Solving time varying many-objective TSP with dynamic [formula omitted]-NSGA-III algorithm

Abstract

Dynamic many-objective traveling salesman problem (DMaTSP) has a lot of applications in routing challenges. The problem environment describe how the layout and number of cities involve in TSP varies over time. In this manuscript a sixteen cities DMaTSP problem is addressed with four fitness objectives : successive minimum distance between the cities, diametric minimum distance between cities and maximizing associated letters and gifts, which varies over six time periods. The paper introduce a prediction-based dynamic many-objective optimization technique termed as Dynamic θ-non-dominated Sorting Genetic Algorithm III (Dθ-NSGA-III). The algorithm θ-NSGA-III, is based on the fundamentals of popular NSGA-III combined with vector angle-based evolutionary algorithm (VaEA). When a change occurs in the problem environment, the prediction set is used to generate the new population, to achieve faster convergence to the new global optimum. Four prediction strategies based on support vector regression (SVR) with linear kernel and radial basis function (RBF) kernel, polynomial interpolation, and cubic spline-based prediction are used for analysis. The validation of the Dθ-NSGA-III algorithm has been carried out on sixteen benchmark functions taken from DIMP, G, JY and DF Test suites. Comparative analysis have been carried out with dynamic algorithms of NSGA-III, MOEA/D, MRP-MOEA and DNSGA-II algorithms. The simulation analysis reveals superior performance of Dθ-NSGA-III with RBF kernel over the benchmark test suites as well as DMaTSP problem in the form of Mean of IGD, Shott’s Spacing, Max. Spread metrics. The proposed Dθ-NSGA-III with prediction approaches solve dynamic many-objective optimization problems with effective run time bit higher than DNSGA-III but lower than DMOEA/D and MRP-MOEA based approach.