We present a very simple family of traveling salesman instances with n cities where the nearest neighbor rule may produce a tour that is Θ(log n) times longer than an optimum solution. Our family works for the graphic, the euclidean, and the rectilinear traveling salesman problem at the same time. It improves the so far best known lower bound in the euclidean case and proves for the first time ...

The goal of this paper is to develop a Decision Support System (DSS) as a journey planner in complex and large multimodal urban network called Rahyar. Rahyar attempts to identify the most desirable itinerary among all feasible alternatives. The desirability of an itinerary is measured by a disutility function, which is defined as a weighted sum of some criteria. The weight...

In developing countries, whereas the urban bus network is a major part of public transportation system, it is necessary to try to find the best design and routing for bus network. Optimum design of school bus routes is very important. Non-optimal solutions for this problem may increase traveling time, fuel consumption, and depreciation rate of the fleet. A new bus routing problem is presented i...

the goal of this paper is to develop a decision support system (dss) as a journey planner in complex and large multimodal urban network called rahyar. rahyar attempts to identify the most desirable itinerary among all feasible alternatives. the desirability of an itinerary is measured by a disutility function, which is defined as a weighted sum of some criteria. the weights represent travelers’...

Traveling wave solutions to a class of dispersive models, ut − utxx + uux = θuuxxx + (1− θ)uxuxx, are investigated in terms of the parameter θ, including two integrable equations, the Camassa-Holm equation, θ = 1/3, and the Degasperis-Procesi equation, θ = 1/4, as special models. It was proved in [H. Liu and Z. Yin, Contemporary Mathematics, 2011, 526, pp273–294] that when 1/2 < θ ≤ 1 smooth so...

1. The TPP is of critical importance to Taiwan. Its importance and implications are reflected in three major aspects. First is the economic implication if Taiwan joins (or failed to join) the TPP bandwagon. Second is the implication on domestic reforms, i.e. using TPP as a driving force for Taiwan to undertake reform initiatives. Last but not least is the political implication for Taiwan as a p...

among numerous np-hard problems, the traveling salesman problem (tsp) has been one of the most explored, yet unknown one. even a minor modification changes the problem’s status, calling for a different solution. the generalized traveling salesman problem (gtsp)expands the tsp to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time O(n2·2n) where n is the number of nodes in the graph. The branch-and-cut algorithm has been applied to solve the problem with a large number of nodes. However,...

We report a universal scaling behavior of the first arrival time of a traveling magnetic domain wall into a finite space-time observation window of a magneto-optical microscope enabling direct visualization of a Barkhausen avalanche in real time. The first arrival time of the traveling magnetic domain wall exhibits a nontrivial fluctuation and its statistical distribution is described by univer...