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Most of the time, people experience difficulty in identifying the best shortest paths to reach their destination while travelling. This becomes the main motive to research the shortest path identification problem. In this work, an undirected network is considered for the research evaluation of the proposed method. Previously, various types of techniques have been developed by many researchers for this shortest path issue in a networking environment. However, most of them exhibit computational complexity issues when updating their weights for every iteration. Based on this observation, the proposed work plans to solve SPP (Shortest Path Problem) in an undirected network using Fuzzy Dijkstra's approach based on improved WSM (Weighted Sum Method) with heuristic optimization. Here, the weight updating process of WSM is optimized by Sea Lion Optimization approach in order to improve the working performance of WSM while combining with Fuzzy Dijkstra method. The proposed concept is evaluated in MATLAB, and the performance evaluation is done using time consumption, energy utilization, network lifetime and prediction accuracy by comparing it with Dijkstra, Fuzzy-MPSO and WSDA methods. [ABSTRACT FROM AUTHOR]

Smart surface is a new conveying technology composed of a 2D planar surface presenting a matrix of distributed autonomous blocks. Every block contains a micro-electro-mechanical system (MEMS) actuator that controls the transfer of a possible object located above the block to the neighboring blocks, using air-jet forces. The spatial characteristics of the blocks impose some limits on the memory, energy and computation capabilities of the MEMS blocks. On the other hand, the system can reach several thousands of blocks making necessary to propose scalable algorithmic solutions. This paper studies different distributed algorithms to convey an object from an initial to a target position in the smart surface. The conveying policy emphasizes the long term use of the smart surface and the objects conveying efficiency measured by the time of the transfer. The problem stands as an original case of multi-objective Shortest Path problem (MOSP). Original because the quality of a given path is not evaluated by the sum of the weights of its segments, and because the segment weights change according to the used paths as provided by the algorithm itself. Therefore, the efficiency of a given algorithm is assessed on the basis of its performance during a long period of time. We describe here the best way to combine these two objectives and we propose a scalable incremental distributed protocol for objects conveying. The path optimality is adjusted according to the required calculation complexity. The performances of the different algorithmic and modeling variations are analyzed in terms of memory, time, computation and exchanged messages complexity. The obtained results prove the scalability of the algorithm, with linear computational, memory and convergence time complexity, and confirm the improvement of smart surface usage compared to a naive approach. The system lifespan increases of up to 130% on 40 × 40 smart surface, while the transfer cost (time and energy) is reduced. We show also that the computation time of the path with the incremental algorithm can be significantly reduced without significant degradation of the conveying system performance. For example, in a 40 × 40 smart surface, the number of messages is divided by 4 while the number of conveyed objects is only reduced by a ratio of 4%. • The smartsurface is new distributed conveying plateform • The smarsurface allows the manipulation and the transportation of fragile and tiny objects. • The distributed architecture ensures the modularity and maintainability of the system. • The smartsurface conveying problem is an original problem. • The conveying algorithm manages the tradeoff between the transfer time and the surface lifespan. • The computational complexity of the algorithm is less than O (m) • The algorithm convergence is reached with a time complexity of O (m). [ABSTRACT FROM AUTHOR]

We study two variants of the shortest path problem. Given an integer k , the k -color-constrained and the k -interchange-constrained shortest path problems, respectively, seek a shortest path that uses no more than k colors and one that makes no more than k − 1 alternations of colors. We show that the former problem is NP-hard, when the latter is tractable. The study of these problems is motivated by some limitations in the use of diameter-based metrics to evaluate the topological structure of transit networks. We notably show that indicators such as the diameter or directness of a transit network fail to adequately account for travel convenience in measuring the connectivity of a network and propose a new network indicator, based on solving the k -interchange-constrained shortest path problem, that aims at alleviating these limitations. [ABSTRACT FROM AUTHOR]

Abstract: We study new decision and optimization problems of finding a simple path between two given vertices in an arc weighted directed multigraph such that the path length is equal to a given number or it does not fall into the given forbidden intervals (gaps). A fairly complete computational complexity classification is provided and exact and approximation algorithms are suggested. [ABSTRACT FROM AUTHOR]

We introduce Shortest Connection Game , a two-player game played on a directed graph with edge costs. Given two designated vertices in which the players start, the players take turns in choosing edges emanating from the vertex they are currently located at. This way, each of the players forms a path that origins from its respective starting vertex. The game ends as soon as the two paths meet, i.e., a connection between the players is established. Each player has to carry the cost of its chosen edges and thus aims at minimizing its own total cost. In this work we analyse the computational complexity of Shortest Connection Game . On the negative side, Shortest Connection Game turns out to be computationally hard even on restricted graph classes such as bipartite, acyclic and cactus graphs. On the positive side, we can give a polynomial time algorithm for cactus graphs when the game is restricted to simple paths. [ABSTRACT FROM AUTHOR]

Intelligent Transportation Systems (ITS) are defined as those systems utilizing synergistic technologies and systems engineering concepts to develop and improve transportation systems. In this paper, a novel route selection problem based on the envisaged driving mode with dynamic signals in ITS is proposed. It belongs to a kind of the shortest path problem of dynamic weight-varying networks, and the arc-weights of the network vary with the arc-chosen, so it cannot be solved by the existing greedy algorithms. According to the characteristics of the proposed problem, firstly, a dynamic programming model for the driving mode on a single path is established. Secondly, two algorithms for solving the route selection problem based on the former mode are developed. One is a brute-force algorithm based on matrix expansion with the computational complexity ofO (Nt × n²). The other is an improved adaptive ant colony algorithm with the complexity ofO (Nc × m × n²). Finally, the computational experiments show the advantages and disadvantages of the two effective algorithms with numerical examples. [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]

In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns in deciding in each vertex which edge to traverse next. The decider in each vertex also has to pay the cost of the chosen edge. We want to determine the path where each player minimizes its costs taking into account that also the other player acts in a selfish and rational way. Such a solution is a subgame perfect equilibrium and can be determined by backward induction in the game tree of the associated finite game in extensive form. We show that the decision problem associated with such a path is PSPACE-complete even for bipartite graphs both for the directed and the undirected version. The latter result is a surprising deviation from the complexity status of the closely related game Geography . On the other hand, we can give polynomial time algorithms for directed acyclic graphs and for cactus graphs even in the undirected case. The latter is based on a decomposition of the graph into components and their resolution by a number of fairly involved dynamic programming arrays. Finally, we give some arguments about closing the gap of the complexity status for graphs of bounded treewidth. [ABSTRACT FROM AUTHOR]

• An auxiliary algorithm is proposed to construct initial stage of the MCDM methods. • A multi-objective fuzzy optimization model is formulated. • An extensive comparative analysis is conducted in terms of the addressed methods. • The stability and validity of the results are tested and discussed. • Key findings and managerial insights are provided. This paper examines the performances of the multi-criteria decision-making (MCDM) methods and optimization model in solving multi-attribute shortest path problems such as the safest shortest path under a fuzzy environment. To the best of the knowledge of the authors, this is the first study performing comparative analysis on finding the multi-attribute shortest path by employing well-known techniques in terms of computational effort and results in a fuzzy environment. To this end, the safest shortest path problem, where the risk and distance values concerning arcs on a directed network are defined as triangular fuzzy numbers, is handled. The solution process is carried out under two main headings: (i) To start the solution with MCDM methods, an auxiliary algorithm that constructs a fuzzy decision matrix is proposed. Then, Fuzzy-Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS), Fuzzy Simple Additive Weighting (F-SAW), and Fuzzy Evaluation Based on Distance from Average Solution (F-EDAS), that are fuzzy-based MCDM methods, are employed to rank the alternative paths. (ii) A multi-objective fuzzy optimization model is formulated, and the most reasonable paths are obtained considering different α-cut levels. Following that, comparative analysis is performed through a set of scenarios considering the different weights of the criteria to see the variability in the rankings. Besides, the addressed fuzzy-based MCDM methods are compared in terms of computational complexity. Overall, the main findings and managerial insights regarding the effectiveness and performance of the methods discussed in the solution process are provided. [ABSTRACT FROM AUTHOR]

Abstract: A supply chain network design needs to consider the future probability of reconfiguration due to some problems of disaster or price changes. The objective of this article is to design a reconfigurable supply chain network by optimizing inventory allocation and transportation routing. A two-stage programming is composed according to Benders decomposition by allocating inventory in advance and anticipating the changes of transportation routings; thus the transportation routing is stochastic in nature. In addition, the fuzzy shortest path is developed to solve the problem complexity in terms of the multi-criteria of lead time and capacity with an efficient computational method. The results and analysis indicate that the proposed two-stage programming with fuzzy shortest path surpasses the performance of shortest path problem with time windows and capacity constraint (SPPTWCC) in terms of less computational time and CPU memory consumption. Finally, management decision-making is discussed among other concluding remarks. [Copyright &y& Elsevier]

We consider a time-dependent network with a continuous-time variable, in which time constraints are imposed both on the arrival times and on the waiting times at the nodes. Under certain continuity assumptions, we prove the existence of optimal paths, and we show that the optimal value function is lower-semicontinuous. We present an exact solution algorithm, which computes both the optimal value function and the corresponding optimal paths. This algorithm is based on a Dijkstra-like interpretation of a decreasing order of time algorithm, which allows the generalization of this method to a heuristic search algorithm. Moreover, we present an approximation procedure for the computation of the optimal value function and the corresponding optimal paths in a time-dependent first-in first-out (FIFO) network. This method allows for the iterative construction of paths of monotone decreasing cost, starting from a path that is computable in polynomial time. We prove the correctness and termination of both algorithms. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013 [ABSTRACT FROM AUTHOR]

In this study, we introduce a Fuzzy Time-Dependent Network (FTDN) and analyze its shortest path problem. The FTDN is a network in which travel times are represented as fuzzy sets and are also time-dependent. Under these circumstances, the shortest path problem on the FTDN is far more complex in comparison with the shortest path problem on the existing networks. To highlight the complexity, we show that on the FTDN, "standard" shortest path algorithms (e.g., the well-known Dijkstra algorithm) are not able to come up with solutions. Subsequently, we construct a suitable method which is suitable to deal with the shortest problem. A fuzzy programming model is presented for finding the shortest path on the FTDN. The proposed model is handled through the techniques which combine mechanisms of fuzzy simulation and genetic optimization. In this particular setting, fuzzy simulation is exploited to estimate the value of uncertain functions, which do not exist in the general networks. The proposed model is evaluated with the use of numerical experimentation. A comparative analysis demonstrates that the proposed model leads to the shortest path while standard algorithms are not capable of finding the path when dealing with the shortest path problem on the FTDN. [ABSTRACT FROM AUTHOR]

We present a novel approach for reducing the computational complexity of updating homologies produced by a wide class of popular state-of-the-art algorithms in comparative computational biology. The algorithms that we consider use hidden Markov models (HMMs) and a Viterbi recursion to evaluate matches between sequences, or between a sequence and models. Such updates occur frequently in practice as researchers discover errors in biological sequences or analyze multiple nearly similar sequences, e.g., in a family of proteins that underwent mutations during evolution. The proposed algorithm interprets the Viterbi recursion as an update of an optimal minimum spanning tree in a shortest path problem. We propose the novel concept of a relative node tolerance bound and show how it can be used to guarantee that one or more partial subtrees of a minimum spanning tree obtained before encountering the perturbations remain optimal. We also describe how to compute and use in real-time the relative node tolerance bounds to skip most unperturbed parts of a sequence while computing the new optimal solution. To further reduce the computational overhead associated with the tolerance bound evaluation, we present and exploit a statistical analysis of the matching procedure that estimates how many columns in the dynamic program that corresponds to the matching problem are affected by a change in a preceding column. The resulting "reusable" Viterbi decoding algorithm can update a matching result in less than a third to a fifth of the time required to compute a new match by performing a normal matching procedure, i.e., running a Viterbi algorithm with updated sequences against a base hidden Markov model. [ABSTRACT FROM PUBLISHER]

This paper presents a new maximum likelihood (ML) symbol detection algorithm for multiple-input multiple-output (MIMO) systems. To achieve the ML performance with low complexity, we search the integer points corresponding to symbol vectors in increasing order of the distance from the unconstrained least-squares solution. For each integer point, we test if it is the ML solution, and continue the integer point search until one of searched points is determined to be the ML solution. We present an efficient iterative search strategy, which is based on the shortest path algorithm for a graph. The simulation results show that the proposed algorithm has the lower complexity compared to the sphere decoding for channel matrices having low condition numbers. For further complexity reduction, we propose to use scaling, lattice-reduction, and regularization techniques. By applying these techniques, the computational complexity of proposed algorithm is reduced significantly when the channel matrix has a high condition number. [ABSTRACT FROM AUTHOR]

This paper solves the online obstacle avoidance problem using the Hamilton-Jacobi-Bellman (HJB) theory. Formulating the shortest path problem as a time optimal control problem, the shortest paths are generated by following the negative gradient of the return function, which is the solution of the HJB equation. To account for multiple obstacles, we avoid obstacles optimally one at a time. This is equivalent to following the pseudo-return function, which is an approximation of the true return function for the multi-obstacle problem. Paths generated by this method are near-optimal and guaranteed to reach the goal, at which the pseudo-return function is shown to have a unique minimum. The proposed method is computationally very efficient, and applicable for online applications. Examples for circular obstacles demonstrate the advantages of the proposed approach over traditional path planning methods. [ABSTRACT FROM PUBLISHER]