Ensuring Diversity in a Backtrack and GA Optimization Method for Delivery Schedule

Delivery route optimization greatly improves the delivery efficiency in terms of all resources including human resources and energy consumption. In our application scenario the distribution network requires solving several tens to hundreds (max. 1500-2000) cities Traveling Salesman Problems (TSP) within interactive response time (around 3 seconds) with expert-level accuracy (below 3% level of error rate). Moreover, since domain experts have to adjust the solutions due to boundary conditions that can not be formally expressed (such as human convenience, road conditions, and social aspects), understandability and flexibility of the applied heuristics are necessary. To meet all these requirements, a Backtrack and Restart Genetic Algorithm (Br-GA) was proposed. This method combines Backtracking and GA having simple heuristics such as 2-opt and NI (Nearest Insertion) so that, in case of stagflation, GA can restarts with the state of populations going back to the state in the generation before stagflation. Here, a refinement of this algorithm is introduced, which aims at ensuring diversity of initial solutions, which are subject to mutation. We introduce a formal definition of a diversity degree as well as a technique to compose new random individuals, which follow a required degree of diversity.