The purpose of this paper is to describe TABUROUTE, a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route. This is done by means of a generalized insertion procedure previously developed by the authors. During the course of the algorithm, infeasible solutions are allowed. Numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics, and TABUROUTE often produces the best known solutions.vehicle routing problem, tabu search, generalized insertion

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This paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem. The combination of the two methods results in an efficient algorithm (GENIUS) which outperforms known alternative heuristics in terms of solution quality and computing time.

W e describe a tabu search algorithm for the vehicle routing problem with split deliveries. At each iteration, a neighbor solution is obtained by removing a customer from a set of routes where it is currently visited and inserting it either into a new route or into an existing route that has enough residual capacity. The algorithm also considers the possibility of inserting a customer into a route without removing it from another route. The insertion of a customer into a route is done by means of the cheapest insertion method. Computational experiments are reported for a set of benchmark problems, and the results are compared with those obtained by the algorithm proposed by Dror and Trudeau.

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.