A systematic study on meta-heuristic approaches for solving the graph coloring problem

Mostafaie, Taha; Khiyabani, Farzin Modarres; Navimipour, Nima Jafari

doi:10.1016/j.cor.2019.104850

Cited by 42 publications

(22 citation statements)

References 114 publications

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“…Genetic Algorithm (GA), a meta-heuristic, is used not just for traditional optimisation (linear, convex) problems, but is also effective for solving distinct and nonlinear issues (Mostafaie, Khiyabani, and Navimipour 2020). NSGA-III is a Non-dominated sorting genetic algorithm and is a powerful method for overcoming the complexity of constraints faced in multi-objective optimisation problems (Xu et al 2015).…”

Section: Vikor and Nsga III Methodsmentioning

confidence: 99%

“…This algorithm identifies multiple Pareto front regions and is quick for obtaining Pareto optimal sets (Tavana et al 2016). In general, GA has varying advantages such as high convergence and low computational time and further provides significant reduction in search space to obtain global/near-optimal solutions (Torabi, Ghomi, and Karimi 2006;Mostafaie, Khiyabani, and Navimipour 2020). It is evident from the above literature that the VIKOR and NSGA-III methods are best suited for the nature of the problem explored in this study.…”

Section: Vikor and Nsga III Methodsmentioning

confidence: 99%

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Impact of financial risk on supply chains: a manufacturer-supplier relational perspective

Ghadge

Jena

Kamble

et al. 2020

International Journal of Production Research

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This study aims to analyse the manufacturer-supplier relational perspective under the influence of exogenous financial risk. Following corporate finance theory, a multi-objective decision model for supplier selection and order allocation is developed to maximise the total profit of the manufacturer, and minimise the implicit equity stake and financial risk faced by selected suppliers. A two-echelon supply chain is explored under the influence of foreign exchange risk, default risk, market risk and price fluctuation risk, and solved using an NSGA-III algorithm. Three case scenarios are analysed to explore the influence of a set of financial risk on the manufacturer-supplier relationship and the behaviour of suppliers concerning risk profile, both in the short and long-term horizon. The results are analysed from both the manufacturer as well as supplier perspective, and the optimal conditions are discussed under the cascading risk circumstances. The study provides multiple insights into the impact of financial risk on supply chain relationship and will be valuable for dealing with similar uncertain economic environment. The research is likely to be of benefit beyond supply chain managers, like investors and financial risk managers in making informed decisions. The need to focus on systemic risk in supply chains is evident from the study.

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Section: Vikor and Nsga III Methodsmentioning

confidence: 99%

Section: Vikor and Nsga III Methodsmentioning

confidence: 99%

Impact of financial risk on supply chains: a manufacturer-supplier relational perspective

Ghadge

Jena

Kamble

et al. 2020

International Journal of Production Research

View full text Add to dashboard Cite

show abstract

“…Graph coloring in graph theory is a problem of assigning colors to the vertices and edges of a graph [18][19][20]. In this paper, we consider the graph coloring problem of assigning colors to vertices, such that no adjacent vertices of a graph exist of the same color.…”

Section: Graph Coloringmentioning

confidence: 99%

“…In this paper, we develop a load balancing technique in edge cloud computing environments with mobile devices. The proposed load balancing technique is based on a traditional graph problem called graph coloring [18][19][20] that minimizes the number of colors on vertices while satisfying a property (no adjacent vertices exhibit the same color). By analogy, the vertices of a graph can be considered as mobile devices, the edges of a graph can be considered as nearby discoverable mobile devices, and the distinctive graph colors are considered as distinctive edge servers.…”

Section: Introductionmentioning

confidence: 99%

A Load Balancing Algorithm for Mobile Devices in Edge Cloud Computing Environments

Lim

Lee

2020

Electronics

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As current data centers and servers are growing in size by orders of magnitude when needed, load balancing is a great concern in scalable computing systems, including mobile edge cloud computing environments. In mobile edge cloud computing systems, a mobile user can offload its tasks to nearby edge servers to support real-time applications. However, when users are located in a hot spot, several edge servers can be overloaded due to suddenly offloaded tasks from mobile users. In this paper, we present a load balancing algorithm for mobile devices in edge cloud computing environments. The proposed load balancing technique features an efficient complexity by a graph coloring-based implementation based on a genetic algorithm. The aim of the proposed load balancing algorithm is to distribute offloaded tasks to nearby edge servers in an efficient way. Performance results show that the proposed load balancing algorithm outperforms previous techniques and increases the average CPU usage of virtual machines, which indicates a high utilization of edge servers.

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“…GCP is very challenging for genetic algorithms because of its vast solution space. Hence, designing and choosing the right genetic operators in population-based methods are important for the following reasons [53][54][55][56]:…”

Section: The Need For Complexity Analysis and Stochastic Convergence mentioning

confidence: 99%

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

Marappan

Sethumadhavan

2020

Mathematics

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The graph coloring problem is an NP-hard combinatorial optimization problem and can be applied to various engineering applications. The chromatic number of a graph G is defined as the minimum number of colors required to color the vertex set V(G) so that no two adjacent vertices are of the same color, and different approximations and evolutionary methods can find it. The present paper focused on the asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number. The asymptotic analysis of different crossover and mutation operators helps in choosing the better evolutionary operator to minimize the problem search space and computational complexity. The choice of the right genetic operators facilitates an evolutionary algorithm to achieve faster convergence with lesser population size N through an adequate distribution of promising genes. The selection of an evolutionary operator plays an essential role in reducing the bounds for minimum color obtained so far for some of the benchmark graphs. This research also focuses on the necessary and sufficient conditions for the global convergence of evolutionary algorithms. The stochastic convergence of recent evolutionary operators for solving graph coloring is newly analyzed.

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A systematic study on meta-heuristic approaches for solving the graph coloring problem

Cited by 42 publications

References 114 publications

Impact of financial risk on supply chains: a manufacturer-supplier relational perspective

Impact of financial risk on supply chains: a manufacturer-supplier relational perspective

A Load Balancing Algorithm for Mobile Devices in Edge Cloud Computing Environments

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

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