The double traveling salesman problem with partial last‐in‐first‐out loading constraints

Abstract

In this paper, we introduce the Double Traveling Salesman Problem with Partial Last-In-First-Out Loading Constraints (DTSPPL), a pickup-and-delivery single-vehicle routing problem where all pickup operations must be performed before any delivery one because the pickup and delivery areas are geographically separated. The vehicle collects items in the pickup area and loads them into its container, a horizontal stack. After performing all pickup operations, the vehicle begins delivering the items in the delivery area. Loading and unloading operations must obey a partial Last-In-First-Out (LIFO) policy, i.e., a version of the LIFO policy that may be violated within a given reloading depth. The objective of the DTSPPL is to minimize the total cost, which involves the total distance traveled by the vehicle and the number of reloaded items due to violations of the standard LIFO policy. We formally describe the DTSPPL by means of two Integer Linear Programming (ILP) formulations, and propose a heuristic algorithm based on the Biased Random-Key Genetic Algorithm (BRKGA) to find high-quality solutions. The performance of the proposed solution approaches is assessed over a broad set of instances. Computational results have shown that both ILP formulations were able to solve only the smaller instances, whereas the BRKGA obtained better solutions for almost all instances, requiring shorter computational time.

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

“…In contrast, the BRKGA needs more computing time to reach solutions of similar quality as it is reported in Chagas et al. (2022) that needs at least one hour of computing time. It is worth noting that the overall averages of the BRKGA for the Best GAP, Avg GAP, and HIT with a time limit of 10 seconds cannot reach the results obtained by the ILS with only a time limit of 1 second.…”

“…Source code of BRKGA is available in Chagas et al. (2022) and is written in C++ programming language, working with a given time limit. Our metaheuristic is implemented in the C++ programming language using the GNU Compiler Collection.…”

“…The DTSPPL can be formulated using an ILP model that was introduced by Chagas et al. (2022). The formulation uses the following binary decision variables: $$x^q_{ij}, \forall q \in Q, (i,j) \in A^{q}$$ represents the route of the vehicle in each area, taking value 1 if the vehicle traverses arc $$(i, j)$$ in area q , and value 0 otherwise.…”

“…Furthermore, the improved GA has the best performance than the standard GA. Finally, Chagas et al (2022) state a variant of the DTSPMS, being a particular case that they called DTSPPL. They propose two ILP formulations, which optimally solve instances with up to eight customers within a time limit of one hour.…”

The Double Traveling Salesman Problem with Multiple Stacks and a Choice of Container Types

“…Gendreau et al [23] used tabu search and Iori et al [24] a branch-and-cut algorithm for vehicle routing problems with two-dimensional loading constraints. Fuellerer et al [25] used ant colony optimization for a vehicle routing problem with three-dimensional loading constraints, and Chagas et al [26] considered partial last-in-first-out loading constraints. Iori [27] presented a survey on combined routing and loading problems and is recommended for further details about related problems.…”