,证明算法收敛速度快,并能够获得满足约束条件的优解集合,能适应较差网络条件下的多条路径选择,算法是可行和有效的。     

求解多背包问题的混合遗传算法

针对多背包问题最优解的求解,设计了一种新的价值密度;在此基础上结合传统的贪心算法,提出了一种求解多背包问题的混合遗传算法。该算法采用整数编码,并采用轮盘赌选择方法,对背包资源利用不足的可行解进行修正处理,对不可行解进行修复处理。并在大量的数值实验的基础上,将该方法与传统方法及简单遗传算法进行比较,实验结果表明,该混合遗传算法提高了问题求解的速度和精度,有一定的优越性。     

Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization

The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail.     

求解SAT问题的拟人退火算法

该文利用一个简单的变换，将可满足性（SAT）问题转换为一个求相应目标函数最小值的优化问题，提出了一种用于跳出局部陷阱的拟人策略，基于模拟退火算法和拟人策略，为SAT问题的高效近注解得出了拟人退火算法（PA），该方法不仅具有模拟退火算法的全局收敛性质，而且具有一定的并行性，继承性。数值实验表明，对于本文随机产生的测试问题例，采用拟人策略的模拟退火算法的结果优于局部搜索算法，模拟退火算法以及近来国际上流行的WALKSAT算法，因此拟人退火算法是可行的和有效的。     

Transit network design by Bee Colony Optimization

The transit network design problem is one of the most significant problems faced by transit operators and city authorities in the world. This transportation planning problem belongs to the class of difficult combinatorial optimization problem, whose optimal solution is difficult to discover. The paper develops a Swarm Intelligence (SI) based model for the transit network design problem. When designing the transit network, we try to maximize the number of satisfied passengers, to minimize the total number of transfers, and to minimize the total travel time of all served passengers. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristics. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm, is competitive with other approaches in the literature, and it can generate high-quality solutions.     

求解Job Shop调度问题的混合蚁群算法研究

为了解决单一算法求解Job Shop调度问题存在的不足，该文提出了一种混合算法，将蚁群算法用于全局搜索。针对蚁群算法易于陷入局部最优的情况，提出了一种基于关键工序的邻域搜索方法，将使用此邻域搜索方法的TS算法作为局部搜索策略。利用TS算法较强的局部搜索能力，提高了蚁群算法的优化能力，达到改善Job Shop调度问题解的质量。实验结果表明，混合算法在较短的时间内，找到了FT10、LA24、LA36等典型benchmarks问题的最优解，得到的makespan的平均值较并行遗传算法(PGA)和TSAB算法均有所提高。     

Recursive estimation algorithms for power controls of wireless communication networks

Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access （DS/CDMA） channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.     

基于蚂蚁搜索度约束最小生成树的改进算法

针对度约束最小生成树问题,对基本的蚁群算法进行改进。提出了度信息的概念来改进转移概率,保证算法获得可行解;同时采用基于度的禁忌表这种数据结构来表示度约束生成树,并与深度优先搜索的思想结合,保证得到树的连通性;将遗传算法中的变异特征引入蚁群算法,对生成树进行局部优化。不仅提高算法的效率,而且避免早熟收敛。通过数值试验验证新算法的可行性,并与其他算法进行比较,取得了良好的效果。     

基于变长基因型遗传算法的多供应点应急物资调度优化

如何及时高效地调度应急物资以减小突发事件带来的伤害成为社会关注的焦点问题。在综合考虑新冠肺炎疫情这类特殊突发事件特点的前提下,构建了一类多供应点多式联运应急物资调度网络,并以运输成本最低、时间惩罚最少、配送员被感染风险最小为优化目标建立了一类多目标调度优化模型。考虑到基于聚类思想的优化算法在解决多供应点,尤其是多目标调度优化问题中缩减可行域方法科学性存疑的局限性,提出了一类考虑完全可行域思想的变长基因型混合小生境遗传算法,并借助23个基准测试实例验证了这一算法的有效性,更新了部分实例的现有最优解。在此基础上,通过比较多供应点应急物资多式联运算例中四类遗传算法的仿真结果进一步验证了混合小生境等改进策略的优越性。     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

基于新模型的多目标Memetic算法及收敛分析

将多目标函数优化问题转化成单目标约束优化问题.对转化后的问题提出了基于约束主导原理的选择方法,克服了多数方法只使用Pareto优胜关系作为选择策略而没有采用偏好信息这一缺陷;Memetic算法是求解多目标优化问题最有效的方法之一,它融合了局部搜索和进化计算.新的多目标Memetic算法引进C-metric,将模拟退火算法与遗传算法结合起米,改善了全局搜索能力.用概率论的有关知识证明了算法的收敛性.仿真结果表明该方法对不同的试验函数均可求出一组沿着Pareto前沿分布均匀且散布广泛的非劣解.     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.