Xiangjing Lai

Path relinking for the fixed spectrum frequency assignment problem

Frequency assignment is a key issue in wireless communication systems.We introduce a population-based path relinking method to solve this problem.The method is assessed on 42 well-known benchmark instances in the literature.The method is able to discover improved best results (new upper bounds) for 19 instances. The fixed spectrum frequency assignment problem (FS-FAP) is a highly relevant application in modern wireless systems. This paper presents the first path relinking (PR) approach for solving FS-FAP. We devise four relinking operators to generate intermediate solutions (or paths) and a tabu search procedure for local optimization. We also adopt a diversity-and-quality technique to maintain population diversity. To show the effectiveness of the proposed approach, we present computational results on the set of 42 benchmark instances commonly used in the literature and compare them with the current best results obtained by any other existing methods. By showing improved best results (new upper bounds) for 19 instances, we demonstrate the effectiveness of the proposed PR approach. We investigate the impact of the relinking operators and the population updating strategy. The ideas of the proposed could be applicable to other frequency assignment problems and search problems.

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 algorithms 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. HighlightsThe equitable coloring problem (ECP) is a NP-hard combinatorial problem.We introduce a backtracking based iterated tabu search (BITS) algorithm for the ECP.We assess the algorithms performance on a large set of ECP benchmark instances.We report new upper bounds for 21 benchmark instances.

Iterated maxima search for the maximally diverse grouping problem

The maximally diverse grouping problem (MDGP) is to partition the vertices of an edge-weighted and undirected complete graph into m groups such that the total weight of the groups is maximized subject to some group size constraints. MDGP is a NP-hard combinatorial problem with a number of relevant applications. In this paper, we present an innovative heuristic algorithm called iterated maxima search (IMS) algorithm for solving MDGP. The proposed approach employs a maxima search procedure that integrates organically an efficient local optimization method and a weak perturbation operator to reinforce the intensification of the search and a strong perturbation operator to diversify the search. Extensive experiments on five sets of 500 MDGP benchmark instances of the literature show that IMS competes favorably with the state-of-the-art algorithms. We provide additional experiments to shed light on the rationality of the proposed algorithm and investigate the role of the key ingredients.

A learning-based path relinking algorithm for the bandwidth coloring problem

This paper proposes a learning-based path relinking algorithm (LPR) for solving the bandwidth coloring problem and the bandwidth multicoloring problem. Based on the population path-relinking framework, the proposed algorithm integrates a learning-driven tabu optimization procedure and a path-relinking operator. LPR is assessed on two sets of 66 common benchmark instances, and achieves highly competitive results in terms of both solution quality and computational efficiency compared to the state-of-the-art algorithms in the literature. Specifically, the algorithm establishes 7 new upper bounds while matching the best known results for 56 cases. The impacts of the learning mechanism and the path relinking operators are investigated, confirming their critical role to the success of the proposed algorithm.

Iterated variable neighborhood search for the capacitated clustering problem

The NP-hard capacitated clustering problem (CCP) is a general model with a number of relevant applications. This paper proposes a highly effective iterated variable neighborhood search (IVNS) algorithm for solving the problem. IVNS combines an extended variable neighborhood descent method and a randomized shake procedure to explore effectively the search space. The computational results obtained on three sets of 133 benchmarks reveal that the proposed algorithm competes favorably with the state-of-the-art algorithms in the literature both in terms of solution quality and computational efficiency. In particular, IVNS discovers an improved best known result (new lower bounds) for 28 out of 83 most popular instances, while matching the current best known results for the remaining 55 instances. Several essential components of the proposed algorithm are investigated to understand their impacts on the performance of algorithm.

A two-phase tabu-evolutionary algorithm for the 0–1 multidimensional knapsack problem

Abstract The 0–1 multidimensional knapsack problem is a well-known NP-hard combinatorial optimization problem with numerous applications. In this work, we present an effective two-phase tabu-evolutionary algorithm for solving this computationally challenging problem. The proposed algorithm integrates two solution-based tabu search methods into the evolutionary framework that applies a hyperplane-constrained crossover operator to generate offspring solutions, a dynamic method to determine search zones of interest, and a diversity-based population updating rule to maintain a healthy population. We show the competitiveness of the proposed algorithm by presenting computational results on the 281 benchmark instances commonly used in the literature. In particular, in a computational comparison with the best algorithms in the literature on multiple data sets, we show that our method on average matches more than twice the number of best known solutions to the harder problems than any other method and in addition yields improved best solutions (new lower bounds) for 4 difficult instances. We investigate two key ingredients of the algorithm to understand their impact on the performance of the algorithm.

On feasible and infeasible search for equitable graph coloring

An equitable legal k-coloring of an undirected graph G = (V, E) is a partition of the vertex set V into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one (this is called the equity constraint). As a variant of the popular graph coloring problem (GCP), the equitable coloring problem (ECP) involves finding a minimum k for which an equitable legal k-coloring exists. In this paper, we present a study of searching both feasible and infeasible solutions with respect to the equity constraint. The resulting algorithm relies on a mixed search strategy exploring both equitable and inequitable colorings unlike existing algorithms where the search is limited to equitable colorings only. We present experimental results on 73 DIMACS and COLOR benchmark graphs and demonstrate the competitiveness of this search strategy by showing 9 improved best-known results (new upper bounds).

Solution-based tabu search for the maximum min-sum dispersion problem

Abstract The maximum min-sum dispersion problem (Max-Minsum DP) is an important representative of a large class of dispersion problems. Having numerous applications in practice, the NP-hard Max-Minsum DP is however computationally challenging. This paper introduces an effective solution-based tabu search (SBTS) algorithm for solving the Max-Minsum DP approximately. SBTS is characterized by the joint use of hash functions to determine the tabu status of candidate solutions and a parametric constrained swap neighborhood to enhance computational efficiency. Experimental results on 140 benchmark instances commonly used in the literature demonstrate that the proposed algorithm competes favorably with the state-of-the-art algorithms both in terms of solution quality and computational efficiency. In particular, SBTS improves the best-known results for 80 out of the 140 instances, while matching 51 other best-known solutions. We conduct a computational analysis to identify the respective roles of the hash functions and the parametric constrained swap neighborhood.

Adaptive feasible and infeasible tabu search for weighted vertex coloring

Abstract The Weighted Vertex Coloring Problem of a vertex weighted graph is to partition the vertex set into k disjoint independent sets such that the sum of the costs of these sets is minimized, where the cost of each set is given by the maximum weight of a vertex (representative) in that set. To solve this NP-hard problem, we present the adaptive feasible and infeasible search algorithm (AFISA) that relies on a mixed search strategy exploring both feasible and infeasible solutions. From an initial feasible solution, AFISA seeks improved solutions by oscillating between feasible and infeasible regions. To prevent the search from going too far from feasibility boundaries, we introduce a control mechanism that adaptively makes the algorithm to go back and forth between feasible and infeasible solutions. To explore the search space, we use a tabu search optimization procedure to ensure an intensified exploitation of candidate solutions and an adaptive perturbation strategy to escape local optimum traps. We show extensive experimental results on 161 benchmark instances and present new upper bounds that are useful for future studies. We assess the benefit of the key features of the proposed approach. This work demonstrates that examining both feasible and infeasible solutions during the search is a highly effective search strategy for the considered coloring problem and could beneficially be applied to other constrained problems as well.

Two-stage solution-based tabu search for the multidemand multidimensional knapsack problem

Abstract The multidemand multidimensional knapsack problem (MDMKP) is a significant generalization of the popular multidimensional knapsack problem with relevant applications. In this work we investigate for the first time how solution-based tabu search can be used to solve this computationally challenging problem. For this purpose, we propose a two-stage search algorithm, where the first stage aims to locate a promising hyperplane within the whole search space and the second stage tries to find improved solutions by exploring the reduced subspace defined by the hyperplane. Computational experiments on 156 benchmark instances commonly used in the literature show that the proposed algorithm competes favorably with the state-of-the-art results. We analyze several key components of the algorithm to highlight their impacts on the performance of the algorithm.