In this paper, the 0-1 Knapsack Problem (KP) which occurs in many different applications is studied and a new genetic algorithm to solve the KP is proposed. In our methodology, n items are represented by n genes on a bit array that compactly stores the values 0 or 1. When calculating fitness values of items, coefficients of items whose values are 1 in the bit array are summed. Roulette wheel method is used for choosing parents; in this way it is provided that strong individuals produce more children. Crossover is applied in such a way that roulette wheel is rotated on genes with the same index of parents, that the dominant parent can transfer its genes to the child. Mutation is applied for randomly chosen 25% genes and this process is repeated for the number of individuals. The algorithm is written in C programming language and is tested on randomly generated instances. In order to find the optimal solutions of these problems, a program that has been written by dynamic programming technique is used. It is seen that the algorithm yields optimal solutions for all instances.

In this paper, The Multidimensional Knapsack Problem (MKP) which occurs in many different applications is studied and a genetic algorithm to solve the MKP is proposed. Unlike the technique of the classical genetic algorithm, initial population is not randomly generated in the proposed algorithm, thus the solution space is scanned more efficiently. Moreover, the algorithm is written in C programming language and is tested on randomly generated instances. It is seen that the algorithm yields optimal solutions for all instances.

No abstract

No abstract

In this paper, computer aided games, which motivate and bring out the mathematical abilities of students, have been studied by inspiring "Bachet's Game". The winning strategies of the games are based on modular arithmetic. Winning algorithms and mathematical models are included in the paper.Levels of the logical and math games which have been proved to be beneficial for students in order to gain ability of appropriate selection and application of analytical technics and strategies in terms of problems could be applied in compliance with age group of students and be permanent during the academic life of the student as a result of its character.