In this article the main optimization problems in the municipal services companies were presented. These problems concern the issue of vehicle routing. The mathematical models of these problems were described. The function of criterion and the conditions on designating the vehicle routing were defined. In this paper the hybrid algorithm solving the presented problems was proposed. The hybrid algorithm consists of two heuristic algorithms: the ant and the genetic algorithm. In this paper the stages of constructing of the hybrid algorithm were presented. A structure of the data processed by the algorithm, a function of adaptation, a selection of chromosomes, a crossover, a mutation and an inversion were characterized. A structure of the data was presented as string of natural numbers. In selection process the roulette method was used and in the crossover process the operator PMX was presented. This algorithm was verified in programming language C #. The process of verification was divided into two stages. In the first stage the best parameters of the hybrid algorithm were designated. In the second stage the algorithm was started with these parameters and the result was compared with the random search algorithm. The random search algorithm generates 2000 routes and the best result is compared with the hybrid algorithm.
Optimization of multi objective vehicle routing problem using a new hybrid algorithm based on particle swarm optimization and artificial bee colony algorithm considering Precedence constraints
