Restricted Dynamic Programming Heuristic for Precedence Constrained Bottleneck Generalized TSP

We develop a restricted dynamical programming heuristic for a complicated traveling salesman problem: a) cities are grouped into clusters, resp. Generalized TSP; b) precedence constraints are imposed on the order of visiting the clusters, resp. Precedence Constrained TSP; c) the costs of moving to the next cluster and doing the required job inside one are aggregated in a minimax manner, resp. Bottleneck TSP; d) all the costs may depend on the sequence of previously visited clusters, resp. Sequence-Dependent TSP or Time Dependent TSP. Such multiplicity of constraints complicates the use of mixed integer-linear programming, while dynamic programming (DP) benefits from them; the latter may be supplemented with a branch-and-bound strategy, which necessitates a “DP-compliant” heuristic. The proposed heuristic always yields a feasible solution, which is not always the case with heuristics, and its precision may be tuned until it becomes the exact DP

Pricing routines for vehicle routing with time windows on road networks

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternative paths in an auxiliary multi-graph, and then using that multi-graph within a branch-and-price algorithm. We show that, if one works with the original road network rather than the multi-graph, then one can solve the pricing subproblem more quickly, in both theory and practice

Kiertovaihtoalgoritmi ja muunnoksia yleistetylle ajoneuvoreititysongelmalle

Vehicle routing problems have numerous applications in fields such as transportation, supply logistics and network design. The optimal design of these routes fall in the category of NP-hard optimization problems, meaning that the computational complexity increases extremely fast with increasing problem size. The Generalized Vehicle Routing Problem (GVRP) is a general problem type that includes a broad variety of other problems as special cases. The main special feature of the GVRP is that the customers are grouped in clusters. For each cluster, only one customer is visited. In this thesis, we implement a heuristic algorithm to solve GVRP instances in reasonable time. Especially, we include a cyclic exchange method that considers a very large search neighborhood. In addition, we study the related Capacitated m-Ring-Star Problem (CmRSP). We present the Distance-Constrained Capacitated m-Ring-Star Problem (DCmRSP) and show that it contains the Multivehicle Covering Tour Problem (MCTP) as a special case. We show that DCmRSP instances can be transformed to (distance-constrained) GVRP with minor adaptations and solved with the same heuristic algorithm. Our algorithm is able to find best known solutions to all GVRP test instances; for two of them, our method shows strict improvement. The transformed CmRSP and MCTP instances are solved successfully by the same algorithm with adequate performance.Ajoneuvoreititysongelmilla on lukuisia sovelluksia muun muassa logistiikan ja verkostosuunnittelun aloilla. Tällaisten reittien optimaalinen ratkaiseminen kuuluu NP-vaikeiden optimointiongelmien kategoriaan, eli ratkaisuun vaadittava laskentateho kasvaa erittäin nopeasti ongelman koon suhteen. Yleistetty ajoneuvoreititysongelma (Generalized Vehicle Routing Problem, GVRP) on ongelmatyyppi, joka kattaa joukon muita reititysongelmia erikoistapauksina. GVRP:n selkein erityispiirre on asiakkaiden jako ryppäisiin: kussakin ryppäässä on käytävä tasan yhden asiakkaan luona. Tässä diplomityössä esitellään ja toteutetaan heuristinen algoritmi, joka etsii kohtalaisessa ajassa ratkaisuja GVRP-ongelmiin. Menetelmä sisältää kiertovaihtoalgoritmin, joka kykenee etsimään ratkaisuja hyvin laajasta ympäristöstä. Tutkimuksen kohteena on lisäksi m-rengastähtiongelma (Capacitated m-Ring-Star Problem, CmRSP). Esittelemme ongelman etäisyysrajoitetun version (DCmRSP), ja näytämme, että kyseiseen ongelmaan sisältyy usean ajoneuvon peittävän reitin ongelma (Multivehicle Covering Tour Problem). Näytämme, että DCmRSP-ongelman pystyy pienin muutoksin muuntamaan GVRP-ongelmaksi ja ratkaisemaan samalla heuristisella algoritmilla. Algoritmi löytää parhaat tunnetut ratkaisut kaikkiin GVRP-testitehtäviin. Kahdessa tapauksessa ratkaisu on parempi aiemmin löydettyihin nähden. Algoritmi kykenee ratkaisemaan muunnetut CmRSP- ja MCTP-testitehtävät kohtalaisella ratkaisulaadulla