scholarly journals 2-Quasitotal Fuzzy Graphs and Their Total Coloring

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
V. N. Srinivasa Rao Repalle ◽  
Fekadu Tesgera Agama
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Real Life ◽  
Register Allocation ◽  
Total Coloring ◽  
Fuzzy Graph ◽  
Traffic Light ◽  
Numerical Examples ◽  
Combinatorial Optimization Problems ◽  
Fuzzy Graphs

Coloring of fuzzy graphs has many real-life applications in combinatorial optimization problems like traffic light system, exam scheduling, and register allocation. The coloring of total fuzzy graphs and its applications are well studied. This manuscript discusses the description of 2-quasitotal graph for fuzzy graphs. The proposed concept of 2-quasitotal fuzzy graph is explicated by several numerical examples. Moreover, some theorems related to the properties of 2-quasitotal fuzzy graphs are stated and proved. The results of these theorems are compared with the results obtained from total fuzzy graphs and 1-quasitotal fuzzy graphs. Furthermore, it defines 2-quasitotal coloring of fuzzy total graphs and which is justified.

scholarly journals Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Mamo Abebe Ashebo ◽  
V. N. Srinivasa Rao Repalle
Keyword(s):  
Optimization Problems ◽  
Real Life ◽  
Chromatic Polynomial ◽  
Fuzzy Graph ◽  
Traffic Light ◽  
Chromatic Polynomials ◽  
Combinatorial Optimization Problems ◽  
Fuzzy Graphs ◽  
Vertex Set ◽  
Fuzzy Vertex

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on α-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.

scholarly journals A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 551 ◽  
Author(s):  
Liangsong Huang ◽  
Yu Hu ◽  
Yuxia Li ◽  
P. K. Kishore Kumar ◽  
Dipak Koley ◽  
...  
Keyword(s):  
Graph Theory ◽  
Optimization Problems ◽  
Real Life ◽  
Road Transport ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Real World Problem ◽  
Neutrosophic Graph ◽  
Definition Of

Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

scholarly journals Stability concepts in bargaining games

2021 ◽  
Author(s):  
Somnath Kundu
Keyword(s):  
Combinatorial Optimization ◽  
Cost Sharing ◽  
Optimization Problems ◽  
Real Life ◽  
Profit Sharing ◽  
Bargaining Games ◽  
Bargaining Process ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Stability Concepts

In this thesis we discuss some novel concepts of stability in bargaining games, over a network setting. So far, the studies on bargaining games were done as profit sharing problems, whose underlying combinatorial optimization problems are of packing type. In our work, we study bargaining games from a cost sharing perspective, where the underlying combinatorial optimization problems are covering type problems. Unlike previous studies, where bargaining processes are restricted to only two players, we study bargaining games over a more generic hypergraph setting, which allows any bargaining process to be formed among any number of players. In previous studies of bargaining games, the objects that are being negotiated are assumed to be uniform and only the outcomes of the negotiations are allowed to be different. However, in our study, we accommodate possibilities of non-uniform weights of the objects that are being negotiated, which is closer to any real life scenario. Finally we extend our study to incorporate socially aware players by introducing a relaxed and innovative definition of stability.

scholarly journals Enhanced Hyper-Cube Framework Ant Colony Optimization for Combinatorial Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 286
Author(s):  
Ali Ahmid ◽  
Thien-My Dao ◽  
Ngan Van Le
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Real Life ◽  
Ant Colony ◽  
Combinatorial Optimization Problems ◽  
The Right ◽  
Design Cost ◽  
Laminated Structures

Solving of combinatorial optimization problems is a common practice in real-life engineering applications. Trusses, cranes, and composite laminated structures are some good examples that fall under this category of optimization problems. Those examples have a common feature of discrete design domain that turn them into a set of NP-hard optimization problems. Determining the right optimization algorithm for such problems is a precious point that tends to impact the overall cost of the design process. Furthermore, reinforcing the performance of a prospective optimization algorithm reduces the design cost. In the current study, a comprehensive assessment criterion has been developed to assess the performance of meta-heuristic (MH) solutions in the domain of structural design. Thereafter, the proposed criterion was employed to compare five different variants of Ant Colony Optimization (ACO). It was done by using a well-known structural optimization problem of laminate Stacking Sequence Design (SSD). The initial results of the comparison study reveal that the Hyper-Cube Framework (HCF) ACO variant outperforms the others. Consequently, an investigation of further improvement led to introducing an enhanced version of HCFACO (or EHCFACO). Eventually, the performance assessment of the EHCFACO variant showed that the average practical reliability became more than twice that of the standard ACO, and the normalized price decreased more to hold at 28.92 instead of 51.17.

scholarly journals Fuzzy covering location problems with different aggregation operators

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 513-522 ◽  
Author(s):  
Darko Drakulic ◽  
Aleksandar Takaci ◽  
Miroslav Maric
Keyword(s):  
Combinatorial Optimization ◽  
Fuzzy Sets ◽  
Optimization Problems ◽  
Real Life ◽  
Aggregation Operators ◽  
Location Problems ◽  
Important Class ◽  
Combinatorial Optimization Problems ◽  
Life Problems ◽  
Standard Models

Covering location problems is well-known and very important class of combinatorial optimization problems. Standard models for covering location problems cannot encompass real-life problems, because real-life problems contain some degree of uncertainty. The use of fuzzy sets in modeling covering location problems allows the implementation of these conditions. Depending on the type of problems, it is necessary to use different aggregation operators in calculating solution?s quality. The aim of this study is introducing of fuzzy sets with different corresponding conorms in modeling most known types of covering location problems.

scholarly journals Load Balancing Based on Optimization Algorithms: An Overview

2019 ◽  
Vol 4 (2019) ◽  
pp. 3-12
Author(s):  
Fatma Mbarek ◽  
Volodymyr Mosorov
Keyword(s):  
Combinatorial Optimization ◽  
Load Balancing ◽  
Communication Networks ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Real Life ◽  
Continuous Optimization ◽  
Combinatorial Optimization Problems ◽  
Life Problems ◽  
Continuous Optimization Problems

Combinatorial optimization challenges are rooted in real-life problems, continuous optimization problems, discrete optimization problems and other significant problems in telecommunications which include, for example, routing, design of communication networks and load balancing. Load balancing applies to distributed systems and is used for managing web clusters. It allows to forward the load between web servers, using several scheduling algorithms. The main motivation for the study is the fact that combinatorial optimization problems can be solved by applying optimization algorithms. These algorithms include ant colony optimization (ACO), honey bee (HB) and multi-objective optimization (MOO). ACO and HB algorithms are inspired by the foraging behavior of ants and bees which use the process to locate and gather food. However, these two algorithms have been suggested to handle optimization problems with a single-objective. In this context, ACO and HB have to be adjusted to multiobjective optimization problems. This paper provides a summary of the surveyed optimization algorithms and discusses the adaptations of these three algorithms. This is pursued by a detailed analysis and a comparison of three major scheduling techniques mentioned above, as well as three other, new algorithms (resulting from the combination of the aforementioned techniques) used to efficiently handle load balancing issues.

scholarly journals Stability concepts in bargaining games

2021 ◽  
Author(s):  
Somnath Kundu
Keyword(s):  
Combinatorial Optimization ◽  
Cost Sharing ◽  
Optimization Problems ◽  
Real Life ◽  
Profit Sharing ◽  
Bargaining Games ◽  
Bargaining Process ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Stability Concepts

In this thesis we discuss some novel concepts of stability in bargaining games, over a network setting. So far, the studies on bargaining games were done as profit sharing problems, whose underlying combinatorial optimization problems are of packing type. In our work, we study bargaining games from a cost sharing perspective, where the underlying combinatorial optimization problems are covering type problems. Unlike previous studies, where bargaining processes are restricted to only two players, we study bargaining games over a more generic hypergraph setting, which allows any bargaining process to be formed among any number of players. In previous studies of bargaining games, the objects that are being negotiated are assumed to be uniform and only the outcomes of the negotiations are allowed to be different. However, in our study, we accommodate possibilities of non-uniform weights of the objects that are being negotiated, which is closer to any real life scenario. Finally we extend our study to incorporate socially aware players by introducing a relaxed and innovative definition of stability.

Extrapolating from Limited Uncertain Information in Large-Scale Combinatorial Optimization Problems to Obtain Robust Solutions

2016 ◽  
Vol 25 (01) ◽  
pp. 1660005
Author(s):  
Laura Climent ◽  
Richard J. Wallace ◽  
Barry O'Sullivan ◽  
Eugene C. Freuder
Keyword(s):  
Combinatorial Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Real Life ◽  
Data Uncertainty ◽  
Uncertain Information ◽  
Combinatorial Optimization Problems ◽  
Lack Of Information ◽  
Life Problems ◽  
A Current

Data uncertainty in real-life problems is a current challenge in many areas, including Operations Research (OR) and Constraint Programming (CP). This is especially true given the continual and accelerating increase in the amount of data associated with real-life problems, to which Large Scale Combinatorial Optimization (LSCO) techniques may be applied. Although data uncertainty has been studied extensively in the literature, many approaches do not take into account the partial or complete lack of information about uncertainty in real-life settings. To meet this challenge, in this paper we present a strategy for extrapolating data from limited uncertain information to ensure a certain level of robustness in the solutions obtained. Our approach is motivated and evaluated with real-world applications of harvesting and supplying timber from forests to mills and the well known knapsack problem with uncertainty.

Solving the University course timetabling problem using bat inspired algorithm

2021 ◽  
Vol 47 (2) ◽  
pp. 674-685
Author(s):  
Ushindi Limota ◽  
Egbert Mujuni ◽  
Allen Mushi
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Real Life ◽  
Bat Algorithm ◽  
Discrete Version ◽  
Timetabling Problem ◽  
Combinatorial Optimization Problems ◽  
University Course Timetabling ◽  
Metaheuristic Methods

Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization problem, a discrete version of BA for CPT has been proposed and tested using real-life data from the Dar es Salaam University College of Education (DUCE). The algorithm has produced promising results, as in each execution test, it generated a timetable in which all hard constraints were met and soft constraints were significantly satisfied within a few iterations. Keywords: Combinatorial optimization, Timetabling problem, Metaheuristic algorithms, Bat algorithm.

Sign in / Sign up

Export Citation Format

Share Document