Solving the Generalized Vertex Cover Problem by Genetic Algorithm

In this paper an evolutionary approach to solving the generalized vertex cover problem (GVCP) is presented. Binary representation and standard genetic operators are used along with the appropriate objective function. The experiments were carried out on randomly generated instances with up to 500 vertices and 100000 edges. Performance of the genetic algorithm (GA) is compared with CPLEX solver and 2-approximation algorithm based on LP relaxation. The genetic algorithm outperformed both CPLEX solver and 2-approximation heuristic

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

An Efficient Genetic Algorithm for Solving the Multi-Level Uncapacitated Facility Location Problem

In this paper a new evolutionary approach for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. Binary encoding scheme is used with appropriate objective function containing dynamic programming approach for finding sequence of located facilities on each level to satisfy clients' demands. The experiments were carried out on the modified standard single level facility location problem instances. Genetic algorithm (GA) reaches all known optimal solutions for smaller dimension instances, obtained by total enumeration and CPLEX solver. Moreover, all optimal/best known solutions were reached by genetic algorithm for a single-level variant of the problem