三维装箱问题的组合启发式算法

通过组合拟人启发式和模拟退火算法,提出了三维装箱问题的组合启发式算法.拟人启发式算法的主要思想来源于日常砌墙中的策略.利用找点法以及水平和垂直参考线规则来控制装填过程.用模拟退火算法改进拟人启发式.经过一些数据的测试,实验结果表明,该算法能够同文献中的优秀算法竞争.     

超启发式交叉熵算法求解分布式装配柔性作业车间调度问题

本文针对一类新型两阶段分布式装配柔性作业车间调度问题(DAFJSP),建立问题模型,以最小化最大完工时间为优化目标并提出一种超启发式交叉熵算法(HHCEA)进行求解.首先,设计基于工序序列、工厂分配和产品序列的三维向量编码规则和结合贪婪策略的解码规则,同时提出4种启发式方法以提高初始解的质量.然后,设计高低分层结构的HHCEA,高层为提高对搜索方向的引导性,采用交叉熵算法(CEA)学习和积累优质排列的信息,其中各排列由结合问题特点设计的11种启发式操作(即11种有效的邻域操作)构成;低层为增加在解空间中的搜索深度,将高层确定的每个排列中的启发式操作依次重复执行指定次数并在执行过程中加入基于模拟退火的扰动机制,以此作为一种新的启发式方法执行搜索.最后,通过仿真实验与算法对比验证HHCEA可有效求解DAFJSP.     

基于混合蛙跳和遗传规划的跨单元调度方法

针对运输能力受限条件下的跨单元问题,提出了一种基于混合蛙跳与遗传规划的超启发式算法.将改进的混合蛙跳算法作为超启发式算法的高层框架,为跨单元调度问题搜索启发式规则,同时利用遗传规划产生可以兼顾多因素的优质规则,用于扩充超启发式算法的规则集.实验表明,提出的算法可以有效地搜索出优异的规则组合,并且通过遗传规划产生的规则可以在很大程度上改善候选规则集,提升算法性能.     

布朗运动模拟退火算法

针对传统模拟退火算法计算效率较低的问题,文中将布朗运动和模拟退火相结合,提出一种智能启发式算法.该算法将布朗运动中粒子运动时间和模拟退火温度联系在一起,布朗运动的粒子运动时间等效于退火温度的倒数,通过理论分析得到基于布朗运动的邻域函数模型以及相应的温度下降函数.温度下降函数具有更快的退温特性,保证算法执行过程中具有更高的效率.数值实验结果表明,该算法具有搜索速度快、稳定性高和易于实现的特点,能显著提高求解全局优化问题的计算效率.     

求解三维装箱问题的混合模拟退火算法

提出了一个高效求解三维装箱问题(Three Dimensional Container Loading Problem 3D-CLP)的混合模拟退火算法.三维装箱问题要求装载给定箱子集合的一个子集到容器中,使得被装载的箱子总体积最大.文中介绍的混合模拟退火算法基于三个重要算法:(1)复合块生成算法,与传统算法不同的是文中提出的复合块不只包含单一种类的箱子,而是可以在一定的限制条件下包含任意种类的箱子.(2)基础启发式算法,该算法基于块装载,可以按照指定装载序列生成放置方案.(3)模拟退火算法,以复合块生成和基础启发式算法为基础,将装载序列作为可行放置方案的编码,在编码空间中采用模拟退火算法进行搜索以寻找问题的近似最优解.文中采用1500个弱异构和强异构的装箱问题数据对算法进行测试.实验结果表明,混合模拟退火算法的填充率超过了目前已知的优秀算法.     

混合启发式算法在排课问题上的应用

对排课问题做出了形式化描述,提出了一种用于排课的混合启发式算法,该算法合并使用了模拟退火和迭代局部搜索两种算法。先依据图着色算法产生初始可行解,然后应用模拟退火算法寻找最优解,为使算法更好地跳出局部最优,实现全局搜索,在模拟退火算法应用过程中,迭代使用两个邻域,标准邻域和双Kempe链邻域。实验结果表明,此算法能够很好地提高解的质量。     

给予模拟退火研制批量计划问题的两阶段算法

本文建立了一种轧制批量计划问题的数学模型,提出一种改进的两阶段启发式算法,并对其求解。该算法是由启发式算法和模拟退火算法组成的,基于实际生产数据的仿真结果证实了该算法的有效性。     

柔性作业车间调度问题的一种启发式算法

为了研究多目标柔性作业车间调度问题,基于甘特图和搭积木经验进行了分析,提出了一种组合优先规则和基于此优先规则的启发式算法.组合优先规则面向完工时间、关键机床负荷和总负荷三个指标,改变规则中各数据项的比例可调整三个指标所占的比例;算法采用随机方式调整三个指标的比例,并微调最优解对应的比例.能随机产生多个高质量调度解.算法...     

正三角形容器内等圆Packing问题的启发式算法

等圆Packing问题研究如何将n个单位半径的圆形物体互不嵌入地置入一个边长尽量小的正三角形容器内,作为一类经典的NP难度问题,其有着重要的理论价值和广泛的应用背景.模拟退火算法是一种随机的全局寻优算法,通过将启发式格局更新策略与基于梯度法的局部搜索策略融入模拟退火算法,并与二分搜索相结合,提出一种求解正三角形容器内等圆Packing问题的启发式算法.该算法将启发式格局更新策略用来产生新格局和跳坑,用梯度法搜索新产生格局附近能量更低的格局,并用二分搜索得到正三角形容器的最小边长.对41个算例进行测试的实验结果表明,文中算法改进了其中38个实例的目前最优结果,是求解正三角形容器内等圆Packing问题的一种有效算法.     

图着色问题的启发式搜索蚂蚁算法

针对经典的图着色问题，该文在随机序列启发式搜索求解的基础上，引进蚂蚁算法优化思想，设计了一种新型算法，有效地避免了启发式搜索易陷入局部极小的缺陷。通过给地图着色和仿真实验结果表明，该方法对图着色问题的求解是可行、有效的，且具有通用性。     

A graph coloring constructive hyper-heuristic for examination timetabling problems

In this work we investigate a new graph coloring constructive hyper-heuristic for solving examination timetabling problems. We utilize the hierarchical hybridizations of four low level graph coloring heuristics, these being largest degree, saturation degree, largest colored degree and largest enrollment. These are hybridized to produce four ordered lists. For each list, the difficulty index of scheduling the first exam is calculated by considering its order in all lists to obtain a combined evaluation of its difficulty. The most difficult exam to be scheduled is scheduled first (i.e. the one with the minimum difficulty index). To improve the effectiveness of timeslot selection, a?roulette wheel selection mechanism is included in the algorithm to probabilistically select an appropriate timeslot for the chosen exam. We test our proposed approach on the most widely used un-capacitated Carter benchmarks and also on the recently introduced examination timetable dataset from the 2007 International Timetabling Competition. Compared against other methodologies, our results demonstrate that the graph coloring constructive hyper-heuristic produces good results and outperforms other approaches on some of the benchmark instances.     

Iterated local search using an add and delete hyper-heuristic for university course timetabling

Hyper-heuristics are (meta-)heuristics that operate at a higher level to choose or generate a set of low-level (meta-)heuristics in an attempt of solve difficult optimization problems. Iterated local search (ILS) is a well-known approach for discrete optimization, combining perturbation and hill-climbing within an iterative framework. In this study, we introduce an ILS approach, strengthened by a hyper-heuristic which generates heuristics based on a fixed number of add and delete operations. The performance of the proposed hyper-heuristic is tested across two different problem domains using real world benchmark of course timetabling instances from the second International Timetabling Competition Tracks 2 and 3. The results show that mixing add and delete operations within an ILS framework yields an effective hyper-heuristic approach.     

超启发算法研究进展综述

超启发算法是一类新兴的优化方法,通过机器学习、算法选择、算法生成等技术求解组合优化等问题,具备跨问题领域求解的能力。针对超启发算法研究进展进行综述和讨论。首先,梳理超启发算法的定义、结构、特点和分类;其次,归纳选择式超启发算法和生成式超启发算法的研究进展及相关技术,包括选择低层启发式算法采用的学习方法,迭代计算中的移动接受策略,低层启发式算法的生成方法;最后,讨论现有超启发算法研究中存在的不足及未来的研究方向。     

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.     

Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling

This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.     

Grammatical evolution as a hyper-heuristic to evolve deterministic real-valued optimization algorithms

Hyper-heuristic methodologies have been extensively and successfully used to generate combinatorial optimization heuristics. On the other hand, there have been almost no attempts to build a hyper-heuristic to evolve an algorithm for solving real-valued optimization problems. In our previous research, we succeeded to evolve a Nelder–Mead-like real function minimization heuristic using genetic programming and the primitives extracted from the original Nelder–Mead algorithm. The resulting heuristic was better than the original Nelder–Mead method in the number of solved test problems but it was slower in that it needed considerably more cost function evaluations to solve the problems also solved by the original method. In this paper we exploit grammatical evolution as a hyper-heuristic to evolve heuristics that outperform the original Nelder–Mead method in all aspects. However, the main goal of the paper is not to build yet another real function optimization algorithm but to shed some light on the influence of different factors on the behavior of the evolution process as well as on the quality of the obtained heuristics. In particular, we investigate through extensive evolution runs the influence of the shape and dimensionality of the training function, and the impact of the size limit set to the evolving algorithms. At the end of this research we succeeded to evolve a number of heuristics that solved more test problems and in fewer cost function evaluations than the original Nelder–Mead method. Our solvers are also highly competitive with the improvements made to the original method based on rigorous mathematical convergence proofs found in the literature. Even more importantly, we identified some directions in which to continue the work in order to be able to construct a productive hyper-heuristic capable of evolving real function optimization heuristics that would outperform a human designer in all aspects.     

Adaptive selection of heuristics for assigning time slots and rooms in exam timetables

This paper presents an iterative adaptive approach which hybridises bin packing heuristics to assign exams to time slots and rooms. The approach combines a graph-colouring heuristic, to select an exam in every iteration, with bin-packing heuristics to automate the process of time slot and room allocation for exam timetabling problems. We start by analysing the quality of the solutions obtained by using one heuristic at a time. Depending on the individual performance of each heuristic, a random iterative hyper-heuristic is used to randomly hybridise the heuristics and produce a collection of heuristic sequences to construct solutions with different quality. Based on these sequences, we analyse the way in which the bin packing heuristics are automatically hybridised. It is observed that the performance of the heuristics used varies depending on the problem. Based on these observations, an iterative hybrid approach is developed to adaptively choose and hybridise the heuristics during solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme which is concerned with developing methods to design and adapt heuristics automatically. The approach is tested on the exam timetabling track of the second International Timetabling Competition, to evaluate its ability to generalise on instances with different features. The hyper-heuristic with low-level graph-colouring and bin-packing heuristics approach was found to generalise well over all the problem instances and performed comparably to the state of the art approaches.     

THE COMBINATORIAL ANT SYSTEM

This paper presents a new distributed algorithm based on Ant System (AS) concepts called Combinatorial Ant System (CAS). It is oriented to solve static discrete-state combinatorial optimization problems. Our approach consists of mapping the solution space of the combinatorial optimization problem in the space where the ants will walk, and defining the transition probability and the pheromone update formula of the Ant System, according to the objective function of the Combinatorial Optimization Problem. We test our approach on the graph partitioning, graph coloring and traveling salesman problems.     

A greedy gradient-simulated annealing selection hyper-heuristic

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic is presented as a solution method. A selection hyper-heuristic as a high level methodology operates on the space formed by a fixed set of low level heuristics which operate directly on the space of solutions. The move acceptance and heuristic selection methods are the main components of a selection hyper-heuristic. The proposed hyper-heuristic in this study combines a simulated annealing move acceptance method with a learning heuristic selection method and manages a set of low level constraint oriented heuristics. A key goal in hyper-heuristic research is to build low cost methods which are general and can be reused on unseen problem instances as well as other problem domains desirably with no additional human expert intervention. Hence, the proposed method is additionally applied to a high school timetabling problem, as well as six other problem domains from a hyper-heuristic benchmark to test its level of generality. The empirical results show that our easy-to-implement hyper-heuristic is effective in solving the Yeditepe course timetabling problem. Moreover, being sufficiently general, it delivers a reasonable performance across different problem domains.     

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM.