Grzegorz Pawlak

A Parallel Branch-and-Bound Approach to the Rectangular Guillotine Strip Cutting Problem

This paper presents a parallel branch-and-bound method to address the two-dimensional rectangular guillotine strip cutting problem. Our paper focuses on a parallel branching schema. We present a series of computational experiments to evaluate the strength of the approach. Optimal solutions have been found for some benchmark instances that had unknown solutions until now. For many other instances, we demonstrate that the proposed approach is time effective. The efficiency of the parallel version of the algorithm is compared and the speedup, when increasing the number of processors, is clearly demonstrated with an upper bound calculated by a specialised heuristic procedure.

An integrated model for the transshipment yard scheduling problem

A hub-and-spoke railway system is an efficient way of handling freight transport by land. A modern rail–rail train yard consists of huge gantry cranes that move the containers between the trains. In this context, we consider a rail–rail transshipment yard scheduling problem (TYSP) where the containers arrive to the hub and need to be placed on a train that will deliver them to their destination. In the literature, the problem is decomposed hierarchically into five subproblems, which are solved separately. First, the trains have to be grouped into bundles in which they visit the yard. Next, the trains have to be assigned to tracks within these bundles, namely parking positions. Then the final positions for the containers on trains have to be determined. Next, the container moves that need to be performed are assigned to the cranes. Finally, these moves have to be sequenced for each crane for processing. In this paper, an integrated MILP model is proposed, which aims to solve the TYSP as a single optimization problem. The proposed formulation also enables us to define more robust and complex objective functions that include key characteristics from each of the above-mentioned subproblems. The strength of our proposed formulation is demonstrated via computational experiments using the data from the literature. Indeed, the results show that the TYSP can be solved without the use of decomposition techniques and more insight can be obtained from the same input data used to solve particular single decomposed subproblems.

Five phase and genetic hive hyper-heuristics for the cross-domain search

In this paper we present two hyper-heuristics: Five Phase Approach (5Ph) and Genetic Hive (GH), developed for the Cross-Domain Heuristic Search Challenge held in 2011. Performance of both methods is studied. Experience gained in construction of the hyper-heuristics is presented. Conclusions and recommendations for the future advancement of hyper-heuristic methodologies are discussed.

Mind the gap: A study of Tube tour

The problem considered in this paper can be expressed as a question: Is it possible to visit all Tube lines in a day? This is a new type of combinatorial optimization problem which generalizes classic problems like TSP, set cover. It has similarities with classic combinatorial optimization problems and ties with operations research applications. We call the graphs corresponding to the city railway systems subway graphs. Examples and properties of such graphs are described in the paper. We show that our problem is NP-hard. Algorithms solving the problem are proposed and their performance is studied both analytically and experimentally on transportation networks of several big cities of the world.

Grid branch-and-bound for permutation flowshop

Flowshop is an example of a classic hard combinatorial problem. Branch-and-bound is a technique commonly used for solving such hard problems. Together, the two can be used as a benchmark of maturity of parallel processing environment. Grid systems pose a number of hurdles which must be overcome in practical applications. We give a report on applying parallel branch-and-bound for flowshop in grid environment. Methods dealing with the complexities of the environment and the application are proposed, and evaluated.

Scheduling production tasks in a two-stage FMS

The paper is concerned with construction of a heuristic algorithm for an existing two-machine FMS. The system contains two dedicated machines with an automatic transport system served by one robot. There are three storage places: unlimited input and output buffers and a limited transitional one. The jobs are grouped into batches of identical parts. The parts are produced in a flow shop production environment. The parameters like release dates and set-up times for batches are taken into account. Furthermore, some of the parts need an additional operation processed by cooperatives between the first and second operation of the job. The heuristic algorithm has been constructed for the makespan criterion. Appropriate computational experiments validated the model and the algorithm proposed.

Fast truck-packing of 3D boxes

Abstract We present formulation and heuristic solution of a container packing problem observed in a household equipment factory’s sales and logistics department. The main feature of the presented MIP model is combining several types of constraints following from the considered application field. The developed best-fit heuristic is tested on the basis of a computational experiment. The obtained results show that the heuristic is capable of constructing good solutions in a very short time. Moreover, the approach allows easy adjustment to additional loading constraints.

Complexity of Scheduling Problem in Single-Machine Flexible Manufacturing System with Cyclic Transportation and Unlimited Buffers

The paper concerns complexity studies on the scheduling problem arising in a simple flexible manufacturing system. The system consists of a single machine, one depot (both with unlimited buffers), and one vehicle (automated guided vehicle). The vehicle operates according to the regular metro strategy. This means that it travels in cycles of the constant length, without stops, transporting at most one job at a time between the depot and the machine. The machine executes available jobs in the non-preemptive way. The goal is to minimize the schedule length, i.e., to minimize the number of vehicle cycles necessary to transport and execute all jobs in the system. We prove the strong NP-hardness of this problem and show that any list algorithm has the worst-case performance ratio equal to 2. Moreover, we mention that special cases of the considered problem, with zero transportation times from the depot to the machine and from the machine to the depot, are polynomially solvable.

Mind the gap: a heuristic study of subway tours

What is the minimum tour visiting all lines in a subway network? In this paper we study the problem of constructing the shortest tour visiting all lines of a city railway system. This combinatorial optimization problem has links with the classic graph circuit problems and operations research. A broad set of fast algorithms is proposed and evaluated on simulated networks and example cities of the world. We analyze the trade-off between algorithm runtime and solution quality. Time evolution of the trade-off is also captured. Then, the algorithms are tested on a range of instances with diverse features. On the basis of the algorithm performance, measured with various quality indicators, we draw conclusions on the nature of the above combinatorial problem and the tacit assumptions made while designing the algorithms.

Scheduling Tasks and Vehicles in FMSs — Network Flow Model

A problem of simultaneous task scheduling and vehicle routing in a flexible flow shop, is considered. The problem of finding a feasible vehicle schedule for the given machine schedule is reduced to the one of finding a maximum flow in the a three-partite network. On the other hand, if a minimum number of vehicles is looked for, then the problem must be reduced to the one of finding maximal flow of a minimum cost in the network with irregular cost function.