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Some Approximation Algorithms for Minimum Vertex Cover in a Hypergraph

The paper presents five algorithms for minimum vertex cover in a hypergraph. We consider: exact-backtracking, LJC, SBT, RSBT and MSBT algorithms. For a set of randomly generated hypergraphs tests have been performed to compare the aforementioned procedures.

Evolutionary Method in Grouping of Units

This paper deals with the clustering problem, where an order of elements plays a pivotal role. This formulation is very usable for wide range of Decision Support System (DSS) applications. The proposed clustering method consists of two stages. The first is a stage of data matrix reorganization, using a specialized evolutionary algorithm. The second stage is a final clustering step and is performed using a simple clustering method.

Solving the k-centre problem as a method for supporting the Park and Ride facilities location decision

In this article we analyze the problem of optimal location of transportation hubs in Warsaw, namely the Park and Ride location problem (P&RP).We take into account the expected travel time using public transport between particular points of the trip. In the currently existing P&R system we have 14 hub locations, and in this case the maximum travel time exceeds 50 minutes. The P&R problem can be reduced to the centers location problem (in our particular approach - the dominating set problem, DS), which is an NP hard problem. In order to determine the optimal locations for P&R two methods: the greedy and the tabu search algorithms were chosen and implemented. According to the computational experiments for the travel time restriction to 50 minutes, we obtain the DS composed of 3 hubs, in contrast to the existing 14 elements. The analysis of the P&R location in time domain is presented in this article in the context of further development of the Warsaw public transportation network, which seems to be interesting.

Graph based approach to the minimum hub problem in transportation network

In this paper we consider a hub location problem in a real multimodal public transportation network. This problem is also known as the park-and-ride problem. Hubs stations are special facilities that serve as switches in such a network. In practice the set of hubs has a strategic importance, because all of the traffic that passes through the network can be controlled by these elements. From the theoretical point of view, the minimal hub problem is NP hard. Two different approaches to this problem are presented. The first group of methods bases on the greedy algorithms. In the second group the evolutionary strategy is used. The computational results for these algorithms proved a significant efficiency, what can be clearly expressed in terms of an input data reduction and also in quality measure values for the obtained solutions of this problem.

The Kernel and Shell Structure as a Tool for Improving the Graph of Transportation Connections

A model of a transportation system is expected to be useful in simulations of a real system to solve given transportation tasks. A connection graph is routinely used to describe a transportation system. Vertices can be train stations, bus stops, airports etc. The edges show direct connections between vertices. A direct approach can be difficult and computational problems can arise in attempts to organize or optimize such a transportation system. Therefore, a method for aggregating such graphs was introduced, using a general kernel and shell structure and its particular instances: i i-clique structured graphs of connections and a hub and spoke transformation of the source graph. These structures enable the concentration and ordering of transport between vertices and reduction of the analyzed graph. To obtain the desired structures, several versions of a specialized evolutionary algorithm were developed and applied.

Machine-part grouping in flexible manufacturing:Formalisation and the use of genetic algorithms

Abstract The classical machine-part grouping problem of flexible manufacturing is considered. Against the background of the multiplicity of the “general” forms of the objective functions, pertinent to the problem, on the one hand, and of the specific problem formulations, requiring highly specialized methods and techniques for their treatment it is argued that the use of simple, generic approaches, which are at the same time flexible, is advisable. The primary issue is in adaptability to a definite problem formulation and the possibility of constraint verification. A discussion is presented of certain basic precepts of the objective function formulation. This is followed by an example of application of the effective genetic algorithm to the specific case of the bond-energy-based objective function. The genetic algorithm applied features not only effectiveness, but also high adaptability from application of evolving set of operators.

A Hybrid Approach to a Classification Problem

In this paper we present an applications of the argument reduction algorithm as a preprocessing method of decision tables for classifier system. The software tool for classification problem is described. This tool has a hybrid structure consists of proposed reduction strategies mixed with the classical decision rules generator based on genetic algorithms. This tool achieves significant benefits from argument reduction during analysis process of data dependencies.