A two-stage algorithm based on greedy ant colony optimization for travelling thief problem

Abstract

The travelling thief problem (TTP) combines two NP-hard problems, traveling salesman problem (TSP) and knapsack problem (KP), which is more complicated for solving. In TTP, the salesman needs to choose the travel route and select the items at the same time to maximize the profit. Consequently, the resolution of TTP essentially encompasses two stages, including route planning and item selection. In the first-stage of route planning, conventional algorithms solely on distance minimization and ignore the attributes of items. To address this issue, an item classification algorithm (ICA) is proposed to compute an optimized combination of items in advance based on their profits and distribution patterns. Furthermore, a greedy ant colony optimization (GACO) is proposed to plan travel route which places the city, where the selected item located, at the later segment of the travel route, optimizing the salesman’s profit. Hence, GACO can produce a travel route that facilitates the optimization in the second-stage item selection scheme. Experimental results illustrate that GACO is more facilitative in optimizing TTP compared to the route obtains by traditional Lin–Kernighan (LK) heuristic rules. With regard to item selection in the second-stage, the traditional algorithm’s item selection strategy requires the design of complex rules, and usually only local search is performed on items, which makes the algorithm prone to falling into local optima. This paper designs a genetic item search strategy (GISS) based on genetic algorithm (GA), GISS does not require the design of complex rules and can perform an effective global search on items. The experimental results also show the efficacy of GISS in item selection schemes for TTP, which can outperform other state-of-the-art algorithms. © The Author(s) 2025.