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Analysis of the influence of the 2-phase tabu search on the performance of the MAECP algorithm.
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Given an undirected graph G=(V,E) and a positive integer k, an equitable legal k-coloring of G is a partition of the vertex set V into k disjoint independent sets such that the cardinalities of any two independent sets differ by one at most. The equitable coloring problem is to find the smallest k for which an equitable legal k-coloring exists. The...
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... this section, we carry out additional experiments to investigate the 10 benefits of two important ingredients of the proposed MAECP algorithm: 11 the backbone-based crossover and the 2-phase infeasible tabu search. 12 These experiments were performed on a selection of 23 instances (shown 13 in Tables 3 and 4) with unknown optimal solutions. ...Context 2
... summarize in Table 3 the comparative results of MAECP against these 3 two variants with the same information as in Table 2. Specifically, we 4 report for each compared algorithm (MAECP, MA HTS, MA FISA), the 5 best result k best , the average result k avg , the standard deviation k std , the 6 number of successful runs over 20 runs SR/20 to achieve k best and the 7 average computation time in seconds t(s) to attain k best . The results show 8 that MAECP substantially performs better than MA HTS and MA FISA 9 in terms of best value (k best )and average value (k avg ...Similar publications
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Citations
... For several grouping problems (e.g., knapsack problem (Zhou et al., 2022), coloring problem (Sun et al., 2020)), it is observed that exploring intermediary infeasible solutions by relaxing some problem constraints is highly beneficial for finding high-quality solutions. In the case of KPF, we relax the knapsack constraint and employ the following extended evaluation function F to assess the quality of any solution S in Ω. ...
The knapsack problem (KP) with forfeits is a generalized KP that aims to select some items, among a set of candidate items, to maximize a profit function without exceeding the knapsack capacity. Moreover, a forfeit cost is incurred and deducted from the profit function when both incompatible items are placed in the knapsack. This problem is a relevant model for a number of applications and is however computationally challenging. We present a hybrid heuristic method for tackling this problem that combines the evolutionary search with adaptive feasible and infeasible search to find high‐quality solutions. A streamlining technique is designed to accelerate the evaluation of candidate solutions, which increases significantly the computational efficiency of the algorithm. We assess the algorithm on 120 test instances and demonstrate its dominance over the best performing approaches in the literature. Particularly, we show 94 improved lower bounds. We investigate the essential algorithmic components to understand their roles.
... Crossover is another important ingredient of a memetic algorithm and should be designed with care in order to favor transmissions of useful information from parents to ospring [13], while respecting the problem specic structure. One popular way of designing meaningful crossover for grouping problems such as CTSP is to explore the so-called backbone information, which typically corresponds to solution attributes shared by elite solutions [32,12,11,39]. In this work, we follow this idea and design a dedicated backbone crossover for CTSP. ...
The colored traveling salesmen problem is a node routing problem with multiple salesmen, where the cities are divided into m exclusive city sets and one shared city set. The objective is to minimize the total traveling distance of m Hamiltonian circuits (routes) under the following constraints: each exclusive city is to be visited by the corresponding salesman, while each shared city can be visited by any salesman. In this work, we present the first grouping memetic algorithm for solving this challenging problem. The algorithm includes three main components: (i) a greedy randomized heuristic for population initialization; (ii) a dedicated local search procedure for local optima exploration; (iii) a backbone-based crossover operator for solution recombination. We show computational results on three sets of 65 popular benchmark instances to demonstrate the competitiveness of our algorithm. We especially report improved upper bounds for 38 instances (for more than 58% cases). We also present first computational results with the general CPLEX solver, including 10 proven optimal solutions. Finally, we shed lights on the impacts of the key components of the algorithm. We make the code of the algorithm publicly available.
... Recall those memetic algorithms that combine evolutionary algorithms and local search are highly effective in solving various combinatorial optimization problems [11], [20], [21], [32]. The combined effect of global recombinant search and the powerful local search offers the memetic framework sufficient balance between intensification and diversification of the search process. ...
The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications. The MWVCP seeks a vertex cover of an undirected graph such that the sum of the weights of the selected vertices is as small as possible. In this paper, we present an effective algorithm to solve the MWVCP. First, a master-apprentice evolutionary algorithm based on two individuals is conducted to enhance the diversity of solutions. Second, a hybrid tabu search combined configuration checking and solution-based tabu search is introduced to intensify local search procedure. Harnessing the power of the evolutionary strategy and a novel variant of hybrid tabu search, Master-Apprentice Evolutionary Algorithm with Hybrid Tabu Search, MAE-HTS, is presented. Results of extensive computational experiments using standard benchmark instances and other large-scale instances demonstrate the efficacy of our algorithm in terms of solution quality, running time, and robustness compared to state-of-the-art heuristics from the literature and the commercial MIP solver Gurobi. We also systematically analyze the role of each individual component of the algorithm which when worked in unison produced superior outcomes. In particular, MAE-HTS produced improved solutions for 2 out of 126 public benchmark instances with better running time. In addition, our MAE-HTS outperforms other state-of-the-art algorithms DLSWCC and NuMWVC for 72 large scale MWVCP instances by obtaining the best results for 64 ones, while other two reference algorithms can only obtain 27 best results at most.
... For a comprehensive review of these problems, the reader is referred to the following references for the GCP: local search heuristics [19], exact algorithms [32] and new developments on heuristics till 2013 [17]. For the ECP, both [40] and [42] provide a brief review of main heuristic algorithms. ...
... The hybrid tabu search (HTS) algorithm [42] is another important algorithm exploring both equity-feasible and equity-infeasible solutions and applying an additional novel cyclic exchange neighborhood. Finally, the latest memetic algorithm (MAECP) [40] is a population-based hybrid algorithm combining a backbone crossover operator, a two-phase feasible and infeasible local search and a quality-and-distance pool updating strategy. MAECP has reported excellent results on the set of existing benchmark instances in the literature. ...
... • the memetic algorithm (MAECP, 2020) [40]. ...
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications and, however, are computationally difficult. In this work, a general population-based weight learning framework for solving graph coloring problems is presented. Unlike existing methods for graph coloring that are specific to the considered problem, the presented work targets a generic objective by introducing a unified method that can be applied to different graph coloring problems. This work distinguishes itself by its solving approach that formulates the search of a solution as a continuous weight tensor optimization problem and takes advantage of a gradient descent method computed in parallel on graphics processing units. The proposed approach is also characterized by its general global loss function that can easily be adapted to different graph coloring problems. The usefulness of the proposed approach is demonstrated by applying it to solve two typical graph coloring problems and performing extensive computational studies on popular benchmarks. Improved best-known results (new upper bounds) for the equitable graph coloring problem are reported for several large graphs.
... Memetic algorithm (MA) represents a type of evolutionary algorithms, which is optimized using a neighborhood search-based improvement procedure within a classical genetic algorithm framework [38][39][40][41]. Considering the out performance of MA in many other fields, this study proposes a MA improved by a local neighborhood searching procedure, which is named as MALNS, to identify the bottleneck suppliers. ...
With the development of lean manufacturing and economic globalization, supply networks increasingly become complex and large-scale, within which thousands of firms inter-depend with each other. Due to these increasing inter-dependencies, disruption of a quite few critical suppliers, namely bottleneck suppliers, can induce high loss to a supply network and even make the whole network dysfunction. Identification of bottleneck suppliers is significantly important for supply network risk management. Thus, in this paper, a method based on a memetic algorithm with local neighborhood search (MALNS) is proposed to identify bottleneck suppliers in a two-stage supply network. Firstly, a model based on multipartite network is designed to describe the product supply-demand relations between multiple manufacturers and suppliers, which considers the different roles of manufacturer and supplier and differentiates the products that suppliers supply. To assess the loss caused by supplier disruptions, two performance metrics of supply networks, average product availability rate and manufacturer functioning rate, are presented. Then, a MALNS-based method is proposed to identify bottleneck suppliers, i.e., suppliers whose disruption will decrease both performance metrics most greatly. Finally, a case study based on a real automobile supply network is presented to validate the applicability and effectiveness of the proposed method.
... The graph coloring problem is proved to be an NP-Complete problem [6] and many heuristics for graph coloring problem [7]- [11], equitable coloring problem [12], [13], k-coloring problem [14], [15], minimum sum coloring problem [16] and weighted vertex coloring problem [17] have been proposed in the literature. In this study, we propose a hybrid evolutionary algorithm [18] for the vertexweighted k-coloring problem. ...
Graph coloring is one of the main optimization problems widely studied in the literature. In this study, we propose a novel evolutionary algorithm called Integrated Crossover Based Evolutionary Algorithm with its unique crossover operator and local search technique for coloring vertex-weighted graphs. The integrated crossover operator targets to use the domain-specific information in the individuals and the local search technique aims to explore neighborhood solutions using weighted-swap operations. The performance of the proposed work is evaluated on synthetic benchmarks and DIMACS instances by comparing it with leading evolutionary algorithms from the literature. The experimental study indicates that our algorithm outperforms the related work in 71% of the test cases and achieves the same result in 17% of the test cases provided in the synthetic benchmarks. The experiments performed on DIMACS benchmarks denote that our algorithm finds the best number of colors in 70 out of 73 graphs, so the proposed work is very successful in coloring vertex-weighted graphs within a reasonable amount of time.
... Newer works focused on the coloring of graphs are consisting of [10] and [11]. Authors of [10] created population-based memetic algorithm for solving the equitable coloring problem. ...
... Newer works focused on the coloring of graphs are consisting of [10] and [11]. Authors of [10] created population-based memetic algorithm for solving the equitable coloring problem. The equitable coloring problem deals with finding the smallest k for which an equitable legal k-coloring exists. ...
... • the tabu search algorithm (TabuEqCol) [9] • the backtracking based iterated tabu search (BITS) [26] • the feasible and infeasible search algorithm (FISA) [41] • the hybrid tabu search (HTS) [43] • the memetic algorithm MAECP [40]. ...
... heuristics, in particular, the best-performing heuristics used in Section 6 as reference algorithms, while referring the reader to [15,33] for a comprehensive review for the GCP and the recent studies such as [26,41,40,43] for the ECP. ...
... The hybrid tabu search (HTS) algorithm [43] is another important algorithm exploring both equity-feasible and equity-infeasible solutions and ap-plying an additional novel cyclic exchange neighborhood. Finally, the memetic algorithm (MAECP) [40] is a population-based hybrid algorithm combining a backbone crossover operator, a two-phase feasible and infeasible local search and a quality-and-distance pool updating strategy. It is worth mentioning that FISA, HTS and MAECP cover the current best-known results on the benchmark instances used in the last section for the ECP. ...
A grouping problem involves partitioning a set of items into mutually disjoint groups or clusters according to some guiding decision criteria and imperative constraints. Grouping problems have many relevant applications and are computationally difficult. In this work, we present a general weight learning based optimization framework for solving grouping problems. The central idea of our approach is to formulate the task of seeking a solution as a real-valued weight matrix learning problem that is solved by first order gradient descent. A practical implementation of this framework is proposed with tensor calculus in order to benefit from parallel computing on GPU devices. To show its potential for tackling difficult problems, we apply the approach to two typical and well-known grouping problems (graph coloring and equitable graph coloring). We present large computational experiments and comparisons on popular benchmarks and report improved best-known results (new upper bounds) for several large graphs.
