Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.

An Attraction Map Framework of a Complex Multi-Echelon Vehicle Routing Problem with Random Walk Analysis

The paper aims to investigate the basin of attraction map of a complex Vehicle Routing Problem with random walk analysis. The Vehicle Routing Problem (VRP) is a common discrete optimization problem in field of logistics. In the case of the base VRP, the positions of one single depot and many customers (which have product demands) are given. The vehicles and their capacity limits are also fixed in the system and the objective function is the minimization of the length of the route. In the literature, many approaches have appeared to simulate the transportation demands. Most of the approaches are using some kind of metaheuristics. Solving the problems with metaheuristics requires exploring the fitness landscape of the optimization problem. The fitness landscape analysis consists of the investigation of the following elements: the set of the possible states, the fitness function and the neighborhood relationship. We use also metaheuristics are used to perform neighborhood discovery depending on the neighborhood interpretation. In this article, the following neighborhood operators are used for the basin of attraction map: 2-opt, Order Crossover (OX), Partially Matched Crossover (PMX), Cycle Crossover (CX). Based on our test results, the 2-opt and Partially Matched Crossover operators are more efficient than the Order Crossover and Cycle Crossovers.

Random walk analysis of cave maps for exemplary gypsum caves-mazes of Western Ukraine

The paper presents a new method of quantitative parameterization of net geomorphological structures with the use of random walk formalism and an analysis of Hurst exponent distribution derived from random walk experiments. As examples, horizontally developed gypsum caves were elaborated. The provided methodology is able to uniquely characterize cave systems.