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A number of problems in several areas such as power transmission and distribution, communication and transportation can be formulated as a stochastic-flow network (SFN). The system reliability of an SFN can be computed in terms of all the upper boundary points, called d-MinCuts (d-MCs). Several algorithms have been proposed to find all the d-MCs in an SFN. Here, some recent studies in the literature on search for all d-MCs are investigated. We show that some existing results and the corresponding algorithms are incorrect. Then, correct versions of the results are established. By modifying an incorrect algorithm, we also propose an improved algorithm. In addition, complexity results on a number of studies are shown to be erroneous and correct counts are provided. Finally, we present comparative numerical results in the sense of performance profile of Dolan and Moré showing the proposed algorithm to be more efficient than some existing algorithms.

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We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is developed. The proposed method of cuts generation, separation and strengthening is compared to the Gomory, linear branching and coordinated cutting plane methods. The computational results show that the proposed method is promising but becomes complicated as number of variables increases.

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Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capacity inverse problem under the bottleneck-type and the sum-type weighted Hamming distances. In the bottleneck-type case, the binary search technique is applied to present an algorithm for solving the problem in O(nm log n) time. In the sum-type case, it is shown that the inverse problem is strongly NP-hard even on bipartite networks

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The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start algorithm that in each iteration constructs a randomized greedy solution and applies local search to it. Path-relinking stores elite solutions and to find better solutions explores the paths between different solutions. Experimental results show the performance of our algorithm on many benchmark problems compared to the other algorithms.

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First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory can be modeled and solved by an integer programming model and a metaheuristic approach.

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In an uncapacitated facility location problem, the aim is to find the best locations for facilities on a specific network in order to service the existing clients at the maximum total profit or minimum cost. In this paper, we investigate the uncapacitated facility location problem where the profits of the demands and the opening costs of the facilities are uncertain values. We first present the belief degree-constrained, expected value and tail value at risk programming models of the problem under investigation. Then, we apply the concepts of the uncertainty theory to transform these uncertain programs into the corresponding deterministic optimization models. The efficient algorithms
are provided for deriving the optimal solutions the problem under investigation.

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This paper considers the progressively Type-II censoring and determines the optimal sample size using a Bayesian prediction approach. To this end, two criteria, namely the Bayes risk function of the point predictor for a future progressively censored order statistic and the designing cost of the experiment are considered. In the Bayesian prediction, the general entropy loss function is applied. We find the optimal sample size such that the Bayes risk function and the cost of the experiment do not exceed two pre-fixed values. To show the usefulness of the results, some numerical computations are presented.