Wyniki wyszukiwania - BazTech

1

New genetic algorithm based on dissimilarities and similarities

Al-Jawadi R., Studniarski M., Younus A.

Computer Science

|

2018

|

Vol. 19 (1)

23--41

EN

Optimization is essential for nding suitable answers to real life problems. In particular, genetic (or more generally, evolutionary) algorithms can provide satisfactory approximate solutions to many problems to which exact analytcal results are not accessible. In this paper we present both theoretical and experimental results on a new genetic algorithm called Dissimilarity and Simlarity of Chromosomes (DSC). This methodology constructs new chromosomes starting with the pairs of existing ones by exploring their dissimilarities and similarities. To demonstrate the performance of the algorithm, it is run on 17 two-dimensional, one four-dimensional and two ten-dimensional optimization problems described in the literature, and compared with the well-known GA, CMA-ES and DE algorithms. The results of tests show the superiority of our strategy in the majority of cases.

2

Higher-order conditions for local equilibria in a discontinuous Gale economic model

Michalak A., Studniarski M.

Control and Cybernetics

|

2017

|

Vol. 46, no. 1

37--47

EN

The paper introduces the concept of a strict local equilibrium of order k in the Gale economic model. We obtain higher-order necessary and suﬃcient conditions for such equilibria without assuming continuity of the utility functions. These conditions are formulated in terms of generalized lower and upper directional derivatives, introduced by Studniarski (1986). A stability theorem for strict local equilibria of order k is also included.

3

Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model

Michalak A., Studniarski M.

Opuscula Mathematica

|

2014

|

Vol. 34, no. 4

827--835

EN

In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.

4

Stopping criteria for a general model of genetic algorithm

Studniarski M.

Prace Naukowe Politechniki Warszawskiej. Elektronika

|

2009

|

z. 169

173-181

EN

We consider a general Markov chain model of genetic algorithm described in [3], Chapters 5 and 6. For this model, we establish an upper bound for the number of iterations which must be executed in order to find an optimal (or approximately optimal) solution with a prescribed probability. For the classical genetic algorithm with bitwise mutation, our result reduces to the main theorem of [1] in the case of one optimal solution, and gives some improvement over it in the case of many optimal solutions.

5

Weak sharp minima in multiobjective optimization

Studniarski M.

Control and Cybernetics

|

2007

|

Vol. 36, no 4

925-937

EN

We extend some necessary and sufficient conditions for strict local Pareto minima of order m obtained by Jiménez (2002) to the case of weak ψ-sharp local Pareto minima, i.e., to the case when the local solution is not necessarily unique.

6

Stability properties of weak sharp minima

Studniarski M., Taha A. W. A.

Control and Cybernetics

|

2003

|

Vol. 32, no 2

351-359

EN

In this paper, stability theorems of Studniarski (1989) are extended to include the stability of weak sharp local minimum points for a nonsmooth mathematical programming problem.

7

Necessary optimality conditions for nonsmooth two-dimensional control systems described by Roesser's model

Studniarski M.

Control and Cybernetics

|

1998

|

Vol. 27, no 1

51-61

EN

Necessary optimality conditions for nonlinear nonsmooth two-dimensional discrete control systems are derived. Under additional convexity assumptions, these conditions can be obtained in the form of a maximum principle. For some special cases, sufficient optimality conditions are also presented.