The double traveling salesman problem is a variation of the basic traveling salesman problem where targets can be reached by two salespersons operating in parallel. The real problem addressed by this work concerns the optimization of the harvest sequence for the two independent arms of a fruit-harvesting robot. This application poses further constraints, like a collision-avoidance function. The proposed solution is based on a self-organizing map structure, initialized with as many artificial neurons as the number of targets to be reached. One of the key components of the process is the combination of competitive relaxation with a mechanism for deleting and creating artificial neurons. Moreover, in the competitive relaxation process, information about the trajectory connecting the neurons is combined with the distance of neurons from the target. This strategy prevents tangles in the trajectory and collisions between the two tours. Results of tests indicate that the proposed approach is efficient and reliable for harvest sequence planning. Moreover, the enhancements added to the pure self-organizing map concept are of wider importance, as proved by a traveling salesman problem version of the program, simplified from the double version for comparison.