求解最大割问题的交叉熵算法

交叉熵方法（Cross Entropy）是近几年发展而来的一种启发式方法,在求解组合优化问题中显示出其简单有效的特点,将运用交叉熵方法（CE）寻求图论中一个典型的NP困难问题—最大割问题的最优解。为了解决最大割问题,CE方法借助Bernoulli分布的思想,将一个确定性的网络转换成一个具有一定随机性的关联网络,接下来首先按照一个多维的Bernoulli概率分布生成样本,同时计算出随机割;其次,基于前一步的数据,更新Bernoulli概率分布P参数,使得分布参数逐步逼近最优值产生最大割的稳定估计值。数值实验表明,CE方法具有很好的稳定性和收敛性,最终也获得了比较好的近似解。     

Discrete cuckoo search algorithm for the travelling salesman problem

In this paper, we present an improved and discrete version of the Cuckoo Search (CS) algorithm to solve the famous traveling salesman problem (TSP), an NP-hard combinatorial optimisation problem. CS is a metaheuristic search algorithm which was recently developed by Xin-She Yang and Suash Deb in 2009, inspired by the breeding behaviour of cuckoos. This new algorithm has proved to be very effective in solving continuous optimisation problems. We now extend and improve CS by reconstructing its population and introducing a new category of cuckoos so that it can solve combinatorial problems as well as continuous problems. The performance of the proposed discrete cuckoo search (DCS) is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that DCS is superior to some other metaheuristics.     

Solution of Optimization Problems with Fractional-Linear Objective Functions and Additional Linear Constraints on Permutations

The statement of a problem of Euclidean combinatorial optimization with a fractional-linear objective function on a common set of permutations and with additional linear constraints is formulated. A problem with a fractional-linear objective function is transformed into that with a linear objective function. An approach is proposed to the solution of such problems, and a method of combinatorial truncation of solutions of problems of combinatorial type with fractional-linear objective functions on permutations is developed.     

耦合强度对量子绝热算法求解最大割的影响

本文分析基于量子绝热近似的不同顶点的最大割问题求解.该算法将无向图的顶点等效为量子比特,各个顶点间的边等效为两个量子比特之间的耦合,边的权重值等效为量子比特间的耦合强度.采用Python语言编写算法程序,模拟了6–13个顶点的完全无向图的最大割问题求解情况.实验结果表明,当完全无向图顶点个数取为8,12,13,同时耦合强度为1.0时,所求解最大割问题哈密顿量的期望值不收敛.进一步调整模拟计算中量子比特间耦合强度数值,观察期望值变化.实验发现,对于顶点数为12的完全无向图,耦合强度取0.95时,其期望值获得收敛.对于顶点数为8和13的完全无向图情形,当耦合强度取0.75时,所计算得到的期望值随演化时间变化收敛.由此推测超过13个顶点的完全无向图在用量子绝热算法求解最大割问题时,可将量子比特耦合强度归一化到0.75左右,使期望值有效收敛.     

Quantum inspired evolutionary algorithm for ordering problems

This paper proposes a new quantum-inspired evolutionary algorithm for solving ordering problems. Quantum-inspired evolutionary algorithms based on binary and real representations have been previously developed to solve combinatorial and numerical optimization problems, providing better results than classical genetic algorithms with less computational effort. However, for ordering problems, order-based genetic algorithms are more suitable than those with binary and real representations. This is because specialized crossover and mutation processes are employed to always generate feasible solutions. Therefore, this work proposes a new quantum-inspired evolutionary algorithm especially devised for ordering problems (QIEA-O). Two versions of the algorithm have been proposed. The so-called pure version generates solutions by using the proposed procedure alone. The hybrid approach, on the other hand, combines the pure version with a traditional order-based genetic algorithm. The proposed quantum-inspired order-based evolutionary algorithms have been evaluated for two well-known benchmark applications – the traveling salesman problem (TSP) and the vehicle routing problem (VRP) – as well as in a real problem of line scheduling. Numerical results were obtained for ten cases (7 VRP and 3 TSP) with sizes ranging from 33 to 101 stops and 1 to 10 vehicles, where the proposed quantum-inspired order-based genetic algorithm has outperformed a traditional order-based genetic algorithm in most experiments.     

A simulated annealing algorithm for dynamic layout problem

Increased level of volatility in today's manufacturing world demanded new approaches for modelling and solving many of its well-known problems like the facility layout problem. Over a decade ago Rosenblatt published a key paper on modelling and solving dynamic version of the facility layout problems. Since then, various other researchers proposed new and improved models and algorithms to solve the problem. Balakrishnan and Cheng have recently published a comprehensive review of the literature about this subject. The problem was defined as a complex combinatorial optimisation problem. The efficiency of SA in solving combinatorial optimisation problems is very well known. However, it has recently not been applied to DLP based on the review of the available literature. In this research paper a SA-based procedure for DLP is developed and results for test problems are reported.

Scope and purpose

One of the characteristic of today's manufacturing environments is volatility. Under a volatile environment (or dynamic manufacturing environment) demand is not stable. To operate efficiently under such environments facilities must be adaptive to changing demand conditions. This requires solution of the dynamic layout problem (DLP). DLP is a complex combinatorial optimisation problem for which optimal solutions can be found for small size problems. This research paper makes use of a SA algorithm to solve the DLP. Simulated annealing (SA) is a well-established stochastic neighbourhood search technique. It has a potential to solve complex combinatorial optimisation problems. The paper presents in detail how to apply SA to solve DLP and an extensive computational study. The computational study shows that SA is quite effective in solving dynamic layout problems.     

Combinatorial complexity problem reduction by the use of artificial vaccines

A general method to reduce computing time for large combinatorial optimization problems by the use of a novel proposal is presented. It is based on reducing the problem complexity by the systematic application of vaccines, it is inspired in the concept of immunization derived from Artificial Immune Systems. The method can be applied practically to any combinatorial problem program solver such as genetic algorithms, memetic algorithms, artificial immune systems, ant colony optimization, the Dantzig–Fulkerson–Johnson algorithm, etc., providing optimal and suboptimal routes outperforming the selected algorithm itself. As a direct consequence of reducing problem complexity, the method provides a means to bring combinatorial optimization open problems that are too big to be treated by known techniques to a tractable point where acceptable solutions can be obtained. To demonstrate the proposed methodology the Traveling Salesman Problem for huge quantity of cities was used, we tested the method with modern evolutionary algorithms and the Concorde program. Comparative experiments that shows the effectiveness of the method are presented.     

A GES/TS algorithm for the job shop scheduling

The job shop scheduling problem is a difficult combinatorial optimization problem. This paper presents a hybrid algorithm which combines global equilibrium search, path relinking and tabu search to solve the job shop scheduling problem. The proposed algorithm used biased random sampling to have a better covering of the solution space. In addition, a new version of N6 neighborhood is applied in a tabu search framework. In order to evaluate the algorithm, comprehensive tests are applied to it using various standard benchmark sets. Computational results confirm the effectiveness of the algorithm and its high speed. Besides, 19 new upper bounds among the unsolved problems are found.     

Quantum-inspired evolutionary algorithms with a new termination criterion, H/sub /spl epsi// gate, and two-phase scheme

From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.     

Embedding Remaining Useful Life Predictions into a Modified Receding Horizon Task Assignment Algorithm to Solve Task Allocation Problems

The Task Allocation problem is one of the fundamental combinatorial optimization problems with applications on various domains. Solving a Task Allocation problem consists in, given a set of tasks to be performed and a set of resources, defining which resource will perform each task in order to optimize an objective function. In this paper, we present a modified version of the Receding Horizon Task Assignment (RHTA) algorithm to solve multiple vehicle task assignment problems. In the proposed method, we generate a rejection list to reduce the number of candidate missions that are evaluated in each iteration of the RHTA algorithm. In addition, we incorporate in the mathematical formulation of the problem a set of constraints that limit the maximum mission duration that can be assigned to each vehicle. These constraints represent the predicted Remaining Useful Life (RUL) of each vehicle. Our model takes into account the execution time of each task and assumes that all vehicles must finish their missions at a base. The proposed model allows the vehicles to go to a base for maintenance during their missions. Numerical experiments are carried out using twenty benchmark problem instances. The results show that incorporating RUL predictions into task allocation problems increases the quality and the robustness of solutions.     

一类组合优化问题的混合进化算法

针对问题空间为全排列集合的一类组合优化问题,提出了一种混合进化算法。在自然进位制编码的基础上,算法采用了遗传算法的单点交叉算子和进化规划的高斯扰动算子,并运用了精英保留策略;算法实现时采用逐位运算法实现大数值运算,避免了运算溢出,减少了运算量。分析和模拟计算结果表明,新算法具有可行性、有效性和通用性。     

Enhancing optimal feeder assignment of the multi-head surface mounting machine using genetic algorithms

The problem of minimizing the time required to populate a printed circuit board using a multi-head surface mounting machine is considered in this paper. The multi-head surface mounting machine is becoming increasingly popular due to its merit of picking or placing multiple components simultaneously in one pick-and-place operation, which reduces much portion of the assembly time. The complexity of the optimization problem of minimizing the assembly time results in that acquiring its desired solution is difficult. The total assembly time depends on two optimization problems: feeder assignment problem and pick-and-place sequencing problem. Although these two problems are interrelated, they are solved, respectively. Feeder assignment problem is one crucial problem of affecting surface mounting machine's productivity directly. Optimal feeder assignment can decrease sum of time of moving along slots, moving from slot to PCB and moving from PCB to slot for placement heads griping components after predetermining pick-and-place sequence. For it is of a combinatorial nature and NP-hard, there is no exact algorithm for it. As an efficient and useful procedure for solving the combinatorial optimization problems, the genetic algorithm with specific crossover and mutation operators is proposed in this paper. The running results show that the proposed method performs better than the conventional methods.     

Design of water distribution networks using accelerated momentum particle swarm optimisation technique

Optimisation of looped water distribution networks (WDNs) has been recognised as an NP-hard combinatorial problem which cannot be easily solved using traditional mathematical optimisation techniques. This article proposes the use of a new version of heuristic particle swarm optimisation (PSO) for solving this problem. In order to increase the convergence speed of the original PSO algorithm, some accelerated parameters are introduced to the velocity update equation. Furthermore, momentum parts are added to the PSO position updating formula to get away from trapping in local optimums. The new version of the PSO algorithm is called accelerated momentum particle swarm optimisation (AMPSO). The proposed AMPSO is then applied to solve WDN design problems. Some illustrative and comparative illustrative examples are presented to show the efficiency of the introduced AMPSO compared with some other heuristic algorithms.     

Job Shop Scheduling with the Best-so-far ABC

The Job Shop Scheduling Problem (JSSP) is known as one of the most difficult scheduling problems. It is an important practical problem in the fields of production management and combinatorial optimization. Since JSSP is NP-complete, meaning that the selection of the best scheduling solution is not polynomially bounded, heuristic approaches are often considered. Inspired by the decision making capability of bee swarms in the nature, this paper proposes an effective scheduling method based on Best-so-far Artificial Bee Colony (Best-so-far ABC) for solving the JSSP. In this method, we bias the solution direction toward the Best-so-far solution rather a neighboring solution as proposed in the original ABC method. We also use the set theory to describe the mapping of our proposed method to the problem in the combinatorial optimization domain. The performance of the proposed method is then empirically assessed using 62 benchmark problems taken from the Operations Research Library (OR-Library). The solution quality is measured based on “Best”, “Average”, “Standard Deviation (S.D.)”, and “Relative Percent Error (RPE)” of the objective value. The results demonstrate that the proposed method is able to produce higher quality solutions than the current state-of-the-art heuristic-based algorithms.     

蚁群优化算法在求解随机组合优化问题中的应用综述*

不确定条件下的优化问题更贴近真实世界环境,因而日益受到广泛关注。综述了蚁群优化在求解一组不确定条件下的组合优化问题,即随机组合优化问题方面的应用。首先介绍了不确定条件下组合优化问题的概念分类模型,给出了随机组合优化问题的一般定义;然后指出了其与求解传统确定性组合优化问题的不同之处,即目标函数的计算存在不确定性,并详细论述了目前解决方法的进展;最后分析了该领域值得重点关注的几个研究方向,并对其未来发展进行了展望。     

大规模分布式资源搜索技术研究进展*

针对分布式资源搜索技术及其分类的特点,分别从基于网格的搜索技术的穷举式、集中式、路由式,以及基于P2P系统的搜索技术的集中式、全分布式非结构化、混合式、全分布式结构化等几个方面,对当前研究的分布式资源搜索技术进行了归纳总结,并且对该研究领域需要解决的问题进行了总结,对进一步研究的方向进行了展望。     

Using computational learning strategies as a tool for combinatorial optimization

In this paper, we describe how a basic strategy from computational learning theory can be used to attack a class of NP‐hard combinatorial optimization problems. It turns out that the learning strategy can be used as an iterative booster: given a solution to the combinatorial problem, we will start an efficient simulation of a learning algorithm which has a “good chance” to output an improved solution. This boosting technique is a new and surprisingly simple application of an existing learning strategy. It yields a novel heuristic approach to attack NP‐hard optimization problems. It does not apply to each combinatorial problem, but we are able to exactly formalize some sufficient conditions. The new technique applies, for instance, to the problems of minimizing a deterministic finite automaton relative to a given domain, the analogous problem for ordered binary decision diagrams, and to graph coloring. This revised version was published online in June 2006 with corrections to the Cover Date.     

Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem

Hyper heuristics is a relatively new optimisation algorithm. Numerous studies have reported that hyper heuristics are well applied in combinatorial optimisation problems. As a classic combinatorial optimisation problem, the row layout problem has not been publicly reported on applying hyper heuristics to its various sub-problems. To fill this gap, this study proposes a parallel hyper-heuristic approach based on reinforcement learning for corridor allocation problems and parallel row ordering problems. For the proposed algorithm, an outer layer parallel computing framework was constructed based on the encoding of the problem. The simulated annealing, tabu search, and variable neighbourhood algorithms were used in the algorithm as low-level heuristic operations, and Q-learning in reinforcement learning was used as a high-level strategy. A state space containing sequences and fitness values was designed. The algorithm performance was then evaluated for benchmark instances of the corridor allocation problem (37 groups) and parallel row ordering problem (80 groups). The results showed that, in most cases, the proposed algorithm provided a better solution than the best-known solutions in the literature. Finally, the meta-heuristic algorithm applied to three low-level heuristic operations is taken as three independent algorithms and compared with the proposed hyper-heuristic algorithm on four groups of parallel row ordering problem instances. The effectiveness of Q-learning in selection is illustrated by analysing the comparison results of the four algorithms and the number of calls of the three low-level heuristic operations in the proposed method.     

A particle swarm optimization algorithm for open vehicle routing problem

This paper presents a real-value version of particle swarm optimization (PSO) for solving the open vehicle routing problem (OVRP) that is a well-known combinatorial optimization problem. In OVRP a vehicle does not return to the depot after servicing the last customer on a route. A particular decoding method is proposed for implementing PSO for OVRP. In the decoding method, a vector of the customer’s position is constructed in descending order. Then each customer is assigned to a route with taking into account feasibility conditions. Finally one-point move has been applied on constructed routes that seem promising to result in a better solution. Experimental evaluations on benchmark data sets demonstrate the competitiveness of the proposed algorithm.     

A tabu search based hybrid evolutionary algorithm for the max-cut problem

This paper presents a tabu search based hybrid evolutionary algorithm (TSHEA) for solving the max-cut problem. The proposed algorithm integrates a distance-and-quality based solution combination operator and a tabu search procedure based on neighborhood combination of one-flip and constrained exchange moves. Comparisons with leading reference algorithms from the literature disclose that the proposed algorithm discovers new best solutions for 15 out of 91 instances, while matching the best known solutions on all but 4 instances. Analysis indicates that the neighborhood combination and the solution combination operator play key roles to the effectiveness of the proposed algorithm.