Computing the Metric Dimension of Hypercube Graphs by Particle Swarm Optimization Algorithms

Murdiansyah, Danang Triantoro; Adiwijaya, Adiwijaya

doi:10.1007/978-3-319-51281-5_18

Cited by 6 publications

(6 citation statements)

References 9 publications

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“…Metaheuristic algorithms (MAs) have become prevalent in many applied disciplines in recent decades because of their higher performance and lower required computing capacity and time than deterministic algorithms in many optimization problems [7]. Only a few algorithms have been proposed to compute heuristically the metric dimension problem [8][9][10][11]. In [8], Kratica et al have developed a genetic algorithm that can be tested on various types of graph instances to find the metric dimension of graphs.…”

Section: Figure 1 the Graph G And Its Resolving Graph R(g)mentioning

confidence: 99%

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Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>

Mohamed,

Amin

2023

MLR

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In this paper, we consider the NP-hard problem of finding the metric dimension of graphs. A set of vertices B of a connected graph G = (V, E) resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. The cardinality of the smallest resolving set of G is the metric dimension of G. The metric dimension problem arises in several different fields, such as robot navigation, telecommunication, and geographical routing protocol. The slime mould algorithm (SMA) is an efficient population-based optimizer based on the oscillation mode of slime mould in nature. The SMA has a specific mathematical model and very competitive results, along with fast convergence for many problems, particularly in realworld cases. SMA has good exploration and exploitation abilities for solving optimization problems. However, complex and high-dimensional SMA may fall into local optimal regions. SA is a very preferable technique among the other heuristic approaches as it provides practical randomness in the search to avoid the local extreme points. However, SA involves a tradeoff between computing time and solution sensitivity. The SA is used to enhance the fitness of the best agent if it falls in a suboptimal region, which will lead to the enhancement of all individuals. We solve the problem as integer linear programming and introduce the hybrid algorithm SMA-SA, which combines simulated annealing SA and SMA for determining the metric dimension of graphs. Comparisons were performed on the graphs: k-home chain graph, tadpole graph, alternate triangular snake graph, and mirror graph. Finally, computational results and comparisons with pure SA, SMA, and PSO algorithms confirm the effectiveness of the proposed SMA-SA for solving metric dimension problem.

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Section: Figure 1 the Graph G And Its Resolving Graph R(g)mentioning

confidence: 99%

“…In [10], a variable neighborhood search approach has been proposed for tackling metric dimension and minimal doubly resolving set problems in order to enhance the current upper bounds. In [11], a particle swarm optimization has been proposed for solving metric dimension problem.…”

Section: Figure 1 the Graph G And Its Resolving Graph R(g)mentioning

confidence: 99%

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>

Mohamed,

Amin

2023

MLR

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“…A few algorithms are proposed in the literature to compute the metric dimension of graphs heuristically. These are genetic algorithm [20], particle swarm optimization [21] and variable neighborhood search [22].…”

Section: Introductionmentioning

confidence: 99%

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Mohamed¹,

Mohaisen²,

Amin³

2023

Intelligent Automation &Amp; Soft Computing

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In this paper, we consider the NP-hard problem of finding the minimum connected resolving set of graphs. A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraph B induced by B is a nontrivial connected subgraph of G. The cardinality of the minimal resolving set is the metric dimension of G and the cardinality of minimum connected resolving set is the connected metric dimension of G. The problem is solved heuristically by a binary version of an enhanced Harris Hawk Optimization (BEHHO) algorithm. This is the first attempt to determine the connected resolving set heuristically. BEHHO combines classical HHO with opposition-based learning, chaotic local search and is equipped with an S-shaped transfer function to convert the continuous variable into a binary one. The hawks of BEHHO are binary encoded and are used to represent which one of the vertices of a graph belongs to the connected resolving set. The feasibility is enforced by repairing hawks such that an additional node selected from V\B is added to B up to obtain the connected resolving set. The proposed BEHHO algorithm is compared to binary Harris Hawk Optimization (BHHO), binary opposition-based learning Harris Hawk Optimization (BOHHO), binary chaotic local search Harris Hawk Optimization (BCHHO) algorithms. Computational results confirm the superiority of the BEHHO for determining connected metric dimension.

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“…On the other hand, only a few algorithms have been proposed to compute heuristically the metric dimension problem [28][29][30]. In [28], a genetic algorithm has been developed for computing the metric dimension of many classes of graph instances including pseudo-Boolean, crew scheduling and graph coloring.…”

mentioning

confidence: 99%

“…Infeasible individuals are changed by the addition of the required nodes in order to become feasible. In [29], PSO is adapted for determining the metric dimension where a real valued vector of vertices is converted to binary valued vector by a linear function and infeasible particles are repaired by adding some vertices until the particles become feasible. e PSO is tested by computing the metric dimension of hypercube graphs.…”

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confidence: 99%

Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem

Mohamed

Mohaisen

Amin

2022

Scientific Programming

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We consider, in this paper, the NP-hard problem of finding the minimum connected domination metric dimension of graphs. A vertex set B of a connected graph G = (V, E) resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraph B ¯ induced by B is a nontrivial connected subgraph of G. A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B. The cardinality of the smallest resolving set of G, the cardinality of the minimal connected resolving set, and the cardinality of the minimal connected domination resolving set are the metric dimension of G, connected metric dimension of G, and connected domination metric dimension of G, respectively. We present the first attempt to compute heuristically the minimum connected dominant resolving set of graphs by a binary version of the equilibrium optimization algorithm (BEOA). The particles of BEOA are binary-encoded and used to represent which one of the vertices of the graph belongs to the connected domination resolving set. The feasibility is enforced by repairing particles such that an additional vertex generated from vertices of G is added to B, and this repairing process is iterated until B becomes the connected domination resolving set. The proposed BEOA is tested using graph results that are computed theoretically and compared to competitive algorithms. Computational results and their analysis show that BEOA outperforms the binary Grey Wolf Optimizer (BGWO), the binary Particle Swarm Optimizer (BPSO), the binary Whale Optimizer (BWO), the binary Slime Mould Optimizer (BSMO), the binary Grasshopper Optimizer (BGO), the binary Artificial Ecosystem Optimizer (BAEO), and the binary Elephant Herding Optimizer (BEHO).

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Computing the Metric Dimension of Hypercube Graphs by Particle Swarm Optimization Algorithms

Cited by 6 publications

References 9 publications

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem

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Computing the Metric Dimension of Hypercube Graphs by Particle Swarm Optimization Algorithms

Cited by 6 publications

References 9 publications

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem&lt;br /&gt; &lt;div&gt; &lt;br /&gt; &lt;/div&gt;

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem&lt;br /&gt; &lt;div&gt; &lt;br /&gt; &lt;/div&gt;

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem

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Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>

Hybridizing Slime Mould Algorithm with Simulated Annealing for Solving Metric Dimension Problem<br /> <div> <br /> </div>