Abstract: This paper summarizes and compares approaches to
solving the knapsack problem and its known application in capital
budgeting. The first approach uses deterministic methods and can be
applied to small-size tasks with a single constraint. We can also
apply commercial software systems such as the GAMS modelling
system. 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. We show the problem representation and
parameter settings for a genetic algorithm framework.
Abstract: In practice, we often come across situations where it is
necessary to make decisions based on incomplete or uncertain data.
In control systems it may be due to the unknown exact mathematical
model, or its excessive complexity (e.g. nonlinearity) when it is
necessary to simplify it, respectively, to solve it using a rule base. In
the case of databases, searching data we compare a similarity
measure with of the requirements of the selection with stored data,
where both the select query and the data itself may contain vague
terms, for example in the form of linguistic qualifiers. In this paper,
we focus on the processing of uncertain data in databases and
demonstrate it on the example multi-criteria decision making in the
selection of variants, specified by higher number of technical
parameters.
Abstract: In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.
Abstract: In this paper, we deal with the Steiner tree problem
(STP) on a graph in which a fuzzy number, instead of a real number,
is assigned to each edge. We propose a modification of the shortest
paths approximation based on the fuzzy shortest paths (FSP)
evaluations. Since a fuzzy min operation using the extension
principle leads to nondominated solutions, we propose another
approach to solving the FSP using Cheng's centroid point fuzzy
ranking method.
Abstract: Finding the shortest path between two positions is a
fundamental problem in transportation, routing, and communications
applications. In robot motion planning, the robot should pass around
the obstacles touching none of them, i.e. the goal is to find a
collision-free path from a starting to a target position. This task has
many specific formulations depending on the shape of obstacles,
allowable directions of movements, knowledge of the scene, etc.
Research of path planning has yielded many fundamentally different
approaches to its solution, mainly based on various decomposition
and roadmap methods. In this paper, we show a possible use of
visibility graphs in point-to-point motion planning in the Euclidean
plane and an alternative approach using Voronoi diagrams that
decreases the probability of collisions with obstacles. The second
application area, investigated here, is focused on problems of finding
minimal networks connecting a set of given points in the plane using
either only straight connections between pairs of points (minimum
spanning tree) or allowing the addition of auxiliary points to the set
to obtain shorter spanning networks (minimum Steiner tree).
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Abstract: Resource-constrained project scheduling is an NPhard
optimisation problem. There are many different heuristic
strategies how to shift activities in time when resource requirements
exceed their available amounts. These strategies are frequently based
on priorities of activities. In this paper, we assume that a suitable
heuristic has been chosen to decide which activities should be
performed immediately and which should be postponed and
investigate the resource-constrained project scheduling problem
(RCPSP) from the implementation point of view. We propose an
efficient routine that, instead of shifting the activities, extends their
duration. It makes it possible to break down their duration into active
and sleeping subintervals. Then we can apply the classical Critical
Path Method that needs only polynomial running time. This
algorithm can simply be adapted for multiproject scheduling with
limited resources.
Abstract: Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the Quine-McCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the Quine-McCluskey method and show that it represents a set covering problem that, unfortunately, is an NP-hard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings.
Abstract: In this paper, we focus on the use of knowledge bases
in two different application areas – control of systems with unknown
or strongly nonlinear models (i.e. hardly controllable by the classical
methods), and robot motion planning in eight directions. The first
one deals with fuzzy logic and the paper presents approaches for
setting and aggregating the rules of a knowledge base. Te second one
is concentrated on a case-based reasoning strategy for finding the
path in a planar scene with obstacles.