In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Multiple criteria decision-making (MCDM) is considered as a complex decision-making (DM) tool involving both quantitative and qualitative factors. In recent years, several MCDM techniques and approaches have been suggested to choosing the optimal probable options. The purpose of this article is to systematically review the applications and methodologies of the MCDM techniques and approaches. This study reviewed a total of 393 articles published from 2000 to 2014 in more than 120 peer reviewed journals (extracted from Web of Science). According to experts’ opinion, these articles were grouped into 15 fields. Furthermore, these articles were categorised based on authors, publication date, name of journals, methods, tools, and type of research (MCDM utilising research, MCDM developing research, and MCDM proposing research). The results of this study indicated that in 2013 scholars have published articles more than in other years. In addition, the analytic hierarchy process (AHP) method in the individual tool...

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Multiple criteria decision-making techniques and their applications – a review of the literature from 2000 to 2014

A multi objective optimization approach for flexible job shop scheduling problem under random machine breakdown by evolutionary algorithms

Modelling and Pareto optimization of mechanical properties of friction stir welded AA7075/AA5083 butt joints using neural network and particle swarm algorithm

This paper provides an extensive review of the popular multi-objective optimization algorithm NSGA-II for selected combinatorial optimization problems viz. assignment problem, allocation problem, travelling salesman problem, vehicle routing problem, scheduling problem, and knapsack problem. It is identified that based on the manner in which NSGA-II has been implemented for solving the aforementioned group of problems, there can be three categories: Conventional NSGA-II, where the authors have implemented the basic version of NSGA-II, without making any changes in the operators; the second one is Modified NSGA-II, where the researchers have implemented NSGA-II after making some changes into it and finally, Hybrid NSGA-II variants, where the researchers have hybridized the conventional and modified NSGA-II with some other technique. The article analyses the modifications in NSGA-II and also discusses the various performance assessment techniques used by the researchers, i.e., test instances, performance metrics, statistical tests, case studies, benchmarking with other state-of-the-art algorithms. Additionally, the paper also provides a brief bibliometric analysis based on the work done in this study.

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A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

Multi-objective optimization for stochastic computer networks using NSGA-II and TOPSIS

Network reliability evaluation for flow networks is an important issue in quality management. Many real-life systems can be modeled as stochastic-flow networks, in which each branch is multistate due to complete failure, partial failure, maintenance, etc. That is, each branch has several capacities with a probability distribution, and may fail. Hence, network reliability is the probability that a specified flow can be transmitted through the network successfully. Although there are many researches related to the evaluation of network reliability for a stochastic-flow network, how to assign a set of multistate components to the network so that the network reliability is maximal is never discussed. Therefore, this paper devotes to evaluating the optimal network reliability under components-assignments subject to a transmission budget, in which the transmission cost depends on each component's capacity. The network reliability under a components-assignment can be computed in terms of minimal paths, and state-space decomposition. Subsequently, we propose an optimization method based on a genetic algorithm. The experimental results show that the proposed method can be executed efficiently in a reasonable time.

Evaluation of Optimal Network Reliability Under Components-Assignments Subject to a Transmission Budget

This study proposes a genetic algorithm based method integrating the minimal paths and the recursive sum of disjoint products to find maximal network reliability with optimal transmission line assignment for a stochastic electric power network. In our problem, a set of transmission lines is ready to be assigned to branches of the electric power network. Because each transmission line combined with several physical lines has multiple states, the capacity of the electric power network associated with any transmission line assignment is stochastic. Network reliability is the probability that the network can transmit d units of electric power from an electric power generator (origin) to a specific area (destination). The discussed problem exhibits the features of network reliability and assignment problems, and thus it is non-deterministic polynomial-time hard. A simple electric power network and a real one are adopted to demonstrate the efficiency of the proposed algorithm while comparing with several approaches.

Cheng-Ta Yeh

Papers

Multi-objective optimization for stochastic computer networks using NSGA-II and TOPSIS

Evaluation of Optimal Network Reliability Under Components-Assignments Subject to a Transmission Budget

Maximal network reliability with optimal transmission line assignment for stochastic electric power networks via genetic algorithms

Using minimal cuts to optimize network reliability for a stochastic computer network subject to assignment budget

Computer network reliability optimization under double-resource assignments subject to a transmission budget