A New Modified Artificial Bee Colony Algorithms And Their Applications To Traveling Salesman Problem

The artificial bee colony algorithm is a new way of thinking to solve most optimization problems which has important academic significance and practical values to the algorithm.However, due to the complexity of the artificial bee colony algorithm, the results of the present study are relatively decentralized and lack of systematic. Therefore, in view of the shortcomings of the artificial bee colony algorithm and combined with previous research, in this paper the modified artificial bee colony algorithm is proposed, which is the more concentrated and systematic, by using of the theory and numerical simulation of combining research methods.Then, the effectiveness and convergence of the modified algorithm are proved. Furthermore, the algorithm applies to traveling salesman problem(TSP), the results show that the modified artificial bee colony algorithm has good performance.The specific research contents can be summarized as:(1) Based on detailed description of the honey bees and drawing on the relevant literature,this paper sums up the basic process of classical artificial bee colony algorithm. In order to quickly understand the classical artificial bee colony algorithm, defines the related professional terms, obtains the basic steps of the classical algorithm, draws the flow chart of the classical algorithm, and summarizes the shortcomings of the classical algorithm.(2) Using the opposition-based learning method and the improved S-type sub-population grouping method to construct the initial population, using a new sensitivity with the pheromone instead of original roulette gambling selection mode, and designs an adaptive adjustment factor function to strengthen the convergence speed and keep the population diversity. So the modified artificial bee colony algorithm is proposed. Then, based on the new test function versions CEC13 of 14 benchmark functions with the dimensions 20 and 40 and applied in the simulation contrast experiment between the modified algorithm and other fives. The results shows that the modified artificial bee colony algorithm effectively solves the shortcomings, which are the slow search speed, diversity of population and easily falling into the local optimum, and has better effect in the aspects of the concentration and stability.(3) The modified artificial bee colony algorithm is proved to be a finite homogeneous Markov chain. Then, according to the improved probability selection formula, it is proved that the evolution direction of the whole population is monotonous. And the Markov chain population is convergent to the global optimal solution with probability 1 for modified artificial bee colony algorithm. At last, by using the martingale convergence theorem, it is showed that the modified artificial bee colony algorithm is almost strong convergence.(4) The modified artificial bee colony algorithm is applied to TSP. The comparison results show that the modified artificial bee colony algorithm is always the first one to achieve optimal path and optimal path is shorter compared to the artificial bee colony algorithm which proved the modified artificial bee colony algorithm is effective.