Sandro Pirkwieser

Variable neighborhood search coupled with ILP-based very large neighborhood searches for the (periodic) location-routing problem

This work deals with the application of a variable neighborhood search (VNS) to the capacitated location-routing problem (LRP) as well as to the more general periodic LRP (PLRP). For this, previous successful VNS algorithms for related problems are considered and accordingly adapted as well as extended. The VNS is subsequently combined with three very large neighborhood searches (VLNS) based on integer linear programming: Two operate on whole routes and do a rather coarse, yet powerful optimization, with the more sophisticated one also taking the single customers into account, and the third operates on customer sequences to do a more fine-grained optimization. Several VNS plus VLNS combinations are presented and very encouraging experimental results are given. Our method clearly outperforms previous PLRP approaches and is at least competitive to leading approaches for the LRP.

A variable neighborhood search approach for the two-echelon location-routing problem

We consider the two-echelon location-routing problem (2E-LRP), a well-known problem in freight distribution arising when establishing a two-level transport system with limited capacities. The problem is a generalization of the location routing problem (LRP), involving strategic (location), tactical (allocation) and operational (routing) decisions at the same time. We present a variable neighborhood search (VNS) based on a previous successful VNS for the LRP, accordingly adapted as well as extended. The proposed algorithm provides solutions of high quality in short time, making use of seven different basic neighborhood structures parameterized with different perturbation size leading to a total of 21 specific neighborhood structures. For intensification, two consecutive local search methods are applied, optimizing the transport costs efficiently by considering only recently changed solution parts. Experimental results clearly show that our method is at least competitive regarding runtime and solution quality to other leading approaches, also improving upon several best known solutions.

Multiple Variable Neighborhood Search Enriched with ILP Techniques for the Periodic Vehicle Routing Problem with Time Windows

In this work we extend a VNS for the periodic vehicle routing problem with time windows (PVRPTW) to a multiple VNS (mVNS) where several VNS instances are applied cooperatively in an intertwined way. The mVNS adaptively allocates VNS instances to promising areas of the search space. Further, an intertwined collaborative cooperation with a generic ILP solver applied on a suitable set covering ILP formulation with this mVNS is proposed, where the mVNS provides the exact method with feasible routes of the actual best solutions, and the ILP solver takes a global view and seeks to determine better feasible route combinations. Experimental results were conducted on newly derived instances and show the advantage of the mVNS as well as of the hybrid approach. The latter yields for almost all instances a statistically significant improvement over solely applying the VNS in a standard way, often requiring less runtime, too.

Combining Lagrangian decomposition with an evolutionary algorithm for the knapsack constrained maximum spanning tree problem

We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document the advantages of the new approach. Most of the upper bounds derived by Lagrangian decomposition are optimal, and together with the evolutionary algorithm, large instances with up to 12000 nodes can be either solved to provable optimality or with a very small remaining gap in reasonable time.

Multilevel variable neighborhood search for periodic routing problems

In this work we present the extension of a variable neighborhood search (VNS) with the multilevel refinement strategy for periodic routing problems. The underlying VNS was recently proposed and performs already well on these problems. We apply a path based coarsening scheme by building fixed (route) segments of customers accounting for the periodicity. Starting at the coarsest level the problem is iteratively refined until the original problem is reached again. This refinement is smoothly integrated into the VNS. Further a suitable solution-based recoarsening is proposed. Results on available benchmark test data as well as on newly generated larger instances show the advantage of the multilevel VNS compared to the standard VNS, yielding better results in usually less CPU time. This new approach is especially appealing for large instances.

Solving the two-dimensional bin-packing problem with variable bin sizes by greedy randomized adaptive search procedures and variable neighborhood search

In this work we present new metaheuristic algorithms to a special variant of the two-dimensional bin-packing, or cutting-stock problem, where a given set of rectangular items (demand) must be produced out of heterogeneous stock items (bins). The items can optionally be rotated, guillotine-cuttable and free layouts are considered. The proposed algorithms use various packing-heuristics which are embedded in a greedy randomized adaptive search procedure (GRASP) and variable neighborhood search (VNS) framework. Our results for existing benchmark-instances show the superior performance of our algorithms, in particular the VNS, with respect to previous approaches.

MetaBoosting: Enhancing Integer Programming Techniques by Metaheuristics

This chapter reviews approaches where metaheuristics are used to boost the performance of exact integer linear programming (IP) techniques. Most exact optimization methods for solving hard combinatorial problems rely at some point on tree search. Applying more effective metaheuristics for obtaining better heuristic solutions and thus tighter bounds in order to prune the search tree in stronger ways is the most obvious possibility. Besides this, we consider several approaches where metaheuristics are integrated more tightly with IP techniques. Among them are collaborative approaches where various information is exchanged for providing mutual guidance, metaheuristics for cutting plane separation, and metaheuristics for column generation. Two case studies are finally considered in more detail: (i) a Lagrangian decomposition approach that is combined with an evolutionary algorithm for obtaining (almost always) proven optimal solutions to the knapsack constrained maximum spanning tree problem and (ii) a column generation approach for the periodic vehicle routing problem with time windows in which the pricing problem is solved by local search based metaheuristics.

Improved packing and routing of vehicles with compartments

We present a variable neighborhood search for the vehicle routing problem with compartments where we incorporate some features specifically aiming at the packing aspect. Among them we use a measure to distinguish packings and favor solutions with a denser packing, propose new neighborhood structures for shaking, and employ best-fit and best-fit-decreasing methods for inserting orders. Our approach yields encouraging results on a large set of test instances, obtaining new best known solutions for almost two third of them.

Finding consensus trees by evolutionary, variable neighborhood search, and hybrid algorithms

The consensus tree problem arises in the domain of phylogenetics and seeks to find for a given collection of trees a single tree best representing it. Usually, such a tree collection is obtained by biologists for a given taxa set either via different phylogenetic inference methods or multiple applications of a non-deterministic procedure. There exist various consensus methods which often have the drawback of being very strict, limiting the resulting consensus tree in terms of its resolution and/or precision. A reason for this typically is the coarse granularity of the tree metric used. To find fully resolved (binary) consensus trees of high quality, we consider the fine-grained TreeRank similarity measure and extend a previously presented evolutionary algorithm (EA) to a memetic algorithm (MA) by including different variants of local search using neighborhoods based on moves of single taxa as well as subtrees. Furthermore, we propose a variable neighborhood search (VNS) with an embedded variable neighborhood descent (VND) based on the same neighborhood structures. Finally sequential and intertwined combinations of the EA and MA with the VNS/VND are investigated. We give results on real and artificially generated data indicating in particular the benefits of the hybrid methods.

A Lagrangian Decomposition/Evolutionary Algorithm Hybrid for the Knapsack Constrained Maximum Spanning Tree Problem

We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Thorough experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document the advantages of our approach. Most of the upper bounds derived by Lagrangian decomposition are optimal, and when additionally applying local search (LS) and combining it with the evolutionary algorithm, large and supposedly hard instances can be either solved to provable optimality or with a very small remaining gap in reasonable time.