Iterated Tabu Search Algorithm Research Articles

Algorithm Portfolios for Solving the Quadratic Assignment Problem

Introduction. The quadratic assignment problem is a well-established NP-hard problem in combinatorial optimization with applications in diverse fields like economics, archaeology, and chemistry. Due to its complexity, research on efficient solution methods remains active, including efforts for parallelization on multiprocessor computing systems. However, effective parallel algorithms are crucial to fully leverage these computational resources. In this context, algorithm unions (portfolios and teams) play a significant role in achieving parallel execution for solving such problems. Research objectives. This work investigates the application of portfolios constructed from modifications of the repeated iterated tabu search algorithm to the quadratic assignment problem. The effectiveness of these portfolios was evaluated through experimental computations. Results. The portfolios, derived from modifications of the repeated iterated tabu search algorithm, were applied to the quadratic assignment problem. For the most demanding test instances, the proposed algorithms were evaluated on the SCIT-4 supercomputer, alongside previously published results from the authors, confirming their competitive performance. Additionally, we assessed the parallel efficiency of these portfolios in solving instances of the quadratic assignment problem. The results demonstrate their ability to accelerate the optimization process (with speedup dependent on problem size and utilized processors), enabling the solution of large-scale problems. Conclusions. The conducted studies demonstrate that employing algorithm portfolios significantly accelerates the solution process for the quadratic assignment problem. Analysis of the results reveals a near-linear speedup factor achieved by the portfolio. For the challenging test instance tai100a, a new best solution value of 21040996 was obtained using a portfolio of 16 algorithms. Keywords: quadratic assignment problem, algorithm portfolios, experimental research, algorithm portfolios efficiency.

Effectiveness of the MineReduce approach in reducing the size of combinatorial optimization problem instances

Previous work has shown that the performance of metaheuristics can benefit from using data mining techniques, which can improve the obtained solutions. In a strategy that has been successfully used for over a decade, data mining techniques are applied to extract patterns from good solutions found in the early stages of the heuristic process, and these patterns are introduced into the solutions generated afterwards. Recently, a novel approach that uses data mining for problem size reduction, called MineReduce, has been proposed and achieved even more impressive results in improving metaheuristics. In this work, we apply the MineReduce approach to improve the performance of a multi-start iterated tabu search algorithm. The results show that with the incorporation of the MineReduce approach, the method can obtain better solutions while spending less time. Additionally, we assessed the effectiveness of the size reduction performed by MineReduce, comparing it to a kernelization algorithm. Despite the lack of guarantees on optimality or size-bounding, the reduction carried out by MineReduce was effective in practice.

A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem.

In this paper, we present a hybrid genetic-hierarchical algorithm for the solution of the quadratic assignment problem. The main distinguishing aspect of the proposed algorithm is that this is an innovative hybrid genetic algorithm with the original, hierarchical architecture. In particular, the genetic algorithm is combined with the so-called hierarchical (self-similar) iterated tabu search algorithm, which serves as a powerful local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm. The results of the conducted computational experiments demonstrate the promising performance and competitiveness of the proposed algorithm.

Hierarchicity-based (self-similar) hybrid genetic algorithm for the grey pattern quadratic assignment problem

In this paper, we present a hierarchicity-based (self-similar) hybrid genetic algorithm for the solution of the grey pattern quadratic assignment problem. This is a novel hybrid genetic search-based heuristic algorithm with the original, hierarchical architecture and it is in connection with what is known as self-similarity—this means that an object (in our case, algorithm) is exactly or approximately similar to constituent parts of itself. The two main aspects of the proposed algorithm are the following: (1) the hierarchical (self-similar) structure of the genetic algorithm itself, and (2) the hierarchical (self-similar) form of the iterated tabu search algorithm, which is integrated into the genetic algorithm as an efficient local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm.

A 2-Level Iterated Tabu Search Algorithm for the Quadratic Assignment Problem

In this paper, a 2-level iterated tabu search (ITS) algorithm for the solution of the quadratic assignment problem (QAP) is considered. The novelty of the proposed ITS algorithm is that the solution mutation procedures are incorporated within the algorithm, which enable to diversify the search process and eliminate the search stagnation, thus increasing the algorithm’s efficiency. In the computational experiments, the algorithm is examined with various implemented variants of the mutation procedures using the QAP test (sample) instances from the library of the QAP instances – QAPLIB. The results of these experiments demonstrate how the different mutation procedures affect and possibly improve the overall performance of the ITS algorithm.

A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model.

A NEW HYBRID GENETIC ALGORITHM FOR THE GREY PATTERN QUADRATIC ASSIGNMENT PROBLEM

In this paper, we propose an improved hybrid genetic algorithm for the solution of the grey pattern quadratic assignment problem (GP-QAP). The novelty is the hybridization of the genetic algorithm with the so-called hierarchical iterated tabu search algorithm. Very fast exploration of the neighbouring solutions within the tabu search algorithm is used. In addition, a smart combination of the tabu search and adaptive perturbations is adopted, which enables a good balance between diversification and intensification during the iterative optimization process. The results from the experiments with the GP-QAP instances show that our algorithm is superior to other heuristic algorithms. Many best known solutions have been discovered for the large-scaled GP-QAP instances. DOI: http://dx.doi.org/10.5755/j01.itc.47.3.20728

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.

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.

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.

METAHEURISTIC APPROACHES FOR THE QUADRATIC MINIMUM SPANNING TREE PROBLEM

Given an undirected graph with costs associated both with its edges and unordered pairs of edges, the quadratic minimum spanning tree problem asks to find a spanning tree that minimizes the sum of costs of all edges and pairs of edges in the tree. We present multistart simulated annealing, hybrid genetic and iterated tabu search algorithms for solving this problem. We report on computational experiments that compare these algorithms on random graphs of size up to 50 vertices. The results indicate that the iterated tabu search algorithm is superior to the other two approaches in terms of both solution quality and computation time.

Solving the Fleet Size and Mix Vehicle Routing Problem with Time Windows via Adaptive Memory Programming

This paper presents a novel Adaptive Memory Programming (AMP) solution approach for the Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW). The FSMVRPTW seeks to design a set of depot returning vehicle routes to service a set of customers with known demands, for a heterogeneous fleet of vehicles with different capacities and fixed costs. Each customer is serviced only once by exactly one vehicle, within fixed time intervals that represent the earliest and latest times during the day that service can take place. The objective is to minimize the total transportation costs, or similarly to determine the optimal fleet composition and dimension following least cost vehicle routes. The proposed method utilizes the basic concept of an AMP solution framework equipped with a probabilistic semi-parallel construction heuristic, a novel solution re-construction mechanism, an innovative Iterated Tabu Search algorithm tuned for intensification local search and frequency-based long term memory structures. Computational experiments on well-known benchmark data sets illustrate the efficiency and effectiveness of the proposed method. Compared to the current state-of-the-art, the proposed method improves the best reported cumulative and mean results over most problem instances with reasonable computational requirements.

Iterated tabu search for identifying community structure in complex networks

This paper presents an iterated tabu search (denoted by ITS) algorithm for optimizing the modularity of community structure in complex networks. The proposed algorithm follows a general framework composed of two phases: basic optimization and postrefinement. When the basic optimization cannot improve the modularity any more, a postrefinement procedure is employed to further optimize the objective function with a global view. For both these two phases, iterated tabu search algorithm is employed to optimize the objective function. Computational results show the high effectiveness of the proposed ITS algorithm compared with six state-of-the-art algorithms in the literature. In particular, our ITS algorithm improves the previous best known modularity for several small and medium size networks.

Iterated Tabu Search for the Unconstrained Binary Quadratic Optimization Problem

Given a set of objects with profits (any, even negative, numbers) assigned not only to separate objects but also to pairs of them, the unconstrained binary quadratic optimization problem consists in finding a subset of objects for which the overall profit is maximized. In this paper, an iterated tabu search algorithm for solving this problem is proposed. Computational results for problem instances of size up to 7000 variables (objects) are reported and comparisons with other up-to-date heuristic methods are provided.