Creating lasso-solutions for the traveling salesman problem with pickup and delivery by Tabu search

We consider the Traveling Salesman Problem with Pickup and Delivery (TSPPD) where the same customers might require both delivery of goods and pickup of other goods. All the goods should be transported from/to the same depot. A vehicle on a TSPPD-tour could often get some practical problems when arranging the load. Even if the vehicle has enough space for all the pickups, one has to consider that they are stored in a way that doesn't block the delivery for the next customer. In real life problems this occurs for instance for breweries when they deliver bottles of beer or mineral water and collect empty bottles from the same customers on the same tour. In these situations we could relax the constraints of only checking Hamiltonian tours, and also try solutions that can visit customers in a way giving rise to a ‘lasso’ model. A solution which first only delivers bottles until the vehicle is partly unloaded, then does both delivery and pickup at the remaining customers and at last picks up the empty bottles from the first visited customers, could in these situations be better than a pure Hamiltonian tour, at least in a practical setting. To find such solutions, we will use the metaheuristic Tabu Search on some well known TSPPD-problems, and compare them to other kinds of solutions on the same problems.