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1.
One of the main challenges for university administration is building a timetable for course sessions. This is not just about building a timetable that works, but building one that is as good as possible. In general, course timetabling is the process of assigning given courses to given rooms and timeslots under specific constraints. Harmony search algorithm is a new metaheuristic population-based algorithm, mimicking the musical improvisation process where a group of musicians play the pitches of their musical instruments together seeking a pleasing harmony. The major thrust of this algorithm lies in its ability to integrate the key components of population-based methods and local search-based methods in a simple optimization model. In this paper, a harmony search and a modified harmony search algorithm are applied to university course timetabling against standard benchmarks. The results show that the proposed methods are capable of providing viable solutions in comparison to previous works.  相似文献   

2.
In this paper we present a decomposed metaheuristic approach to solve a real-world university course timetabling problem. Essential in this problem are the overlapping time slots and the irregular weekly timetables. A first stage in the approach reduces the number of subjects through the introduction of new structures that we call ‘pillars’. The next stages involve a metaheuristic search that attempts to solve the constraints one by one, instead of trying to find a solution for all the constraints at once. Test results for a real-world instance are presented.  相似文献   

3.
In this paper we propose a GRASP matheuristic coupled with an Integer Programming refinement based on Set Partitioning to solve the Cell Formation Problem. We use the grouping efficacy measure to evaluate the solutions. As this measure is nonlinear, we propose a fractional Set Partitioning approach and its linearization. Our method is validated on a set of 35 instances from the literature. The experiments found four unknown solutions. For all instances with known optima, our method is able to determine the optimum solutions.  相似文献   

4.
This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions to be accepted based on some given upper boundary or ‘level’. In this paper, the dynamic force calculated from the attraction-repulsion mechanism is used as a decreasing rate to update the ‘level’ within the search process. The proposed method has been applied to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method has been tested by comparing its results with other reported results from the literature, demonstrating that the method is able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches and the ability of the resultant algorithm to converge all solutions at every search process.  相似文献   

5.
A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed.  相似文献   

6.
Integer programming has always been an alternative for formulating combinatorial problems such as the university timetabling problem. However, the effort required for modeling complicated operational rules, as well as the computational difficulties that result from the size of real problems have discouraged researchers and made them turn their interest to other approaches. In this paper, a two-stage relaxation procedure that solves efficiently the integer programming formulation of a university timetabling problem is presented. The relaxation is performed in the first stage and concerns the constraints that warrantee consecutiveness in multi-period sessions of certain courses. These constraints, which are computationally heavier than the others, are recovered during the second stage and a number of sub-problems, one for each day of the week, are solved for local optima. Comparing to a solution approach that solves the problem in a single stage, computation time is reduced significantly without any loss in quality for the resulting timetables. The new solution approach gives a chance for further improvements in the final timetables, as well as for certain degree of interaction with the users during the construction of the timetables.  相似文献   

7.
In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.  相似文献   

8.
Journal of Heuristics - In this paper, we describe a matheuristic to solve the stochastic facility location problem which determines the location and size of storage facilities, the quantities of...  相似文献   

9.
E-commerce has been continuously growing in the last years to a primary retail market. Recently in France, the threshold of 1 billion of online transactions was overcome. Due to a high demand fluctuation of e-commerce, the workforce sizing for the logistic chain is a challenging problem. Companies have to develop good strategies to have a sustainable workforce size while guaranteeing a high-level service.In this paper, we consider the management of the workforce for a warehouse of an e-commerce company. Specifically, we address issues as i) How the workforce at the warehouse can be determined; ii) What is the daily operational production planning; iii) How the demand peaks can be smoothed, and the production maintained ideally constant over the time horizon.To provide answers to these issues, we introduce the Packaging and Shipping Problem (PSP). The PSP looks for a solution approach that jointly determines the workforce over a multi-period horizon and daily operational plans while minimizing the total logistics cost. We consider two strategies that aim to enhance the flexibility of the process and the efficiency of resources use: reassignment and postponement. To tackle the Packaging and Shipping Problem we propose a model, and a three-phase matheuristic. This heuristic is proved to be competitive with respect to the direct solution of the model with a commercial solver on real-life based instances.  相似文献   

10.
Efficient human resource planning is the cornerstone of designing an effective home health care system. Human resource planning in home health care system consists of decisions on districting/zoning, staff dimensioning, resource assignment, scheduling, and routing. In this study, a two-stage stochastic mixed integer model is proposed that considers these decisions simultaneously. In the planning phase of a home health care system, the main uncertain parameters are travel and service times. Hence, the proposed model takes into account the uncertainty in travel and service times. Districting and staff dimensioning are defined as the first stage decisions, and assignment, scheduling, and routing are considered as the second stage decisions. A novel algorithm is developed for solving the proposed model. The algorithm consists of four phases and relies on a matheuristic-based method that calls on various mixed integer models. In addition, an algorithm based on the progressive hedging and Frank and Wolf algorithms is developed to reduce the computational time of the second phase of the proposed matheuristic algorithm. The efficiency and accuracy of the proposed algorithm are tested through several numerical experiments. The results prove the ability of the algorithm to solve large instances.  相似文献   

11.
12.
In the truck and trailer routing problems (TTRPs) a fleet of trucks and trailers serves a set of customers. Some customers with accessibility constraints must be served just by truck, while others can be served either by truck or by a complete vehicle (a truck pulling a trailer). We propose a simple, yet effective, two-phase matheuristic that uses the routes of the local optima of a hybrid GRASP × ILS as columns in a set-partitioning formulation of the TTRP. Using this matheuristic we solved both the classical TTRP with fixed fleet and the new variant with unlimited fleet. This matheuristic outperforms state-of-the-art methods both in terms of solution quality and computing time. While the best variant of the matheuristic found new best-known solutions for several test instances from the literature, the fastest variant of the matheuristic achieved results of comparable quality to those of all previous method from the literature with an average speed-up of at least 2.5.  相似文献   

13.
The timetabling problem is generally large, highly constrained and discrete in nature. This makes solution by exact optimisation methods difficult. Therefore, often a heuristic search is deemed acceptable providing a simple (non-optimal) solution. This paper discusses the timetabling problem for a university department, where a large-scale integer goal programming (IGP) formulation is implemented for its efficient optimal solution in two phases. The first phase allocates lectures to rooms and the second allocates start-times to lectures. Owing to the size and complicated nature of the model, an initial analysis procedure is employed to manipulate the data to produce a more manageable model, resulting in considerable reductions in problem size and increase of performance. Both phases are modelled as IGPs. Phase 1 is solved using a state-of-the-art IGP optimisation package. However, due to the scale of the model, phase 2 is solved to optimality using a genetic algorithm approach.  相似文献   

14.
Automated examination timetabling has been addressed by a wide variety of methodologies and techniques over the last ten years or so. Many of the methods in this broad range of approaches have been evaluated on a collection of benchmark instances provided at the University of Toronto in 1996. Whilst the existence of these datasets has provided an invaluable resource for research into examination timetabling, the instances have significant limitations in terms of their relevance to real-world examination timetabling in modern universities. This paper presents a detailed model which draws upon experiences of implementing examination timetabling systems in universities in Europe, Australasia and America.  相似文献   

15.
We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).  相似文献   

16.
A practical nurse rostering problem, which arises at a ward of an Italian private hospital, is considered. In this problem, it is required each month to assign shifts to the nursing staff subject to various requirements. A matheuristic approach is introduced, based on a set of neighborhoods iteratively searched by a commercial integer programming solver within a defined global time limit, relying on a starting solution generated by the solver running on the general integer programming formulation of the problem. Generally speaking, a matheuristic algorithm is a heuristic algorithm that uses non trivial optimization and mathematical programming tools to explore the solutions space with the aim of analyzing large scale neighborhoods. Randomly generated instances, based on the considered nurse rostering problem, were solved and solutions computed by the proposed procedure are compared to the solutions achieved by pure solvers within the same time limit. The results show that the proposed solution approach outperforms the solvers in terms of solution quality. The proposed approach has also been tested on the well known Nurse Rostering Competition instances where several new best results were reached.  相似文献   

17.
This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.  相似文献   

18.
The Technician Routing and Scheduling Problem (TRSP) consists in routing staff to serve requests for service, taking into account time windows, skills, tools, and spare parts. Typical applications include maintenance operations and staff routing in telecoms, public utilities, and in the health care industry. In this paper, we present a formal definition of the TRSP, discuss its relation with the Vehicle Routing Problem with Time Windows (VRPTW), and review related research. From a methodological perspective, we describe a matheuristic composed of a constructive heuristic, a parallel Adaptive Large Neighborhood Search, and a mathematical programming based post-optimization procedure that successfully tackles the TRSP. We validate the matheuristic on the Solomon VRPTW instances, where we achieve an average gap of $0.23\,\%$ , and matched 44 out of 55 optimal solutions. Finally, we illustrate how the matheuristic successfully solves a set of TRSP instances extended from the Solomon benchmark.  相似文献   

19.
20.
The problem of packing ellipsoids in the three-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. The introduced approach is able to pack identical and non-identical ellipsoids within a variety of containers. Moreover, it allows the inclusion of additional positioning constraints. This fact makes the proposed approach suitable for constructing large-scale solutions with specific positioning constraints in which density may not be the main issue. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational cost that scales linearly with the number of ellipsoids; and solutions with more than a million ellipsoids are exhibited.  相似文献   

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