Efficiently solving the thief orienteering problem with a max-min ant colony optimization approach

We tackle the Thief Orienteering Problem (ThOP), which is academic multi-component problem: it combines two classical combinatorial problems, namely the Knapsack Problem (KP) and the Orienteering Problem (OP). In this problem, a thief has a time limit to steal items that distributed in a given set of cities. While traveling, the thief collects items by storing them in their knapsack, which in turn reduces the travel speed. The thief has as the objective to maximize the total profit of the stolen items. In this article, we present an approach that combines swarm-intelligence with a randomized packing heuristic. Our solution approach outperforms existing works on almost all the 432 benchmarking instances, with significant improvements.

A weighted-sum method for solving the bi-objective traveling thief problem

Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal solution for the other components. This can be a challenge for single-objective formulations, where the respective influence that each component has on the overall solution quality can vary from instance to instance. In this paper, we study a bi-objective formulation of the traveling thief problem, which has as components the traveling salesperson problem and the knapsack problem. We present a weighted-sum method that makes use of randomized versions of existing heuristics, and that would have won two recent optimization competitions.

Ants can orienteer a thief in their robbery

We address the Thief Orienteering Problem (ThOP), a multi-component problem that combines features of two classic combinatorial optimization problems, namely the Orienteering Problem and Knapsack Problem. Due to the given time constraint and the interaction of the load-dependent movement speed with the chosen route, the ThOP is complex and challenging. We propose a two-phase, swarm-intelligence based approach together with a new randomized packing heuristic. To identify the impact of the respective components, we use automated algorithm configuration. The resulting configurations outperform existing work on more than 90% of the benchmarking instances, with an average improvement of over 300%.

A Non-Dominated Sorting Based Customized Random-Key Genetic Algorithm for the Bi-Objective Traveling Thief Problem

In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP) and Knapsack Problem (KP). In the TTP, a thief has to visit each city exactly once and can pick items throughout their journey. The thief begins their journey with an empty knapsack and travels with a speed inversely proportional to the knapsack weight. We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our method is based on a genetic algorithm with customization addressing problem characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and a custom repair operation to avoid the evaluation of infeasible solutions. Moreover, the independent variables of the TSP and KP components are unified to a real variable representation by using a biased random-key approach. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance of each solution. Furthermore, we provide a comprehensive study which shows the influence of hyperparameters on the performance of our method and investigate the performance of each hyperparameter combination over time. In addition to our experiments, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second place, respectively, thus proving its ability to find high-quality solutions consistently.

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

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.