Mathematical models and decomposition methods for the multiple knapsack problem

We consider the multiple knapsack problem, that calls for the optimal assignment of a set of items, each having a profit and a weight, to a set of knapsacks, each having a maximum capacity. The problem has relevant managerial implications and is known to be very difficult to solve in practice for instances of realistic size. We review the main results from the literature, including a classical mathematical model and a number of improvement techniques. We then present two new pseudo-polynomial formulations, together with specifically tailored decomposition algorithms to tackle the practical difficulty of the problem. Extensive computational experiments show the effectiveness of the proposed approaches

A Novel Multi-objective Optimisation Algorithm for Routability and Timing Driven Circuit Clustering on FPGAs

Circuit clustering algorithms fit synthesised circuits into FPGA configurable logic blocks (CLBs) efficiently. This fundamental process in FPGA CAD flow directly impacts both effort required and performance achievable in subsequent place-and-route processes. Circuit clustering is limited by hardware constraints of specific target architectures. Hence, better circuit clustering approaches are essential for improving device utilisation whilst at the same time optimising circuit performance parameters such as, e.g., power and delay. In this paper, we present a method based on multi-objective genetic algorithm (MOGA) to facilitate circuit clustering. We address a number of challenges including CLB input bandwidth constraints, improvement of CLB utilisation, minimisation of interconnects between CLBs. Our new approach has been validated using the "Golden 20" MCNC benchmark circuits that are regularly used in FPGA-related literature. The results show that the method proposed in this paper achieves improvements of up to 50% in clustering, routability and timing when compared to state-of-the-art approaches including VPack, T-VPack, RPack, DPack, HDPack, MOPack and iRAC. Key contribution of this work is a flexible EDA flow that can incorporate numerous objectives required to successfully tackle real-world circuit design on FPGA, providing device utilisation at increased design performance

Rapid prototyping of distributed systems of electronic control units in vehicles

Existing vehicle electronics design is largely divided by feature, with integration taking place at a late stage. This leads to a number of drawbacks, including longer development time and increased cost, both of which this research overcomes by considering the system as a whole and, in particular, generating an executable model to permit testing. To generate such a model, a number of inputs needed to be made available. These include a structural description of the vehicle electronics, functional descriptions of both the electronic control units and the communications buses, the application code that implements the feature and software patterns to implement the low-level interfaces to sensors and actuators. [Continues.

The 0 -1 multiple knapsack problem

In operation research, the Multiple Knapsack Problem (MKP) is classified as a combinatorial optimization problem. It is a particular case of the Generalized Assignment Problem. The MKP has been applied to many applications in naval as well as financial management. There are several methods to solve the Knapsack Problem (KP) and Multiple Knapsack Problem (MKP); in particular the Bound and Bound Algorithm (B&B). The bound and bound method is a modification of the Branch and Bound Algorithm which is defined as a particular tree-search technique for the integer linear programming. It has been used to obtain an optimal solution. In this research, we provide a new approach called the Adapted Transportation Algorithm (ATA) to solve the KP and MKP. The solution results of these methods are presented in this thesis. The Adapted Transportation Algorithm is applied to solve the Multiple Knapsack Problem where the unit profit of the items is dependent on the knapsack. In addition, we will show the link between the Multiple Knapsack Problem (MKP) and the multiple Assignment Problem (MAP). These results open a new field of research in order to solve KP and MKP by using the algorithms developed in transportation.Master of Science (MSc) in Computational Scienc

Identical parallel machine scheduling problems: structural patterns, bounding techniques and solution procedures

The work is about fundamental parallel machine scheduling problems which occur in manufacturing systems where a set of jobs with individual processing times has to be assigned to a set of machines with respect to several workload objective functions like makespan minimization, machine covering or workload balancing. In the first chapter of the work an up-to-date survey on the most relevant literature for these problems is given, since the last review dealing with these problems has been published almost 20 years ago. We also give an insight into the relevant literature contributed by the Artificial Intelligence community, where the problem is known as number partitioning. The core of the work is a universally valid characterization of optimal makespan and machine-covering solutions where schedules are evaluated independently from the processing times of the jobs. Based on these novel structural insights we derive several strong dominance criteria. Implemented in a branch-and-bound algorithm these criteria have proved to be effective in limiting the solution space, particularly in the case of small ratios of the number of jobs to the number of machines. Further, we provide a counter-example to a central result by Ho et al. (2009) who proved that a schedule which minimizes the normalized sum of squared workload deviations is necessarily a makespan-optimal one. We explain why their proof is incorrect and present computational results revealing the difference between workload balancing and makespan minimization. The last chapter of the work is about the minimum cardinality bin covering problem which is a dual problem of machine-covering with respect to bounding techniques. We discuss reduction criteria, derive several lower bound arguments and propose construction heuristics as well as a subset sum-based improvement algorithm. Moreover, we present a tailored branch-and-bound method which is able to solve instances with up to 20 bins

Applying computational intelligence to a real-world container loading problem in a warehouse environment

One of the problems presented in the day-to-day running of a warehouse is that of optimally selecting and loading groups of heavy rectangular palletised goods into larger rectangular containers while satisfying a number of practical constraints. The research presented in this thesis was commissioned by the logistics department in NSK Europe Ltd, for the purpose of providing feasible solutions to this problem. The problem is a version of the Container Loading Problem in the literature, and it is an active research area with many practical applications in industry. Most of the advances made in this area focus more on the optimisation of container utility i.e. volume or weight capacity, with very few focusing on the practical feasibility of the loading layout or pattern produced. Much of the work done also addresses only a few practical constraints at a time, leaving out a number of constraints that are of importance in real-world container loading. As this problem is well known to be a combinatorial NPhard problem, the exact mathematical methods that exist for solving it are computationally feasible for only problem instances with small sizes. For these reasons, this thesis investigates the use of computational intelligence techniques for solving and providing near-optimum solutions to this problem while simultaneously satisfying a number of practical constraints that must be considered for the solutions provided to be feasible. In proposing a solution to this problem and dealing with all the constraints considered, an algorithmic framework that decomposes the CLPs into sub-problems is presented. Each subproblem is solved using an appropriate algorithm, and a combination of constraints particular to each problem is satisfied. The resulting hybrid algorithm solves the entire problem as a whole and satisfies all the considered constraints. In order to identify and select feasible container layouts that are practical and easy to load, a measure of disorder, based on the concept of entropy in physics and information theory, is derived. Finally, a novel method of directing a Monte-Carlo tree search process using the derived entropy measure is employed, to generate loading layouts that are comparable to those produced by expert human loaders. In summary, this thesis presents a new approach for dealing with real-world container loading in a warehouse environment, particularly in instances where layout complexity is of major importance; such as the loading of heavy palletised goods using forklift trucks. The approach can be used to deal with a number of relevant practical constraints that need to be satisfied simultaneously, including those encountered when the heavy goods are arranged and physically packed into a container using forklift trucks

Bincompletion algorithms for multicontainer packing, knapsack, and covering problems

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogood-based pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, min-cost covering, and bin packing. We show that our bin completion algorithms yield new, state-of-the-art results for the multiple knapsack, bin covering, and min-cost covering problems, outperforming previous algorithms by several orders of magnitude with respect to runtime on some classes of hard, random problem instances. For the bin packing problem, we demonstrate significant improvements compared to most previous results, but show that bin completion is not competitive with current state-of-the-art cutting-stock based approaches. 1