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Nuclear Magnetic Resonance (NMR) Spectroscopy is the second most used technique (after X-ray crystallography) for structural determination of proteins. A computational challenge in this technique involves solving a discrete optimization problem that assigns the resonance frequency to each atom in the protein. This paper introduces LIAN (LInear programming Assignment for NMR), a novel linear programming formulation of the problem which yields state-of-the-art results in simulated and experimental datasets. [ABSTRACT FROM AUTHOR]

An elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm. [ABSTRACT FROM AUTHOR]

In recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm. [ABSTRACT FROM AUTHOR]

The shortest path problem (SPP) is a special network structured linear programming problem that appears in a wide range of applications. Classical SPPs consider only one objective in the networks while some or all of the multiple, conflicting and incommensurate objectives such as optimization of cost, profit, time, distance, risk, and quality of service may arise together in real-world applications. These types of SPPs are known as the multi-objective shortest path problem (MOSPP) and can be solved with the existing various approaches. This paper develops a Data Envelopment Analysis (DEA)-based approach to solve the MOSPP with fuzzy parameters (FMOSPP) to account for real situations where input–output data include uncertainty of triangular membership form. This approach to make a connection between the MOSPP and DEA is more flexible to deal with real practical applications. To this end, each arc in a FMOSPP is considered as a decision-making unit with multiple fuzzy inputs and outputs. Then two fuzzy efficiency scores are obtained corresponding to each arc. These fuzzy efficiency scores are combined to define a unique fuzzy relative efficiency. Hence, the FMOSPP is converted into a single objective Fuzzy Shortest Path Problem (FSPP) that can be solved using existing FSPP algorithms. [ABSTRACT FROM AUTHOR]

The shortest path problem (SPP) is an optimization problem of determining a path between specified source vertex s and destination vertex t in a fuzzy network. Fuzzy logic can handle the uncertainties, associated with the information of any real life problem, where conventional mathematical models may fail to reveal proper result. In classical SPP, real numbers are used to represent the arc length of the network. However, the uncertainties related with the linguistic description of arc length in SPP are not properly represented by real number. We need to address two main matters in SPP with fuzzy arc lengths. The first matter is how to calculate the path length using fuzzy addition operation and the second matter is how to compare the two different path lengths denoted by fuzzy parameter. We use the graded mean integration technique of triangular fuzzy numbers to solve this two problems. A common heuristic algorithm to solve the SPP is the genetic algorithm. In this manuscript, we have introduced an algorithmic method based on genetic algorithm for determining the shortest path between a source vertex s and destination vertex t in a fuzzy graph with fuzzy arc lengths in SPP. A new crossover and mutation is introduced to solve this SPP. We also describe the QoS routing problem in a wireless ad hoc network. [ABSTRACT FROM AUTHOR]

This paper considers a shortest path problem in an imprecise and random environment. The edges in the network represent the approximate time required to cover the distance from one vertex to another vertex while the traffic conditions change randomly for each edge. The approximate time has been defined by using trapezoidal fuzzy number whereas the traffic conditions has been defined in linguistic term. Such type of network problem can be called as Fuzzy Stochastic Shortest Path Problem (FSSPP) in imprecise and random environment. In order to solve the model, a method has been proposed based on the Dijkstra’s algorithm and some numerous example have been solved to present its effectiveness. [ABSTRACT FROM AUTHOR]

In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment. [ABSTRACT FROM AUTHOR]

An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections. In this contribution, we consider SPP through Bellman's algorithm for a network using interval-valued neutrosophic numbers (IVNNs). We proposed a novel algorithm to obtain the neutrosophic shortest path between each pair of nodes. Length of all the edges is accredited an IVNN. Moreover, for the validation of the proposed algorithm, a numerical example has been offered. Also, a comparative analysis has been done with the existing methods which exhibit the advantages of the new algorithm. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set as an extension of fuzzy set has been presented to handle the uncertainty in real-world decision-making problems. In this work, we formulate a shortest path (SP) problem in an interval-valued Pythagorean fuzzy environment. Here, the costs related to arcs are taken in the form of interval-valued Pythagorean fuzzy numbers (IVPFNs). The main contributions of this paper are fourfold: (1) the interval-valued Pythagorean fuzzy optimality conditions in directed networks are described to design of solution algorithm. (2) To do this, an improved score function is used to compare the costs between different paths with their arc costs represented by IVPFNs. (3) Based on these optimality conditions and the improved score function, the traditional Dijkstra algorithm is extended to find the cost of interval-valued Pythagorean fuzzy SP (IVPFSP) and corresponding IVPFSP. (4) Finally, a small sized telecommunication network is provided to illustrate the potential application of the proposed method. [ABSTRACT FROM AUTHOR]

In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to approximate the PCM with a consistent one. One of the approaches is to minimize the distance between the matrices, most often the Euclidean distance. In the paper we consider the problem of minimizing the maximum distance. After applying the logarithmic transformation we are able to formulate the obtained subproblem as a Shortest Path Problem and solve it more efficiently. We analyze the structure of the set of optimal solutions and prove some of its properties. This allows us to provide an iterative algorithm that results in a unique, Pareto-efficient solution. [ABSTRACT FROM AUTHOR]

Network routing problems are often modeled with the assumption that the network structure is deterministic, though they are often subject to uncertainty in many real-life scenarios. In this paper, we study the traveling salesman and the shortest path problems with uncertain topologies modeled by arc failures. We present the formulations that incorporate chance constraints to ensure reliability of the selected route considering all arc failure scenarios. Due to the computational complexity and large scales of these stochastic network optimization problems, we consider two cutting plane methods and a Benders decomposition algorithm to respectively solve them. We also consider to solve the reformulations of the problems obtained by taking the logarithm transformation of the chance constraints. Numerical experiments are performed to obtain results for comparisons among these proposed methods. [ABSTRACT FROM AUTHOR]

The goal of meta-heuristic algorithms such as genetic algorithm is to explore the search space of the combinatorial optimization problems efficiently to locate the optimal solutions, the feasible solutions with the best output values. However, typical meta-heuristic algorithms implicitly assume that the feasible solutions for the given problems can be generated easily, and they can fail to solve the problems with rare feasible solutions in effective manner. In this context, this paper aims to introduce the maze-type shortest path problem as an example of the combinatorial optimization problem with rare feasible solutions and to propose the fitness switching genetic algorithm for solving it. The maze-type shortest path problem is characterized by the maze-type network that contains many dead-ends, and the conventional genetic algorithms based on the population of feasible paths are not appropriate for finding the optimal path in such networks. On the contrary, this paper introduces the fitness switching and fitness leveling operations for maintaining the population of both feasible and infeasible paths during the search procedure. In addition, the infeasible paths are randomly modified by the simple local search of the proposed algorithm to find the feasible paths more quickly. The experiment results show that the proposed algorithm can address the issues in the combinatorial optimization problems with rare feasible solutions very effectively. [ABSTRACT FROM AUTHOR]

This paper addresses a scheduling problem in a flexible supply chain, in which the jobs can be either processed in house, or outsourced to a third-party supplier. The goal is to minimize the sum of holding and delivery costs. This problem is proved to be strongly $\mathcal{NP}$-hard. Consider two special cases, in which the jobs have identical processing times. For the problem with limited outsourcing budgets, a $\mathcal{NP}$-hardness proof, a pseudo-polynomial algorithm and a fully polynomial time approximation scheme are presented. For the problem with unlimited outsourcing budgets, the problem is shown to be equivalent to the shortest path problem, and therefore it is in class $\mathcal{P}$. This shortest-path-problem solution approach is further shown to be applicable to a similar but more applicable problem, in which the number of deliveries is upper bounded. [ABSTRACT FROM AUTHOR]

In optimization, it is common to deal with uncertain and inaccurate factors which make it difficult to assign a single value to each parameter in the model. It may be more suitable to assign a set of values to each uncertain parameter. A scenario is defined as a realization of the uncertain parameters. In this context, a robust solution has to be as good as possible on a majority of scenarios and never be too bad. Such characterization admits numerous possible interpretations and therefore gives rise to various approaches of robustness. These approaches differ from each other depending on models used to represent uncertain factors, on methodology used to measure robustness, and finally on analysis and design of solution methods. In this paper, we focus on the application of a recent criterion for the shortest path problem with uncertain arc lengths. We first present two usual uncertainty models: the interval model and the discrete scenario set model. For each model, we then apply a criterion, called bw-robustness (originally proposed by B. Roy) which defines a new measure of robustness. According to each uncertainty model, we propose a formulation in terms of large scale integer linear program. Furthermore, we analyze the theoretical complexity of the resulting problems. Our computational experiments perform on a set of large scale graphs. By observing the results, we can conclude that the approved solvers, e.g. Cplex, are able to solve the mathematical models proposed which are promising for robustness analysis. In the end, we show that our formulations can be applied to the general linear program in which the objective function includes uncertain coefficients. [ABSTRACT FROM AUTHOR]

In real road networks, the presence of no-left, no-right or no U-turn signs, restricts the movement of vehicles at intersections. These turn prohibitions must be considered when calculating the shortest path between a starting and an ending point in a road network. We propose an extension of Dijkstra’s algorithm to solve the shortest path problem with turn prohibitions. The method uses arc labeling and a network structure with low memory requirements. We compare the proposed method with the dual graph approach in a set of randomly generated networks and Bogotá’s large-scale road network. Our computational experiments show that the performance of the proposed method is better than that of the dual graph approach, both in terms of computing time and memory requirements. We co-developed a Web-based decision support system for computing shortest paths with turn prohibitions that uses the proposed method as the core engine. [ABSTRACT FROM AUTHOR]

Due to various accidents and crime threats to an unspecified number of people, many surveillance technologies have been studied as an interest in individual security continues to increase throughout society. In particular, intelligent video surveillance technology is one of the most active research areas in the field of surveillance; this popularity has been spurred by recent advances in computer vision/image processing and machine learning. The main goal is to automatically detect, recognize, and analyze objects of interest from collected sensor information and then efficiently extract/utilize this useful information, such as by detecting abnormal events or intruders and recognizing objects. Anomalous event detection is a key component of security, and many existing anomaly detection algorithms rely on a foreground subtraction process to detect changes in the foreground scene. By comparing input image frames with a reference image, changed areas of the image can be efficiently detected. However, this technique can be insensitive to static changes and has difficulties in noisy environments since it depends on a reference image. We propose a new strategy for improved dynamic/static change detection that complements the weak points of existing detection methods, which have low robustness in noisy environments. To achieve this goal, we employed a self-organizing map (SOM) for data clustering and regarded the cluster distribution of neurons, represented by the weight of the optimized SOM, as a directed graph problem. We then applied the shortest path algorithm to recognize anomalous events. The real-time monitoring capability of the proposed change detection system was verified by applying it to self-produced test data and the CDnet-2014 dataset. This system showed robustness against noise that was superior to other surveillance systems in various environments. [ABSTRACT FROM AUTHOR]