Traveling Salesman Problem Research Papers (original) (raw)

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a... more

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps. We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.

A new optimization principle is presented. Solutions of problems are partly, but significantly, ruined and rebuilt or recreated afterwards. Performing this type of change frequently, one can obtain astounding results for classical... more

A new optimization principle is presented. Solutions of problems are partly, but significantly, ruined and rebuilt or recreated afterwards. Performing this type of change frequently, one can obtain astounding results for classical optimization problems. The new method is particularly ...

Experiments over a variety of optimization problems indicate that scale-effective convergence is an emergent behavior of certain computer-based agents, provided these agents are organized into an asynchronous team (A-Team). An A-Team is a... more

Experiments over a variety of optimization problems indicate that scale-effective convergence is an emergent behavior of certain computer-based agents, provided these agents are organized into an asynchronous team (A-Team). An A-Team is a problem-solving architecture in which the agents are autonomous and cooperate by modifying one another's trial solutions. These solutions circulate continually. Convergence is said to occur if and when a persistent solution appears. Convergence is said to be scale-effective if the quality of the persistent solution increases with the number of agents, and the speed of its appearance increases with the number of computers. This paper uses a traveling salesman problem to illustrate scale-effective behavior and develops Markov models that explain its occurrence in A-Teams, particularly, how autonomous agents, without strategic planning or centralized coordination, can converge to solutions of arbitrarily high quality. The models also perdict two properties that remain to be experimentally confirmed: • construction and destruction are dual processes. In other words, adept destruction can compensate for inept construction in an A-Team, and vice-versa. (Construction refers to the process of creating or changing solutions, destruction, to the process of erasing solutions.) • solution quality is independent of agent-phylum. In other words, A-Teams provide an organizational framework in which humans and autonomous mechanical agents can cooperate effectively.