Iterated Tabu Search Research Articles

Personalized multi-period tour recommendations

During a trip planning, tourists gather information from different sources, select and rank the places to visit according to their personal interests, and try to devise daily tours among them. This paper addresses the complex selection and touring problem and proposes a “filter-first, tour-second” framework for generating personalized tour recommendations for tourists based on information from social media and other online data sources. Collaborative filtering is applied to identify a subset of optional points of interest that maximize the potential satisfaction, while there are some preselected mandatory points that the tourists must visit. Next, the underlying orienteering problem is solved via an Iterated Tabu Search algorithm. The goal is to generate tours that contain all mandatory points and maximize the total score collected from the optional points visited daily, taking into account different day availabilities and opening hours, limitations on the tour lengths, budgets and other restrictions. Computational experiments on benchmark datasets indicate that the proposed touring algorithm is very competitive. Furthermore, the proposed framework has been evaluated on data collected from Foursquare. The results show the practical utility and the temporal efficacy of the recommended tours.

Solving the Quadratic Assignment Problem by the Repeated Iterated Tabu Search Method

A new repeated iterated tabu search for the quadratic assignment problem is developed. A comparative study of this algorithm and the best existing algorithms for solving this problem has shown its competitiveness with respect to both its performance and quality of solutions.

An iterated tabu search for the multi-compartment vehicle routing problem

We study a variant of the vehicle routing problem that allows vehicles with multiple compartments. The need for multiple compartments frequently arises in practical applications when there are several products of different quality or type, that must be kept or handled separately. The resulting problem is called the multi-compartment vehicle routing problem (MCVRP). We propose a tabu search heuristic and embed it into a iterated local search to solve the MCVRP. In several experiments we analyze the performance of the iterated tabu search and compare it to results from the literature. We find that it consistently produces solutions that are better than existing heuristic algorithms.

An effective iterated tabu search for the maximum bisection problem

Given an edge weighted graph G=(V,E), the maximum bisection problem involves partitioning the vertices of V into two disjoint subsets of equal cardinality such that the weight sum of the edges crossing the two subsets is maximized. In this study, we present an Iterated Tabu Search (ITS) algorithm to solve the problem. ITS employs two distinct search operators organized into three search phases to effectively explore the search space. Bucket sorting is used to ensure a high computational efficiency of the ITS algorithm. Experiments based on 71 well-known benchmark instances of the literature demonstrate that ITS is highly competitive compared to state-of-the-art approaches and discovers improved best-known results (new lower bounds) for 8 benchmark instances. The key ingredients of the algorithm are also investigated.

Multi-neighborhood based iterated tabu search for routing and wavelength assignment problem

The routing and wavelength assignment problem (RWA) has shown to be NP-hard if the wavelength continuity constraint and the objective of minimizing the number of wavelengths are considered. This paper introduces a multi-neighborhood based iterated tabu search algorithm (MN-ITS), which consists of three neighborhoods with a unified incremental evaluation method, to solve the min-RWA problem. The proposed MN-ITS algorithm is tested on a set of widely studied real world instances as well as a set of challenging random ones in the literature. Comparison with other reference algorithms shows that the MN-ITS algorithm is able to improve five best upper bounds obtained by other competitive reference algorithms in the literature. This paper also presents an analysis to show the significance of the unified incremental evaluation technique and the combination of multiple neighborhoods.

Backtracking based iterated tabu search for equitable coloring

An equitable k-coloring of an undirected graph G=(V,E) is a partition of its vertices into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one. As a variant of the graph coloring problem (GCP), the equitable coloring problem (ECP) concerns finding a minimum k for which an equitable k-coloring exists. In this work, we propose a backtracking based iterated tabu search (BITS) algorithm for solving the ECP approximately. BITS uses a backtracking scheme to define different k-ECP instances, an iterated tabu search approach to solve each particular k-ECP instance for a fixed k, and a binary search approach to find a suitable initial value of k. We assess the algorithm׳s performance on a set of commonly used benchmarks. Computational results show that BITS is very competitive in terms of solution quality and computing efficiency compared to the state-of-the-art algorithm in the literature. Specifically, BITS obtains new upper bounds for 21 benchmark instances, while matching the previous best upper bound for the remaining instances. Finally, to better understand the proposed algorithm, we study how its key ingredients impact its performance.

A multilevel tabu search algorithm for balanced partitioning of unstructured grids

SummaryThis paper presents a multilevel algorithm for balanced partitioning of unstructured grids. The grid is partitioned such that the number of interface elements is minimized and each partition contains an equal number of grid elements. The partition refinement of the proposed multilevel algorithm is based on iterative tabu search procedure. In iterative partition refinement algorithms, tie‐breaking in selection of maximum gain vertices affects the performance considerably. A new tie‐breaking strategy in the iterative tabu search algorithm is proposed that leads to improved partitioning quality. Numerical experiments are carried out on various unstructured grids in order to evaluate the performance of the proposed algorithm. The partition results are compared with those produced by the well‐known partitioning package Metis and k‐means clustering algorithm and shown to be superior in terms of edge cut, partition balance, and partition connectivity. Copyright © 2015 John Wiley & Sons, Ltd.

Fitness-scaling adaptive genetic algorithm with local search for solving the Multiple Depot Vehicle Routing Problem

The multi-depot vehicle routing problem is a well-known non-deterministic polynomial-time hard combinatorial optimization problem, which is crucial for transportation and logistics systems. We proposed a novel fitness-scaling adaptive genetic algorithm with local search (FISAGALS). The fitness-scaling technique converts the raw fitness value to a new value that is suitable for selection. The adaptive rates strategy changes the crossover and mutation probabilities depending on the fitness value. The local search mechanism exploits the problem space in a more efficient way. The experiments employed 33 benchmark problems. Results showed the proposed FISAGALS is superior to the standard genetic algorithm, simulated annealing, tabu search, and particle swarm optimization in terms of success instances and computation time. Furthermore, FISAGALS performs better than parallel iterated tabu search (PITS) and fuzzy logic guided genetic algorithm (FLGA), and marginally worse than ILS-RVND-SP in terms of the maximum gap. It performs faster than PITS and ILS-RVND-SP (a combination of iterated local search framework [ILS], a variable neighborhood descent with random neighborhood ordering [RVND] and the the set partitioning [SP] model) and slower than FLGA. In summary, FISAGALS is a competitive method with state-of-the-art algorithms.

Iterated Tabu Search and Variable Neighborhood Descent for packing unequal circles into a circular container

This paper presents an Iterated Tabu Search and Variable Neighborhood Descent (ITS-VND) algorithm for packing unequal circles into a circular container (PUCC). The algorithm adapts the Tabu Search procedure of Iterated Tabu Search algorithms and proposes a Tabu Search and Variable Neighborhood Descent (TS-VND) procedure. We observe there are strong complementarities between the small circles and the large vacant places, and propose the insert neighborhood to match up the small circles with the large vacant places. Although the insert neighborhood is inefficient and time-consuming, it is an important supplement to the classic swap neighborhood as it could arrange the small circles properly. Predicated on these features, we employ the insert neighborhood only at chosen local minima of the swap neighborhood that shows promise for an improvement. The traditional Tabu Search procedure is then transformed into a hybrid procedure composed of two alternative parts, namely Variable Neighborhood Descent and Tabu Search respectively. Besides this reformed procedure, ITS-VND also incorporates other new features, such as an adaptive evaluation function, a novel method for accelerating the neighborhood exploration, and the “collision accidents” criterion for evaluating how intensively the area near the current solution has been explored. The computational results on three well established benchmark sets show that the proposed algorithm not only has a good discovery capability but also can provide good results within a reasonable time. For a total of 84 benchmark instances, the proposed algorithm improves the best-known results on 23 instances, matches 60, and only misses one.

Multi-start iterated tabu search for the minimum weight vertex cover problem

The minimum weight vertex cover problem (MWVCP) is one of the most popular combinatorial optimization problems with various real-world applications. Given an undirected graph where each vertex is w...

Fast simulated annealing for single-row equidistant facility layout

Given n facilities and a flow matrix, the single-row equidistant facility layout problem (SREFLP) is to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a simulated annealing (SA) algorithm for solving this problem. The algorithm provides a possibility to employ either merely pairwise interchanges of facilities or merely insertion moves or both of them. It incorporates an innovative method for computing gains of both types of moves. Experimental analysis shows that this method is significantly faster than traditional approaches. To further speed up SA, we propose a two-mode technique when for high temperatures, at each iteration, only the required gain is calculated and, for lower temperatures, the gains of all possible moves are maintained from iteration to iteration. We experimentally compare SA against the iterated tabu search (ITS) algorithm from the literature. Computational results are reported for SREFLP instances with up to 300 facilities. The results show that the performance of our SA implementation is dramatically better than that of the ITS heuristic.

SOLVING THE WEIGHTED MAX-2-SAT PROBLEM WITH ITERATED TABU SEARCH

Given a CNF formula in which each clause is of length at most two and has an associated positive weight, the weighted Max-2-SAT problem asks to find a truth assignment to the Boolean variables that maximizes the total weight of the satisfied clauses.We develop an iterated tabu search (ITS) algorithm for solving this problem.We report computational results on Max-2-SAT instances of size up to 3000 variables and provide comparisons of ITS to state-of-the-art heuristic methods from the literature, which demonstrate the competitiveness of our approach.

USING ITERATED TABU SEARCH FOR THE TRAVELING SALESMAN PROBLEM

In this paper, we propose an iterated tabu search (ITS) algorithm for the well-known combinatorial optimization problem, the traveling salesman problem (TSP). ITS is based on so-called intensification (improvement) and diversification (reconstruction) (I&D) paradigm. The goal of the intensification is the search for a locally optimal solution in the neighbourhood of the current solution. The diversification is responsible for escaping from the current local optimum and moving towards new regions in the solution space. Using the limited standard tabu search (TS) in the role of an effective intensification (local improvement) procedure resulted in promising solutions obtained during the experimentation with a number of the test data from the library of TSP instances TSPLIB. The results show that the proposed variant of ITS outperforms both the straightforward TS algorithm and the other heuristic algorithms tested.

Maximally diverse grouping: an iterated tabu search approach

The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.

Comparison of Two Diversification Methods to Solve the Quadratic Assignment Problem

The quadratic assignment problem is one of the most studied NP-hard problems. It is known for its complexity which makes it a good candidate for the parallel design. In this paper, we propose and analyze two parallel cooperative algorithms based on hybrid iterative tabu search. The only difference between the two approaches is the diversification methods. Through 15 of the hardest well-known instances from QAPLIB benchmark, our algorithms produce competitive results.

An iterated tabu search heuristic for the Single Source Capacitated Facility Location Problem

This paper discusses the Single Source Capacitated Facility Location Problem (SSCFLP) where the problem consists in determining a subset of capacitated facilities to be opened in order to satisfy the customers’ demands such that total costs are minimized. The paper presents an iterated tabu search heuristic to solve the SSCFLP. The iterated tabu search heuristic combines tabu search with perturbation operators to avoid getting stuck in local optima. Experimental results show that this simple heuristic is capable of generating high quality solutions using small computing times. Moreover, it is also competitive with other metaheuristic approaches for solving the SSCFLP.

Solving a static repositioning problem in bike-sharing systems using iterated tabu search

In this paper, we study the static bike repositioning problem where the problem consists of selecting a subset of stations to visit, sequencing them, and determining the pick-up/drop-off quantities (associated with each of the visited stations) under the various operational constraints. The objective is to minimize the total penalties incurred at all the stations. We present an iterated tabu search heuristic to solve the described problem. Experimental results show that this simple heuristic can generate high quality solutions using small computing times.

An iterated tabu search approach for the clique partitioning problem.

Given an edge-weighted undirected graph with weights specifying dissimilarities between pairs of objects, represented by the vertices of the graph, the clique partitioning problem (CPP) is to partition the vertex set of the graph into mutually disjoint subsets such that the sum of the edge weights over all cliques induced by the subsets is as small as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. The proposed algorithm incorporates tabu search, local search, and solution perturbation procedures. We report computational results on CPP instances of size up to 2000 vertices. Performance comparisons of ITS against state-of-the-art methods from the literature demonstrate the competitiveness of our approach.

A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service

On-time shipment delivery is critical for just-in-time production and quick response logistics. Due to uncertainties in travel and service times, on-time arrival probability of vehicles at customer locations can not be ensured. Therefore, on-time shipment delivery is a challenging job for carriers in congested road networks. In this paper, such on-time shipment delivery problems are formulated as a stochastic vehicle routing problem with soft time windows under travel and service time uncertainties. A new stochastic programming model is proposed to minimize carrier’s total cost, while guaranteeing a minimum on-time arrival probability at each customer location. The aim of this model is to find a good trade-off between carrier’s total cost and customer service level. To solve the proposed model, an iterated tabu search heuristic algorithm was developed, incorporating a route reduction mechanism. A discrete approximation method is proposed for generating arrival time distributions of vehicles in the presence of time windows. Several numerical examples were conducted to demonstrate the applicability of the proposed model and solution algorithm.

An Improved Exact Algorithm for Least-Squares Unidimensional Scaling

Given n objects and an symmetric dissimilarity matrix D with zero main diagonal and nonnegative off-diagonal entries, the least-squares unidimensional scaling problem asks to find an arrangement of objects along a straight line such that the pairwise distances between them reflect dissimilarities represented by the matrix D. In this paper, we propose an improved branch-and-bound algorithm for solving this problem. The main ingredients of the algorithm include an innovative upper bounding technique relying on the linear assignment model and a dominance test which allows considerably reducing the redundancy in the enumeration process. An initial lower bound for the algorithm is provided by an iterated tabu search heuristic. To enhance the performance of this heuristic we develop an efficient method for exploring the pairwise interchange neighborhood of a solution in the search space. The basic principle and formulas of the method are also used in the implementation of the dominance test. We report computational results for both randomly generated and real-life based problem instances. In particular, we were able to solve to guaranteed optimality the problem defined by a Morse code dissimilarity matrix.