Using the concept of swap operation and swap sequence on the sequence of paths of a Traveling Salesman Problem(TSP) Artificial Bee Colony (ABC) algorithm is modified to solve multi-objective TSP. The fitness of a solution is determined using a rule following the dominance property of a multi-objective optimization problem. This fitness is used for the selection process of the onlooker bee phase of the algorithm. A set of rules is used to improve the solutions in each phase of the algorithm. Rules are selected according to their performance using the roulette wheel selection process. At the end of each iteration, the parent solution set and the solution sets after each phase of the ABC algorithm are combined to select a new solution set for the next iteration. The combined solution set is divided into different non-dominated fronts and then a new solution set, having cardinality of parent solution set, is selected from the upper-level non-dominated fronts. When some solutions are required to select from a particular front then crowding distances between the solutions of the front are measured and the isolated solutions are selected for the preservation of diversity. Different standard performance metrics are used to test the performance of the proposed approach. Different sizes standard benchmark test problems from TSPLIB are used for the purpose. Test results show that the proposed approach is efficient enough to solve multi-objective TSP.

在旅行商问题（TSP）的路径序列上使用交换操作和交换序列的概念，对人工蜂群算法（ABC）进行了修改，以解决多目标TSP。使用遵循多目标优化问题的优势属性的规则确定解决方案的适用性。该适合度用于算法的旁听蜂阶段的选择过程。一组规则用于改进算法每个阶段的解决方案。使用轮盘选择过程根据规则的性能选择规则。在每次迭代结束时，将父解决方案集和ABC算法每个阶段之后的解决方案集组合在一起，以为下一次迭代选择新的解决方案集。将合并的解决方案集划分为不同的非支配前沿，然后从上层非支配前沿中选择具有父解决方案集的基数的新解决方案集。当需要从特定前沿选择某些解决方案时，将测量前沿解决方案之间的拥挤距离，并选择隔离的解决方案以保持多样性。使用不同的标准性能指标来测试所提出方法的性能。为此，使用了TSPLIB提供的不同大小的标准基准测试问题。测试结果表明，该方法足以解决多目标TSP问题。当需要从特定前沿选择某些解决方案时，将测量前沿解决方案之间的拥挤距离，并选择隔离的解决方案以保持多样性。使用不同的标准性能指标来测试所提出方法的性能。为此，使用了TSPLIB提供的不同大小的标准基准测试问题。测试结果表明，该方法足以解决多目标TSP问题。当需要从特定前沿选择某些解决方案时，将测量前沿解决方案之间的拥挤距离，并选择隔离的解决方案以保持多样性。使用不同的标准性能指标来测试所提出方法的性能。为此，使用了TSPLIB提供的不同大小的标准基准测试问题。测试结果表明，该方法足以解决多目标TSP问题。