Solving the traveling delivery person problem with limited computational time

The traveling delivery person problem (TDP) is a customer-oriented modification of the traveling salesperson problem, which minimizes the sum of delivery times at clients’ destinations. Besides the classical applications in routing or emergency logistics, it recently arises in other research areas as mission planning in mobile robotics, where the goal is to search a known or unknown environment efficiently. Such an original deployment may require solving a series of instances in a periodical manner with a fixed period in order of units or tens of seconds—a scenario seldom considered in the literature when designing and evaluating a solution method for the problem. This paper addresses the difficulty of evaluating stochastic improving algorithms in less traditional applications such as the one aforementioned. A new metaheuristic for the TDP is designed using a general run-time distribution methodology and time-to-target plots. Evaluated on several sets of benchmark instances, it significantly outperforms the current best approach from the literature under the hard time limit settings with limits ranging from 1 to 100 seconds. Still, as shown on a subset of the instances, it provides competitive results in the traditional sense and with cost targets corresponding to the best-known solutions worsened by about 1%. Lastly, four new best-known solutions of 500-customer instances found by the proposed method are reported.