The traveling salesman problem belongs to an important class of scheduling and routing problems. It is also a subproblem in solving others, such as the warehouse distribution problem. It has been attacked by many mathematical methods with but meager success. Only for special forms of the problem or for problems with a moderate number of points can it be solved exactly, even if very large amounts of computer time are used. Heuristic procedures have been proposed and tested with only slightly better results. This paper describes a computer aided heuristic technique which uses only a modest amount of computer time in real-time to solve large (100-200) point problems. This technique takes advantage of both the computer's and the human's problem-solving abilities. The computer is not asked to solve the problem in a brute force way as in many of today's heuristics, but it is asked to organize the data for the human so that the human can solve the problem easily.The technique used in this paper seems to point to new directions in the field of man-machine interaction and in the field of artificial intelligence.

The traveling salesman problem, (form a circuit through N points with no subloops in such a way as to minimize the length of the circuit), is a close kin to many board wiring problems. It has been attacked by many mathematical methods with only meager results. Only for special forms of the problem or for problems with relatively few points can it be solved exactly even using very large amounts of computer time. Heuristic procedures have been proposed and tested with only slightly better results. This paper will describe a computer-aided heuristic technique which uses only a modest amount of computer time in real time to solve large (100-200) point problems. This technique takes advantage of both the computer's and the human's problem solving abilities. The computer is not asked to solve the problem in a brute force way as is the case in many of today's heuristics but it is asked to organize the data for the human in a fashion that allows the human to solve the problem easily.The techniques employed in this paper require that the computer and the human cooperate to find the solution to the problem in reasonable amounts of both of their times. The computer initially uses a series of heuristics that produce groups of points and some partial connections of these points. The human is asked to connect the points within the groups and then connect the groups in a manner that produces a circuit and appears to the human to maximize the ratio of enclosed area to perimeter. The computer takes this solution and uses another set of heuristics to make improvements. The solution is displayed to the human and if he is satisfied the procedure stops; if not the former procedure is repeated until the human is satisfied that cost for finding a better solution exceeds his estimate of the best possible improvement that could be obtained by fttrther work. The heuristic procedures seek to group points around information obtained from solving a series of mathematical programming problems (assignment problems) and some observed correlations between these problems and the traveling salesman problem.

The literature of various disciplines including engineering, operations research, and management science contains many problems that would have widespread application if methods could be found for solving problems of reasonable size. In general, these problems are combinatoric in nature; moderate to large-scale problems in this class have resisted solution by currently existing algorithms and heuristics. A partial list of these well known problems includes the traveling-salesman problem, the generalized truck-dispatching problem, board wiring, and the construction of minimum cost communication networks with various survival or redundancy demands. The authors report on a man-machine approach for solving the generalized truck-dispatching problem. Their results indicate that the technique is more accurate than previously reported heuristics. They further comment on application of the man-machine technique to other routing, scheduling, and network problems.

A technique which uses Fibonaccion search concepts has been developed to solve optimization problems involving unimodal functions of several variables. The technique has not been proven to be optimal in the sense that the one-dimensional Fibonaccion search is. However, it is valuable for certain kinds of calculations.

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