Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm

• We consider a multi-objective dynamic stochastic districting and routing problem.
• An enhanced co-evolutionary algorithm called PICEA-g-mr is proposed.
• The PICEA-g-mr outperforms two MOEAs on randomly generated instances.
• A procedure for selecting a preferred design for the problem is illustrated.

This study considers a multi-objective dynamic stochastic districting and routing problem in which the customers of a territory stochastically evolve over several periods of a planning horizon, and where the number of service vehicles, the compactness of the districts, the dissimilarity measure of the districts and an equity measure of vehicles profit are considered as objectives. The problem is modeled and solved as a two-stage stochastic program, where in each period, districting decisions are made in the first stage, and the Beardwood–Halton–Hammersley formula is used to approximate the expected routing cost of each district in the second stage. An enhanced multi-objective evolutionary algorithm (MOEA), i.e., the preference-inspired co-evolutionary algorithm using mating restriction, is developed for the problem. The algorithm is tested on randomly generated instances and is compared with two state-of-the-art MOEAs. Computational results confirm the superiority and effectiveness of the proposed algorithm. Moreover, a procedure for selecting a preferred design for the proposed problem is described.