We present a genetic algorithm for solving the traveling salesman problem by genetic algorithms to optimality for traveling salesman problems with up to 442 cities. Mlihlenbein et al. [MGK 88], [MK 89] have proposed a genetic algorithm for the traveling salesman problem, which generates very good but not optimal solutions for traveling salesman problems with 442 and 531 cities. We have improved...

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to th...

Traveling Waves in a Suspension Bridge System by Robert A. Ain, Jr. Dr. Zhonghai Ding, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas In this thesis, we study the traveling waves in a Lazer-McKenna suspension bridge system which is governed by two coupled nonlinear beam and wave equations. The Lazer-McKenna suspension bridge system describes the v...

The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...

This paper is concerned with the traveling wave solutions of delayed reaction– diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To i...

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ε (ε > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ε: for small ε the behaviour is essentially the same as f...

In the single objective period traveling salesman problem (SOPTSP), each of given n cities has to be visited by the traveling salesman a fixed number of times according to some allowable day combinations over a given m day planning period with the objective to minimize the total traveling distance over the whole period. The existing solution methods for the SOPTSP always generate a set of unbal...

The spatial and temporal periodicity of somite formation is controlled by the segmentation clock, in which numerous cells cyclically express hairy-related transcriptional repressors with a posterior-to-anterior phase delay, creating 'traveling waves' of her1 expression. In zebrafish, the first traveling wave buds off from the synchronous oscillation zone in the blastoderm margin. Here we show t...

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of ...