Miloš Šeda

A Minimisation of Network Covering Services in a Threshold Distance

In this paper, we deal with a special version of the set covering problem, which consists in finding the minimum number of service centres providing specialized services for all customers (or larger units, such as urban areas) within a reasonable distance given by a threshold. If a suitable threshold is found that makes it possible to determine a feasible solution of the task, the task is transformed into a general set covering problem. However, this has a combinatorial nature and, because it belongs to the class of NP-hard problems, for a large instance of the problem, it cannot be used to find the optimal solution in a reasonable amount of time. In the paper, we present a solution by means of two stochastic heuristic methods - genetic algorithms and simulated annealing – and, using a test instance from OR-Library, we present the parameter settings of both methods and the results achieved.

Multichannel Queueing Systems and Their Simulation

This paper is concerned with multichannel queueing systems showing how to derive their characteristics if the requirement arrivals correspond to a Poisson process and the service times have the exponential distribution. However, the requirements of stationarity, regularity, and independence of increases needed to model these processes by Markov chains and to define the transition probabilities may not be satisfied, or no information may be available on such parameters. Using randomly generated data, we propose a strategy of processing the requirements in multichannel systems and a way of evaluating the probabilities necessary to express the characteristics of the systems comparing these results with the theoretical ones. It has been discovered that with, as the number of outputs increases, the simulation results converge to the theoretical ones.

Combined Heuristic Approach to Resource-Constrained Project Scheduling Problem

This chapter deals with the resource-constrained project scheduling problem that belongs to NP-hard optimisation problems. There are many different heuristic strategies how to shift activities in time when resource requirements exceed their available amounts. We propose a transformation of the problem to a sequence of simpler instances of (multi)knapsack problems that do not use traditionally predefined activity priorities and enable to maximise limited resources in all time intervals given by start or end of an activity and therefore to reduce the total time.

Fuzzy All-Pairs Shortest Paths Problem

In this paper, we deal with the All-Pairs Shortest Paths Problem (APSPP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. Since the fuzzy min operator based on the extension principle leads to nondominated solutions, we propose another approach to solving the APSPP using a suitable fuzzy ranking method. We also show that the efficiency of computations may be improved by the proposed APSPP modification of the Dijkstra algorithm based on a binary heap data structure.

Minimisation Of Network Covering Services With Predefined Centres.

In this paper, we deal with a special version of the set covering problem, which consists in finding the minimum number of service centres providing specialized services for all customers (or larger units, such as urban areas) within a reasonable distance given by a threshold. If a suitable threshold is found that makes it possible to determine a feasible solution of the task, the task is transformed into a general set covering problem. In order to reflect the importance of the centers, we assign weights to them and, if some centers must be contained in the result, we can either add columns in the reachability matrix with link to these centres or add special constraints in the mathematical model. However, this is of a combinatorial nature and, because it belongs to the class of NP-hard problems, for a large instance of the problem, it cannot be used to find the optimal solution in a reasonable amount of time. In the paper, we present a solution that uses two heuristic methods: genetic algorithm and tabu search.

Stochastic Heuristics for Knapsack Problems

In this paper, we introduce knapsack problem formulations, discuss their time complexity and propose their representation and solution based on the instance size. First, deterministic methods are briefly summarized. They can be applied to small-size tasks with a single constraint. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. The problem representations and parameter settings for a genetic algorithm and simulated annealing frameworks are shown.

Models and Simulations of Queueing Systems

In the queueing theory, it is assumed that requirement arrivals correspond to the Poisson process and the service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of the Markov chains and it is possible to derive characteristics of the system. In the paper, these theoretical approaches are presented and focused on systems with several service lines and the FIFO queue when the number of requirements exceeds the number of lines. Finally, it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied.

Evolutionary Optimization of Controllers

The aim of this paper is to describe a new optimization method that can create control equations of general regulators. For this type of optimization a new method was created and we call it Two-Level Transplant Evolution (TLTE). This method allowed us to apply advanced methods of optimization, for example direct tree reducing of tree structure of control equation. The reduction method was named Arithmetic Tree Reducing (ART). For optimization of control equations of general controllers is suitable combine two evolutionary algorithms. Main goal in the first level of TLTE is the optimization of structure of general controllers. In the second level of TLTE the concrete parameters are optimized and the unknown abstract parameters in structure of equations are set. The method TLTE was created by combination of Transplant Evolution method (TE) and Differential Evolution method (DE). The Transplant Evolution (TE) optimizes structure of solution with unknown abstract parameters and the DE optimizes the parameters in this structure. The parameters are real numbers. The real numbers are not easy find directly in TE without DE. For evaluation of quality of found control equation are described new methods, which allow evaluate their quality. It can be used in the case when the simulation of control process cannot be finished. In results are shown some practical application. In all results we received the control equation that reached better quality of control process, than classical PID controllers and Takahashi‘s modification of PID controller.

Graph and Geometric Algorithms and Efficient Data Structures

Many NP-complete optimization problems may be approximately solved by stochastic or deterministic heuristic methods and it is necessary to find their efficient data representation to minimize iteration computational time. In this chapter, we will touch the Minimum Steiner Tree Problems in Graphs (or Network Steiner Tree Problem), which can be solved by heuristics based on the Minimum Spanning Tree Problem and/or the Shortest Path Problem using a binary heap that enables to implement a priority queue that substantially increases the algorithm efficiency. We will also show a Delaunay triangulation-based way of finding minimal networks connecting a set of given points in the Euclidean plane using straight lines (minimum spanning tree) and its more general case (Steiner minimum tree) where additional points can be considered. Finally, we will deal with visibility graphs, Voronoi diagrams and rapidly exploring trees and focus on their applications in robot motion planning, where the robot should pass around obstacles from a given starting position to a given target position, touching none of them.

Two-Level Transplant Evolution for optimization of controllers

This paper describes the application of Two-Level Transplant Evolution (TE) that can evolve control programs using a variable length linear genome to govern the mapping of a Backus Naur Form grammar definition. TE combines Grammatical Evolution (on the genotype level) with Genetic Programming (tree structures on the phenotype level). To increase the efficiency of Transplant Evolution (TE) the parallel Differential Evolution was added.