Hybrid genetic algorithms for timetabling

Hybrid genetic algorithms are presented that use optimization heuristics and genetic techniques to outperform all existing programs for the timetabling problem. The timetabling problem is very hard (NP-complete) and a general polynomial time deterministic algorithm is not known. An artificial intelligence approach, in a logic programming environment, may be useful for such a problem. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited for this kind of problem, since there exists an easy way to assess a good timetable but not a well-structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solutions. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the problem knowledge and the heuristics, i.e., from the timetable builder. A fundamental issue and a general problem in the decision process and automated reasoning is how to efficiently obtain logic decisions under disjunctive constraints. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present article illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favorably with the best-known programs to solve decisions problems under logic constraints. Complexity of the new algorithms and results of significant experiments are reported. © 1996 John Wiley & Sons, Inc.     

A genetic algorithm for a university weekly courses timetabling problem

The timetabling problem is concerned with the allocation, subject to constraints, of given resources to objects in space and time in such way as to satisfy as nearly as possible a set of desirable objectives. This problem is known to be NP–complete and as such only combinatorial optimization methods can guarantee an optimal timetable. In this paper we propose a sector–based genetic algorithm for solving a university weekly courses timetabling problem. Preliminary experimental results indicate that the algorithm is promising.     

基于贪心法和禁忌搜索的实用高校排课系统研究

在深入分析普通高校排课的流程、特点和难点的基础上，提出一个基于贪心法和禁忌搜索的排课算法。算法采用基于优先级的贪心法构造排课的初始解，进而利用禁忌搜索获得全局较优的排课结果。设计中充分考虑了当前高校课表问题的实际情况，如课程性质对排课的要求、教师的特殊要求等。实现的原型系统同时支持自动排课和交互式排课，对于一些难度较大的问题，可以通过人机交互方式来解决。通过对高校的实际排课数据进行测试，结果表明该算法可行且能够有效地提高排课效率。     

Scatter search technique for exam timetabling

At universities where students enjoy flexibility in selecting courses, the Registrar’s office aims to generate an appropriate exam timetable for numerous courses and large number of students. An appropriate, real-world exam timetable should show fairness towards all students, respecting the following constraints: (a) eliminating or minimizing the number of simultaneous exams; (b) minimizing the number of consecutive exams; (c) minimizing the number of students with two or three exams per day (d) eliminating the possibility of more than three exams per day (e) exams should fit in rooms with predefined capacity; and (f) the number of exam periods is limited. These constraints are conflicting, which makes exam timetabling intractable. Hence, solving this problem in realistic time requires the use of heuristic approaches. In this work, we develop an evolutionary heuristic technique based on the scatter search approach for finding good suboptimal solutions for exam timetabling. This approach is based on maintaining and evolving a population of solutions. We evaluate our suggested technique on real-world university data and compare our results with the registrar’s manual timetable in addition to the timetables of other heuristic optimization algorithms. The experimental results show that our adapted scatter search technique generates better timetables than those produced by the registrar, manually, and by other meta-heuristics.     

A multi-objective evolutionary algorithm for examination timetabling

This paper considers the scheduling of exams for a set of university courses. The solution to this exam timetabling problem involves the optimization of complete timetables such that there are as few occurrences of students having to take exams in consecutive periods as possible but at the same time minimizing the timetable length and satisfying hard constraints such as seating capacity and no overlapping exams. To solve such a multi-objective combinatorial optimization problem, this paper presents a multi-objective evolutionary algorithm that uses a variable-length chromosome representation and incorporates a micro-genetic algorithm and a hill-climber for local exploitation and a goal-based Pareto ranking scheme for assigning the relative strength of solutions. It also imports several features from the research on the graph coloring problem. The proposed algorithm is shown to be a more general exam timetabling problem solver in that it does not require any prior information of the timetable length to be effective. It is also tested against a few influential and recent optimization techniques and is found to be superior on four out of seven publicly available datasets.     

A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling

The post enrolment course timetabling problem (PECTP) is one type of university course timetabling problems, in which a set of events has to be scheduled in time slots and located in suitable rooms according to the student enrolment data. The PECTP is an NP-hard combinatorial optimisation problem and hence is very difficult to solve to optimality. This paper proposes a hybrid approach to solve the PECTP in two phases. In the first phase, a guided search genetic algorithm is applied to solve the PECTP. This guided search genetic algorithm, integrates a guided search strategy and some local search techniques, where the guided search strategy uses a data structure that stores useful information extracted from previous good individuals to guide the generation of offspring into the population and the local search techniques are used to improve the quality of individuals. In the second phase, a tabu search heuristic is further used on the best solution obtained by the first phase to improve the optimality of the solution if possible. The proposed hybrid approach is tested on a set of benchmark PECTPs taken from the international timetabling competition in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed hybrid approach is able to produce promising results for the test PECTPs.     

Local search techniques for large high school timetabling problems

The high school timetabling problem regards the weekly scheduling for all the lectures of a high school. The problem consists in assigning lectures to periods in such a way that no teacher (or class) is involved in more than one lecture at a time, and other constraints are satisfied. The problem is NP-complete and is usually tackled using heuristic methods, This paper describes a solution algorithm (and its implementation) based on local search techniques. The algorithm alternates different techniques and different types of moves and makes use of an adaptive relaxation of the hard constraints. The implementation of the algorithm has been successfully experimented with in some large high schools with various kinds of side constraints     

Applying evolutionary computation to the school timetabling problem: The Greek case

In this contribution, an adaptive algorithm based on evolutionary computation techniques is designed, developed and applied to the timetabling problem of educational organizations. Specifically, the proposed algorithm has been used in order to create feasible and efficient timetables for high schools in Greece. The algorithm has been tested exhaustively with real-world input data coming from many different high schools and has been compared with several other effective techniques in order to demonstrate its efficiency and superior performance. Simulation results showed that the algorithm is able to construct a feasible and very efficient timetable more quickly and easily compared to other techniques, thus preventing disagreements and arguments among teachers and assisting each school to operate with its full resources from the beginning of the academic year. Except from that, due to its inherent adaptive behavior it can be used each time satisfying different specific constraints, in order to lead to timetables, thus meeting the different needs that each school may have.     

混合算法在大学课程表问题中的应用研究

大学课程袁问题是时间表问题之一,也是一个多因素的优化决策问题.文章提出的混合算法,基于动态规划的思想,对大学课程表问题进行分阶段求解,分别采用遗传算法分配时间,采用最佳适应算法分配场地.实验结果表明,这种方法既保证了课表的质量,又有利于工程上实现和扩展.     

Genetic based discrete particle swarm optimization for Elderly Day Care Center timetabling

The timetabling problem of local Elderly Day Care Centers (EDCCs) is formulated into a weighted maximum constraint satisfaction problem (Max-CSP) in this study. The EDCC timetabling problem is a multi-dimensional assignment problem, where users (elderly) are required to perform activities that require different venues and timeslots, depending on operational constraints. These constraints are categorized into two: hard constraints, which must be fulfilled strictly, and soft constraints, which may be violated but with a penalty. Numerous methods have been successfully applied to the weighted Max-CSP; these methods include exact algorithms based on branch and bound techniques, and approximation methods based on repair heuristics, such as the min-conflict heuristic. This study aims to explore the potential of evolutionary algorithms by proposing a genetic-based discrete particle swarm optimization (GDPSO) to solve the EDCC timetabling problem. The proposed method is compared with the min-conflict random-walk algorithm (MCRW), Tabu search (TS), standard particle swarm optimization (SPSO), and a guided genetic algorithm (GGA). Computational evidence shows that GDPSO significantly outperforms the other algorithms in terms of solution quality and efficiency.     

Variable ordering and constraint propagation for constrained CP-nets

A Conditional Preferences network (CP-net) is a known graphical model for representing qualitative preferences. In many real world applications we are often required to manage both constraints and preferences in an efficient way. The goal here is to select one or more scenarios that are feasible according to the constraints while maximizing a given utility function. This problem has been modelled as a CP-net where some variables share a set of constraints. This latter framework is called a Constrained CP-net. Solving the constrained CP-net has been proposed in the past using a variant of the branch and bound algorithm called Search CP. In this paper, we experimentally study the effect of variable ordering heuristics and constraint propagation when solving a constrained CP-net using a backtrack search algorithm. More precisely, we investigate several look ahead strategies as well as the most constrained heuristic for variable ordering during search. The results of the experiments conducted on random Constrained CP-net instances generated through the RB model, clearly show a significant improvement when adopting these techniques for specific graph structures as well as the case where a large number of variables are sharing constraints.     

A new hybrid parallel genetic algorithm for the job‐shop scheduling problem

The job‐shop scheduling problem (JSSP) is considered one of the most difficult NP‐hard problems. Numerous studies in the past have shown that as exact methods for the problem solution are intractable, even for small problem sizes, efficient heuristic algorithms must achieve a good balance between the well‐known themes of exploitation and exploration of the vast search space. In this paper, we propose a new hybrid parallel genetic algorithm with specialized crossover and mutation operators utilizing path‐relinking concepts from combinatorial optimization approaches and tabu search in particular. The new scheme relies also on the recently introduced concepts of solution backbones for the JSSP in order to intensify the search in promising regions. We compare the resulting algorithm with a number of state‐of‐the‐art approaches for the JSSP on a number of well‐known test‐beds; the results indicate that our proposed genetic algorithm compares fairly well with some of the best‐performing genetic algorithms for the problem.     

A hyperheuristic approach to examination timetabling problems: benchmarks and a new problem from practice

Many researchers studying examination timetabling problems focus on either benchmark problems or problems from practice encountered in their institutions. Hyperheuristics are proposed as generic optimisation methods which explore the search space of heuristics rather than direct solutions. In the present study, the performance of tournament-based hyperheuristics for the exam timetabling problem are investigated. The target instances include both the Toronto and ITC 2007 benchmarks and the examination timetabling problem at KAHO Sint-Lieven (Ghent, Belgium). The Toronto and ITC 2007 benchmarks are post-enrolment-based examination timetabling problems, whereas the KAHO Sint-Lieven case is a curriculum-based examination timetabling problem. We drastically improve the previous (manually created) solution for the KAHO Sint-Lieven problem by generating a timetable that satisfies all the hard and soft constraints. We also make improvements on the best known results in the examination timetabling literature for seven out of thirteen instances for the To ronto benchmarks. The results are competitive with those of the finalists of the examination timetabling track of the International Timetabling Competition.     

A genetic algorithm approach for the cutting stock problem

In this paper, a genetic algorithm approach is developed for solving the rectangular cutting stock problem. The performance measure is the minimization of the waste. Simulation results obtained from the genetic algorithm-based approach are compared with one heuristic based on partial enumeration of all feasible patterns, and another heuristic based on a genetic neuro-nesting approach. Some test problems taken from the literature were used for the experimentation. Finally, the genetic algorithm approach was applied to test problems generated randomly. The simulation results of the proposed approach in terms of solution quality are encouraging when compared to the partial enumeration-based heuristic and the genetic neuro-nesting approach.     

UTP中一种分阶段求解算法

大学课程表问题UTP是一个应用广泛的、典型的组合优化和不确定性调度问题,并且已经被证明是NP完全问题。本文提出了一种分阶段解决大学课程表问题的算法,将课程表问题划分为时间安排和空间安排两个阶段,分别采用智能算法和最佳适应算法逐段求解,并最终求得全局较优解。通过设计实验对算法进行分析,结果表明这种分阶段决策算法在保证课表质量的同时能够有效减小遗传算法在求解UTP问题中的复杂度,提高程序的运行速度。     

施工项目调度问题的一种智能优化算法

研究了施工项目进度调度问题,提出了一种基于启发式规则和遗传算法的综合智能优化算法,并在施工项目调度问题的描述、带资源约束的施工项目调度问题的分解方法、遗传算法的编码、交叉、变异方法和解码方法等方面进行了研究。不同规模的数值计算结果表明,该算法在解决复杂工程施工项目调度问题上具有良好的性能,并能较好地适用于带时序、资源约束的施工项目调度问题。     

Train service timetabling in railway open markets by particle swarm optimisation

Railway timetabling is an important process in train service provision as it matches the transportation demand with the infrastructure capacity while customer satisfaction is also considered. It is a multi-objective optimisation problem, in which a feasible solution, rather than the optimal one, is usually taken in practice because of the time constraint. The quality of services may suffer as a result. In a railway open market, timetabling usually involves rounds of negotiations amongst a number of self-interested and independent stakeholders and hence additional objectives and constraints are imposed on the timetabling problem. While the requirements of all stakeholders are taken into consideration simultaneously, the computation demand is inevitably immense. Intelligent solution-searching techniques provide a possible solution. This paper attempts to employ a particle swarm optimisation (PSO) approach to devise a railway timetable in an open market. The suitability and performance of PSO are studied on a multi-agent-based railway open-market negotiation simulation platform.     

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.     

基于遗传算法的QoS多播路由优化算法

研究了带宽、延时、延时抖动和分组丢失率约束以及费用最小的QoS多播路由优化问题,提出了一种启发式遗传算法、该算法采用可变长度染色体(路由串)和它的基因(节点)应用于编码问题。交叉操作在交叉点进行部分染色体(部分路由)交换,变异操作维持种群的多样性。该算法采用简单维护操作维护好所有的不可行的染色体,交叉操作和变异操作相结合保证了最优解的搜索能力和解的全局收敛性。计算机仿真实验证明该算法快速有效,可靠性高。     

分组遗传算法优化大学考试时间表

大学考试时间表是一个多约束条件下的优化问题。传统遗传算法寻优的计算量是指数级的规模,而寻优的操作有可能会破坏时间表的硬约束条件,从而最终得到的解并不一定理想甚至不可行。该文从某高校的实际应用出发,对用图着色模型得到的已经满足了硬约束条件的初始考试时间表,用改进的分组遗传算法在既不破坏硬约束条件也不延长考试周的条件下扩大并平均分配了学生的复习时间,并且还大大减少了寻优的计算量。