Solving the Maximally Balanced Connected Partition Problem in Graphs by Using Genetic Algorithm

This paper exposes a research of the NP-hard Maximally Balanced Connected Partition problem (MBCP). The proposed solution comprises of a genetic algorithm (GA) that uses: binary representation, fine-grained tournament selection, one-point crossover, simple mutation with frozen genes and caching technique. In cases of unconnected partitions, penalty functions are successfully applied in order to obtain the feasible individuals. The effectiveness of presented approach is demonstrated on the grid graph instances and on random instances with up to 300 vertices and 2 000 edges

Genetic Algorithm Approach for Solving the Machine-Job Assignment with Controllable Processing Times

This paper considers a genetic algorithm (GA) for a machine-job assignment with controllable processing times (MJACPT). Integer representation with standard genetic operators is used. In an objective function, a job assignment is obtained from genetic code and for this, fixed assignment processing times are calculated by solving a constrained nonlinear convex optimization problem. Additionally, the job assignment of each individual is improved by local search. Computational results are presented for the instances from literature and modified large-scale instances for the generalized assignment problem (GAP). It can be seen that the proposed GA approach reaches almost all optimal solutions, which are known in advance, except in one case. For large-scale instances, GA obtained reasonably good solutions in relatively short computational time

Algorithms for the restricted linear coloring arrangement problem

The aim of this project is to develop efficient algorithms for solving or approximating the Minimum Restricted Linear Coloring Arrangement Problem. It is the first approach to its algorithms, and we will face the problem from different perspectives: constraint programming, backtracking, greedy, and genetic algorithms. As a second goal we are interested in providing theoretical results for particular graphs