PARALLEL SEARCH-AND-LEARN TECHNIQUE FOR SOLVING LARGE-SCALE TRAVELING-SALESPERSON PROBLEMS

Parallel processing has traditionally been used to achieve higher spee d while solving computational problems of large size. The greater avai lability of parallel and distributed computing opens yet another dimen sion, where parallel computers can be used to obtain solutions of high er quality than uniprocessor solutions. The paper describes a search-a nd-learn technique for obtaining high quality solutions to the travell ing salesperson problem (TSP). The combinatorial search space is decom posed so that multiple processors can simultaneously look for local op timal solutions in the subspaces. The local optima are then compared t o 'learn' which moves are good; a move is defined to be good if all th e search processes have voted in consensus for the move. On the basis of this learning, the original problem is transformed into a constrain ed optimization, where a constraint requires a specific edge to be inc luded in the final tour. The constrained optimization problem is model led as a TSP of smaller size, and is again solved using the parallel s earch technique. This process is repeated until a TSP of manageable si ze is reached which can be solved effectively; the tour obtained at th is last stage is then expanded retrogressively until the tour for the original problem is obtained. The search-and-learn algorithm has been implemented on a Meiko transputer array of 32 nodes. The results of th e implementation for benchmark problems are described.