Hermann Gehring

Two Evolutionary Metaheuristics For The Vehicle Routing Problem With Time Windows

AbstractThe vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective is to design an optimal set of routes that services all customers and satisfies the given constraints, especially the time window constraints. The objective function considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance minimization (secondary criterion). In this paper, two evolution strategies for solving the VRPTW are proposed. The evolution strategies were tested on 58 problems from the literature with sizes varying from 100 to 417 customers and 2 to 54 vehicles. The generated new best known solutions indicate that evolution strategies are effective in reducing both the number of vehicles and the total travel distance

A hybrid genetic algorithm for the container loading problem

Abstract This paper presents a hybrid genetic algorithm (GA) for the container loading problem with boxes of different sizes and a single container for loading. Generated stowage plans include several vertical layers each containing several boxes. Within the procedure, stowage plans are represented by complex data structures closely related to the problem. To generate offspring, specific genetic operators are used that are based on an integrated greedy heuristic. The process takes several practical constraints into account. Extensive test calculations including procedures from other authors vouch for the good performance of the GA, above all for problems with strongly heterogeneous boxes.

A two-phase hybrid metaheuristic for the vehicle routing problem with time windows

Abstract The subject of this paper is a two-phase hybrid metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The objective function of the VRPTW considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance (secondary criterion). The aim of the first phase is the minimization of the number of vehicles by means of a ( μ , λ )-evolution strategy, whereas in the second phase the total distance is minimized using a tabu search algorithm. The two-phase hybrid metaheuristic was subjected to a comparative test on the basis of 356 problems from the literature with sizes varying from 100 to 1000 customers. The derived results show that the proposed two-phase approach is very competitive.

A parallel tabu search algorithm for solving the container loading problem

This paper presents a parallel tabu search algorithm for the container loading problem with a single container to be loaded. The emphasis is on the case of a weakly heterogeneous load. The distributed-parallel approach is based on the concept of multi-search threads according to Toulouse et al. [Issues in designing parallel and distributed search algorithms for discrete optimization problems, Publication CRT-96-36, Centre de recherche sur les transports, Universitede Montreal, Canada, 1996] i.e., several search paths are investigated concurrently. The parallel searches are carried out by differently configured instances of a tabu search algorithm, which cooperate by the exchange of (best) solutions at the end of defined search phases. The parallel search processes are executed on a corresponding number of LAN workstations. The efficiency of the parallel tabu search algorithm is demonstrated by an extensive comparative test including well-known reference problems and loading procedures from other authors.

Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows

This paper describes the parallelization of a two-phase metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The underlying objective function combines the minimization of the number of vehicles in the first search phase of the metaheuristic with the minimization of the total travel distance in the second search phase. The parallelization of the metaheuristic follows a type 3 parallelization strategy (cf. Crainic and Toulouse (2001). In F. Glover and G. Kochenberger (eds.). State-of-the-Art Handbook in Metaheuristics. Norwell, MA: Kluwer Academic Publishers), i.e. several concurrent searches of the solution space are carried out with a differently configured metaheuristic. The concurrently executed processes cooperate through the exchange of solutions. The parallelized two-phase metaheuristic was subjected to a comparative test on the basis of 358 problems from the literature with sizes varying from 100 to 1000 customers. The derived results seem to justify the proposed parallelization concept.

A parallel genetic algorithm for solving the container loading problem

This paper presents a parallel genetic algorithm (PGA) for the container loading problem with a single container to be loaded. The emphasis is on the case of a strongly heterogeneous load. The PGA follows a migration model. Several separate sub-populations are subjected to an evolutionary process independently of each other. At the same time the best individuals are exchanged between the sub-populations. The evolution of the different sub-populations is carried out on a corresponding number of LAN workstations. The quality of the PGA is demonstrated by an extensive comparative test including well-known reference problems and loading procedures from other authors.

Ein Tabu Search-Verfahren für Containerbeladeprobleme mit schwach heterogenem Kistenvorrat

ZusammenfassungGegenstand des Beitrags ist die Entwicklung eines Tabu Search-Verfahrens (TSV) für Containerbeladeprobleme mit schwach heterogenem Kistenvorrat. Das TSV basiert auf einem zweistufigen Verfahrensansatz. Ein integrierter Greedy-Algorithmus dient unmittelbar der Erzeugung von Stauplänen. Vermittelt über eine geeignete Repräsentation zulässiger Problemlösungen wird in einer zweiten Verfahrensstufe eine Tabu-Suche durchgeführt. Das TSV berücksichtigt einige praxisrelevante Restriktionen. Die Performance des TSV wird anhand von Benchmarkproblemen aus der Literatur demonstriert, wobei Containerbeladeverfahren verschiedener Autoren zu Vergleichszwecken herangezogen werden.AbstractThe paper presents a tabu search algorithm (TSA) for weakly heterogeneous container loading problems. The approach includes two integrated components: The generation of different stowage plans by means of a greedy algorithm and a tabu search using an appropriate representation of these plans. The TSA considers some restrictions of practical relevance. The overall algorithm has been applied to numerous benchmark problems and its performance is demonstrated by a numerical comparison with several loading procedures suggested by other authors.

Applying Tabu Search to Container Loading Problems

The container loading problem considered here can be formulated as follows: Let a single container be given and a set of three-dimensional rectangular goods, referred to below as boxes. Determine a feasible arrangement of a subset of all boxes in the container in such a way that the stowed box volume is maximized and all additionally required constraints for loading the container are met.

Planning vehicle transhipment in a seaport automobile terminal using a multi-agent system

A multi-agent system (MAS) for supporting the planning of transhipments of imported finished vehicles via a seaport is presented. The focus is on storage allocation, i.e. the allocation of parking areas for the temporary storage of vehicles, and on deployment scheduling, i.e. the allocation of drivers to the vehicles that have to be moved in the terminal area. These planning tasks, which in practice are usually carried out by different operators, are assigned to two different agent types. A further agent, the coordinator agent, is responsible for combining the local sub-plans into an overall plan in such a way that the demand for drivers in the planning period is minimised and balanced. The MAS is tested using randomly generated problem instances with different distributions of the manufacturer shares in the vehicle streams. The tests verify a certain robustness of the MAS with regard to changes in the problem data, in particular to the number of permanently employed drivers and the cost surcharge for hired drivers. In addition, the results highlight that the minimum overall (relative) costs of the drivers depends on the number of permanently employed drivers and on the level of the cost surcharge for hired drivers.

New Large Benchmark Instances for the Two-Dimensional Strip Packing Problem with Rectangular Pieces

Given a set of rectangular pieces and a rectangular container of fixed width and variable length, the two-dimensional strip packing problem (2D-SPP) aims at orthogonally placing all the pieces within the container such that the pieces do not overlap and the total length of the resulting layout is minimized. Up to now, most of the benchmark instances to the 2D-SPP reported in the literature are rather small. In this paper 360 large random-based instances with 1000 pieces each are introduced. Further essential problem-specific parameters such as the number of item types and the quotient of the container width and the mean item dimension are varied in a systematical way. Results for the 360 instances calculated by a recently developed genetic algorithm are also reported and may serve as reference solutions.