The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Corresp...

Vehicle routing is an area of both practical and theoretical importance. Unfortunately, routing problems are notably difficult to solve since almost all vehicle routing problems are NP-hard. However, we have discovered that when reduced to its simplest form, solving a single vehicle routing problem, without capacity and time window constraints is quite similar to the Traveling Salesman Problem ...

We study the following problem on recon guring shortest paths in graphs: Given two shortest st paths, what is the minimum number of steps required to transform one into the other, where each intermediate path must also be a shortest s-t path and must di er from the previous one by only one vertex. We prove that the shortest recon guration sequence can be exponential in the size of the graph and...

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity ; and there are many other examples. Besides reviewing the path convexities in the literature, ...

In real-world optimization problems, effective path planning is important. The Shortest Path Problem (SPP) model a classical operations research that can be applied to determine an efficient from the starting point end in plan. However, real world, uncertainty often encountered and must faced. Significant factors problem of determining shortest are problems difficult predict, therefore new crit...

Several methods exist for routing messages in a network without using complete routing tables (compact routing). In k-interval routing schemes (k-IRS), links carry up to k intervals each. A message is routed over a certain link if its destination belongs to one of the intervals of the link. We present some results for the necessary value of k in order to achieve shortest-path routing. Even thou...

The most important field of robotics study is path planning. Path planning problem in general an NP-complete problem. Though several attempts have been made using A*, PRM, RRT, and RRT* these algorithms explore too many nodes the state space, not completely captured kinematic constraints, are optimal real-time. In this paper, a Multi-Objective Hybrid Collision- free Optimal Finder (MOHC-OPF) pr...

We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria, from given sequences of displacements, can be solved in polynomial time. The problem is relevant for efficient compiler and library support for communication of non-contiguous data, where tree-structured descriptions with low-degree nodes and small inde...

We consider the problem of computing shortest paths subject to an additional resource constraint such as a hard limit on the (positive) height difference of the path. This is typically of interest in the context of bicycle route planning, or when energy consumption is to be limited. So far, the exact computation of such constrained shortest paths was not feasible on large networks; we show that...