Effective local search algorithms for high school timetabling problems

This paper addresses the high school timetabling problem. The problem consists in building weekly timetables for meetings between classes and teachers with the goal of minimizing violations of specific requirements. In the last decades, several mixed-integer programs have been proposed and tested for this family of problems. However, medium and large size instances are still not effectively solved by these programs using state-of-the-art solvers and the scientific community has given special attention to the devising of alternative soft computing algorithms. In this paper, we propose a soft computing approach based on Iterated Local Search and Variable Neighborhood Search metaheuristic frameworks. Our algorithms incorporate new neighborhood structures and local search routines to perform an effective search. We validated the proposed algorithms on variants of the problem using seven public instances and a new dataset with 34 real-world instances including large cases. The results demonstrate that the proposed algorithms outperform the state-of-the-art approaches in both cases, finding the best solutions in 38 out of the 41 tested instances.     

Iterated local search based on multi-type perturbation for single-machine earliness/tardiness scheduling

We propose an iterated local search based on a multi-type perturbation (ILS-MP) approach for single-machine scheduling to minimize the sum of linear earliness and quadratic tardiness penalties. The multi-type perturbation mechanism in ILS-MP probabilistically combines three types of perturbation strategies, namely tabu-based perturbation, construction-based perturbation, and random perturbation. Despite its simplicity, experimental results on a wide set of commonly used benchmark instances show that ILS-MP performs favourably in comparison with the current best approaches in the literature.     

Iterated local search for the team orienteering problem with time windows

A personalised electronic tourist guide assists tourists in planning and enjoying their trip. The planning problem that needs to be solved, in real-time, can be modelled as a team orienteering problem with time windows (TOPTW). In the TOPTW, a set of locations is given, each with a score, a service time and a time window. The goal is to maximise the sum of the collected scores by a fixed number of routes. The routes allow to visit locations at the right time and they are limited in length. The main contribution of this paper is a simple, fast and effective iterated local search meta-heuristic to solve the TOPTW. An insert step is combined with a shake step to escape from local optima. The specific shake step implementation and the fast evaluation of possible improvements, produces a heuristic that performs very well on a large and diverse set of instances. The average gap between the obtained results and the best-known solutions is only 1.8% and the average computation time is decreased with a factor of several hundreds. For 31 instances, new best solutions are computed.     

The effect of neighborhood structures on tabu search algorithm in solving course timetabling problem

The course timetabling problem must be solved by the departments of Universities at the beginning of every semester. It is a though problem which requires department to use humans and computers in order to find a proper course timetable. One of the most mentioned difficult nature of the problem is context dependent which changes even from departments to departments. Different heuristic approaches have been proposed in order to solve this kind of problem in the literature. One of the efficient solution methods for this problem is tabu search. Different neighborhood structures based on different types of move have been defined in studies using tabu search. In this paper, the effects of moves called simple and swap on the operation of tabu search are examined based on defined neighborhood structures. Also, two new neighborhood structures are proposed by using the moves called simple and swap. The fall semester of course timetabling problem of the Department of Statistics at Hacettepe University is solved utilizing four neighborhood structures and the comparison of the results obtained from these structures is given.     

An iterated local search heuristic for the split delivery vehicle routing problem

This paper concerns the Split Delivery Vehicle Routing Problem (SDVRP). This problem is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) since the customers׳ demands are allowed to be split. We deal with the cases where the fleet is unlimited (SDVRP-UF) and limited (SDVRP-LF). In order to solve them, we implemented a multi-start Iterated Local Search (ILS) based heuristic that includes a novel perturbation mechanism. Extensive computational experiments were carried out on benchmark instances available in the literature. The results obtained are highly competitive, more precisely, 55 best known solutions were equaled and new improved solutions were found for 243 out of 324 instances, with an average and maximum improvement of 1.15% and 2.81%, respectively.     

An iterated local search heuristic for multi-capacity bin packing and machine reassignment problems

This paper proposes an efficient Multi-Start Iterated Local Search for Packing Problems (MS-ILS-PPs) metaheuristic for Multi-Capacity Bin Packing Problems (MCBPP) and Machine Reassignment Problems (MRP). The MCBPP is a generalization of the classical bin-packing problem in which the machine (bin) capacity and task (item) sizes are given by multiple (resource) dimensions. The MRP is a challenging and novel optimization problem, aimed at maximizing the usage of available machines by reallocating tasks/processes among those machines in a cost-efficient manner, while fulfilling several capacity, conflict, and dependency-related constraints. The proposed MS-ILS-PP approach relies on simple neighborhoods as well as problem-tailored shaking procedures. We perform computational experiments on MRP benchmark instances containing between 100 and 50,000 processes. Near-optimum multi-resource allocation and scheduling solutions are obtained while meeting specified processing-time requirements (on the order of minutes). In particular, for 9/28 instances with more than 1000 processes, the gap between the solution value and a lower bound measure is smaller than 0.1%. Our optimization method is also applied to solve classical benchmark instances for the MCBPP, yielding the best known solutions and optimum ones in most cases. In addition, several upper bounds for non-solved problems were improved.     

Iterated local search and simulated annealing algorithms for the inventory routing problem

This paper addresses the inventory routing problem (IRP), which consists in defining the customer visit schedule, the delivery quantities, and the vehicle routing plan to meet the demands of a set of customers over a given time horizon. We consider the variant with a single item, a single supplier, multiple vehicles, and a finite multiperiod planning horizon, minimizing the sum of inventory and travel costs. In addition, we address an alternative objective function that minimizes the logistic ratio, defined as the total travel cost divided by the total quantity delivered to customers. This second objective function, while more realistic in some logistics settings, poses a challenge for integer programming models and exact methods because of its nonlinearity. To our knowledge, no heuristic method has been proposed to address this objective in the IRP variant addressed in this paper. To solve this problem with each of these objective functions, we propose effective metaheuristic algorithms based on iterated local search and simulated annealing. Computational experiments show that these algorithms provide reasonably high‐quality solutions in relatively short running times for both objective functions when compared to other methods for well‐known instances from the literature. Moreover, the algorithms produce new best solutions for some of these instances.     

Multi-start iterated local search for the periodic vehicle routing problem with time windows and time spread constraints on services

In the field of high-value shipment transportation, companies are faced to the malevolence problem. The risk of ambush increases with the predictability of vehicle routes. This paper addresses a very hard periodic vehicle routing problem with time windows, submitted by a software company specialized in transportation problems with security constraints. The hours of visits to each customer over the planning horizon must be spread in the customer's time window. As the aim is to solve real instances, the running time must be reasonable. A mixed integer linear model and a multi-start iterated local search are proposed. Results are reported on instances derived from classical benchmarks for the vehicle routing problem with time windows, and on two practical instances. Experiments are also conducted on a particular case with a single period, the vehicle routing problem with soft time windows: the new metaheuristic competes with two published algorithms and improves six best known solutions.     

A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem

The two-echelon location-routing problem (LRP-2E) is raised by the design of transportation networks with two types of trips: first-level trips serving from one main depot a set of satellite depots, to be located, and second-level trips supplying customers from these satellites. In the proposed multi-start iterated local search (MS-ILS), three greedy randomized heuristics are used cyclically to get initial solutions. Each ILS run alternates between two search spaces: LRP-2E solutions, and travelling salesman (TSP) tours covering the main depot and the customers. The number of iterations allotted to a run is reduced whenever a known solution (stored in a tabu list) is revisited. MS-ILS can be reinforced by a path-relinking procedure (PR), used internally for intensification, as post-optimization, or both. On two sets with 24 and 30 LRP-2E instances, MS-ILS outperforms on average two GRASP algorithms and adding PR brings a further improvement. Our metaheuristic also surpasses a tabu search on 30 instances for a more general problem with several main depots. It is still effective on a particular case, the capacitated location-routing problem (CLRP): In a comparison with four published metaheuristics, only one (LRGTS, Prins et al., 2007) does better.     

Exploring the fitness landscape and the run-time behaviour of an iterated local search algorithm for cost-based abduction

Cost-based abduction (CBA) is an important problem in reasoning under uncertainty, and can be considered a generalization of belief revision. CBA is known to be NP-hard and has been a subject of considerable research over the past decade. In this paper, we investigate the fitness landscape for CBA, by looking at fitness–distance correlation for local minima and at landscape ruggedness. Our results indicate that stochastic local search techniques would be promising on this problem. We go on to present an iterated local search algorithm based on hill-climbing, tabu search, and simulated annealing. We compare the performance of our algorithm to simulated annealing, and to Santos' integer linear programming method for CBA.     

基于均匀局部搜索和可变步长的萤火虫算法

针对萤火虫算法（FA）收敛速度慢和求解精度不高的问题,提出一种基于均匀局部搜索和可变步长策略的萤火虫优化算法（UVFA）。首先,根据均匀设计理论建立局部搜索算子,对FA的搜索过程进行改进,以提升算法的局部开采能力和收敛速度;其次,利用可变步长策略,动态地调整算法搜索步长,以平衡全局和局部的勘探能力和开采能力;最后将均匀局部搜索算子和可变步长进行融合。通过对12个标准测试函数进行仿真实验,结果表明,UVFA的目标函数均值均明显优于FA、明智步长策略的萤火虫算法（WSSFA）、可变步长萤火虫算法（VSSFA）和基于均匀局部搜索的萤火虫优化算法（UFA）,并且时间复杂度明显降低,并且在低维和高维问题中均显示出了较好的质量,具有良好的鲁棒性。     

EASYLOCAL++: an object‐oriented framework for the flexible design of local‐search algorithms

Local search is a paradigm for search and optimization problems, which has recently evidenced to be very effective for a large number of combinatorial problems. Despite the increasing interest of the research community in this subject, there is still a lack of a widely‐accepted software tools for local search. We propose EASY LOCAL , an object‐oriented framework for the design and the analysis of local‐search algorithms. The abstract classes that compose the framework specify and implement the invariant part of the algorithm and are meant to be specialized by concrete classes that supply the problem‐dependent part. The framework provides the full control structures of the algorithms, and the user has only to write the problem‐specific code. Furthermore, the framework comes with some tools that simplify the analysis of the algorithms. The architecture of EASY LOCAL provides a principled modularization for the solution of combinatorial problems by local search and helps the user by deriving a neat conceptual scheme of the application. It also supports the design of combinations of basic techniques and/or neighborhood structures. The framework has been tested in some applicative domains and has proved to be flexible enough in the implementation of algorithms for the solution of various scheduling problems. Copyright © 2003 John Wiley & Sons, Ltd.     

Variable neighborhood descent with iterated local search for routing and wavelength assignment

In this work we treat the Routing and Wavelength Assignment (RWA) with focus on minimizing the number of wavelengths to route demand requests. Lightpaths are used to carry the traffic optically between origin-destination pairs. The RWA is subjected to wavelength continuity constraints, and a particular wavelength cannot be assigned to two different lightpaths sharing a common physical link. We develop a Variable Neighborhood Descent (VND) with Iterated Local Search (ILS) for the problem. In a VND phase we try to rearrange requests between subgraphs associated to subsets of a partition of the set of lightpath requests. In a feasible solution, lightpaths belonging to a subset can be routed with the same wavelength. Thus, the purpose is to eliminate one subset of the partition. When VND fails, we perform a ILS phase to disturb the requests distribution among the subsets of the partition. An iteration of the algorithm alternates between a VND phase and a ILS phase. We report computational experiments that show VND-ILS was able to improve results upon powerful methods proposed in the literature.     

Combining biased randomization with iterated local search for solving the multidepot vehicle routing problem

This paper proposes a hybrid approach for solving the multidepot vehicle routing problem (MDVRP) with a limited number of identical vehicles per depot. Our approach, which only uses a few parameters, combines “biased randomization”—use of nonsymmetric probability distributions to generate randomness—with the iterated local search (ILS) metaheuristic. Two biased‐randomized processes are employed at different stages of the ILS framework in order to (a) assign customers to depots following a randomized priority criterion—this allows for fast generation of alternative allocation maps and (b) improving routing solutions associated with a “promising” allocation map—this is done by randomizing the classical savings heuristic. These biased‐randomized processes rely on the use of the geometric probability distribution, which is characterized by a single and bounded parameter. Being an approach with few parameters, our algorithm does not require troublesome fine‐tuning processes, which tend to be time consuming. Using standard benchmarks, the computational experiments show the efficiency of the proposed algorithm. Despite its hybrid nature, our approach is relatively easy to implement and can be parallelized in a very natural way, which makes it an interesting alternative for practical applications of the MDVRP.     

Memetic Algorithm based on Improved Inver-over operator and Lin-Kernighan local search for the Euclidean traveling salesman problem

In this study, an Improved Inver-over operator is proposed to solve the Euclidean traveling salesman problem (TSP) problem. The Improved Inver-over operator is tested on 14 different TSP examples selected from TSPLIB. The application of the Improved Inver-over operator gives much more effective results regarding to the best and average error values than the Basic Inver-over operator. Then an effective Memetic Algorithm based on Improved Inver-over operator and Lin-Kernighan local search is implemented. To speed up the convergence capability of the presented algorithm, a restart technique is employed. We evaluate the proposed algorithm based on standard TSP test problems and show that the proposed algorithm performs better than other Memetic Algorithm in terms of solution quality and computational effort.