Multi Objective Optimization Algorithm Based On Hybrid Differential And Bacterial Foraging Algorithm

With the rapid development of society, the problems that people need to solve are more and more complex. Especially in the large-scale projects, transportation, industrial design and other production activities, people tend to simultaneously optimise many different perspectives of one problem. These examples are multi-objective optimization problems. When solving multi-objective optimization problems, due to the multiple objectives of mutual restraint and even contradiction, the solution of the multi-objective optimization problem is a not bad solution for each target, we call it the Pareto optimal solution or the non dominated solution. To solve a multi-objective optimization problem, we need to obtain a large and uniformly distributed Pareto optimal solution that is a set of Pareto, for decision-makers to choose from based on their actual demands. In this paper, a new type swarm intelligence optimization algorithm, bacterial foraging optimization algorithm, is applied to study the multi-objective optimization problems. It includes the following contents:(1) Studying the standard bacterial foraging optimization algorithm, analyzing its limitations and finding its improvement direction.(2) Applying the bacterial foraging optimization algorithm to solving multi-objective optimization problems and enhancing the algorithm regarding the characteristics of multi-objective optimization problems.(1) Regarding the chemotaxis, fixed step of algorithm might lead to difficulty to find the optimal solution, which affects the problem of convergence speed and accuracy, thereby providing a flexible step to address the defects.(2) For the problem of multi-objective optimization problems that can not judge the overall solution of the problem according to a certain objective is good or bad, an improved selection strategy is proposed, which is using the Pareto dominance relation to judge the relationship between individuals and normalizing the solutions which have different dimensions to determine the merits and limitations of a unified solution(3) In the operation of replication, the way of replication that simply let the better half of the individual to replace the poor half of the individual, will make the population diversity rapidly decreased and make the algorithm under partial optimization. For this problem, using the differential evolution theory, the poor bacterial individuals and the better individuals are used to generate new individuals, thereby maximizing the convergence rate of the population without the loss of population diversity at the meanwhile.(4) Introducing the external set of storage mechanisms, establishing the external storage policy, finding the optimization solutions by applying the external storage mechanisms to prevent the loss of the optimization solutions.(5) Concerning the migration operations, on the basis of the migration patterns of movement, the outstanding individuals are more likely to be disappeared. Hence, it could lead to reduce the convergence rate. In this paper, combined the migration operation with the dispersion of the solution, and proposed a migration method of grid division. This purposeful migration not only retains the excellent individuals in the population, but also makes the distribution of the obtained solution more uniform.(3) The proposed algorithm is applied to solve the vehicle routing problem, to find the minimum transportation cost and the average waiting time of the customers. First of all according to the model of vehicle routing problem, the bacterial individuals in the algorithm are coded so that it can be applied to the solution of the model, when the algorithm is run to the end, on the calculated decodes the results, making the results more intuitive and easy to understand.This paper utilized an improved bacterial foraging algorithm to test the standard testing functions of multi-objective optimization problems and applying the algorithm in the vehicle routing problem solving. The experimental results illustrated the improved algorithm in terms of convergence and dispersion is better than the comparison algorithm. The improved algorithm is a new method as an effective solution to multi-objective optimization problems...