The theory of invertible algorithms
The traveling salesman problem for cubic graphs.
The Union of Balls and Its Dual Shape.
The use of fuzzy connectives to design real-coded genetic algorithms.
Genetic algorithms are adaptive methods that use principles inspired by natural population genetics to evolve solutions to search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover and mutation. A great problem in the use of genetic algorithms is premature convergence; the search becomes trapped in a local optimum before the global optimum is found. Fuzzy logic techniques may be used for solving this problem. This...
The use of graphics card and nVidia CUDA architecture in the optimization of the heat radiation intensity
The paper focuses on the acceleration of the computer optimization of heat radiation intensity on the mould surface. The mould is warmed up by infrared heaters positioned above the mould surface, and in this way artificial leathers in the automotive industry are produced (e.g. for car dashboards). The presented heating model allows us to specify the position of infrared heaters over the mould to obtain approximately even heat radiation intensity on the whole mould surface. In this way we can obtain...
The use of Schubert polynomials in SYMCHAR.
Theoretical analysis of steady state genetic algorithms
Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are...
Tours de Hanoï et automates
Towards a general principle of evaluation for approximate algorithms
Towards a theory of practice in metaheuristics design: A machine learning perspective
A number of methodological papers published during the last years testify that a need for a thorough revision of the research methodology is felt by the operations research community – see, for example, [Barr et al., J. Heuristics1 (1995) 9–32; Eiben and Jelasity, Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002) 582–587; Hooker, J. Heuristics1 (1995) 33–42; Rardin and Uzsoy, J. Heuristics7 (2001) 261–304]. In particular, the performance evaluation of nondeterministic methods,...
Towards the automated synthesis of a Gröbner bases algorithm.
We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...
Treating the exceptional cases of the MeatAxe.
Tree inclusion problems
Given two trees (a target T and a pattern P) and a natural number w, window embedded subtree problems consist in deciding whether P occurs as an embedded subtree of T and/or finding the number of size (at most) w windows of T which contain pattern P as an embedded subtree. P is an embedded subtree of T if P can be obtained by deleting some nodes from T (if a node v is deleted, all edges adjacent to v are also deleted, and outgoing edges are replaced by edges going from the parent of v (if it exists)...
Treewidth and minimum fill-in on -trapezoid graphs.
Triangulating a Nonconvex Polytope.
Tuning the Zhu-Takaoka string matching algorithm and experimental results
In this paper we present experimental results for string matching algorithms which have a competitive theoretical worst case run time complexity. Of these algorithms a few are already famous for their speed in practice, such as the Boyer–Moore and its derivatives. We chose to evaluate the algorithms by counting the number of comparisons made and by timing how long they took to complete a given search. Using the experimental results we were able to introduce a new string matching algorithm and compared...
Two open problems in communication in edge-disjoint paths modes
Two-variable word equations
Two-variable word equations
We consider languages expressed by word equations in two variables and give a complete characterization for their complexity functions, that is, the functions that give the number of words of the same length. Specifically, we prove that there are only five types of complexities: constant, linear, exponential, and two in between constant and linear. For the latter two, we give precise characterizations in terms of the number of solutions of Diophantine equations of certain types. In particular,...