Combination of Genetic Algorithm with Dynamic Programming for Solving TSP - Hemmak, Allaoua (Université de M'sila, 2017)
This paper presents a combination of Genetic Algorithm (GA) with Dynamic Programming (DP) to solve the well-known Travelling Salesman Problem (TSP). In this work, DP is integrated as a GA operator with a certain probability. In specific, at a given GA generation, the individuals are subdivided into a number of equal segments of genes, and the shortest path on each segment is obtained by applying a DP algorithm. Since the computational complexity of the DP is O (k22k), it becomes of O(1) when k is small. Experimental analyses are conducted to investigate the impact and trade-offs among DP probability, segment size and time processing on the solution quality and computational effort. In addition, we will implement a basic GA approach to compare results and show the contribution of combination of combination approach. Experimental results on benchmark instances showed that the combined GA-DP algorithm reduces significantly the computational effort, produces a clearly improved solution quality and avoids early premature convergence of GA.
Keywords: Combinatorial Optimization, Dynamic Programming, Evolutionary Computing, Genetic Algorithm, Traveling Salesman Problem.