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 and knapsack problem. 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 proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operator to avoid the evaluation of infeasible solutions. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance. Furthermore, we provide a comprehensive study showing the influence of each parameter on the performance. Finally, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.

在本文中，我们提出一种方法来解决经过深入研究的旅行小偷问题（TTP）的双目标变体。TTP是一个多组件问题，它结合了两个经典的组合问题：旅行商问题和背包问题。我们针对BI-TTP（TTP的双目标版本）进行研究，其目标是最大程度地减少总的旅行时间并最大程度地提高所收集物品的利润。我们提出的方法基于偏向随机密钥遗传算法，该算法具有针对特定问题特征的自定义设置。我们通过在初始种群中通过对每个子问题的近似最优解的组合来合并领域知识，并使用定制的维修运营商来避免评估不可行的解。通过基于非支配等级和拥挤距离提取的精英人口，可以解决该问题的双目标方面。此外，我们提供了全面的研究，显示了每个参数对性能的影响。最后，我们讨论了BI-TTP竞赛的结果在EMO-2019和GECCO-2019会议上，我们的方法分别获得了第一和第二名，从而证明了其始终如一的寻找高质量解决方案的能力。