Solving a hard Cutting Stock Problem by machine learning and optimisation

We are working with a company on a hard industrial optimisation problem: a version of the well-known Cutting Stock Problem in which a paper mill must cut rolls of paper following certain cutting patterns to meet customer demands. In our problem each roll to be cut may have a different size, the cutting patterns are semi-automated so that we have only indirect control over them via a list of continuous parameters called a request, and there are multiple mills each able to use only one request. We solve the problem using a combination of machine learning and optimisation techniques. First we approximate the distribution of cutting patterns via Monte Carlo simulation. Secondly we cover the distribution by applying a k-medoids algorithm. Thirdly we use the results to build an ILP model which is then solved

Ant colony optimisation and local search for bin-packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO

A hybrid genetic algorithm for solving a layout problem in the fashion industry.

As of this writing, many success stories exist yet of powerful genetic algorithms (GAs) in the field of constraint optimisation. In this paper, a hybrid, intelligent genetic algorithm will be developed for solving a cutting layout problem in the Belgian fashion industry. In an initial section, an existing LP formulation of the cutting problem is briefly summarised and is used in further paragraphs as the core design of our GA. Through an initial attempt of rendering the algorithm as universal as possible, it was conceived a threefold genetic enhancement had to be carried out that reduces the size of the active solution space. The GA is therefore rebuilt using intelligent genetic operators, carrying out a local optimisation and applying a heuristic feasibility operator. Powerful computational results are achieved for a variety of problem cases that outperform any existing LP model yet developed.Fashion; Industry;

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde

An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approachThis publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/228

A Classification of Hyper-heuristic Approaches

The current state of the art in hyper-heuristic research comprises a set of approaches that share the common goal of automating the design and adaptation of heuristic methods to solve hard computational search problems. The main goal is to produce more generally applicable search methodologies. In this chapter we present and overview of previous categorisations of hyper-heuristics and provide a unified classification and definition which captures the work that is being undertaken in this field. We distinguish between two main hyper-heuristic categories: heuristic selection and heuristic generation. Some representative examples of each category are discussed in detail. Our goal is to both clarify the main features of existing techniques and to suggest new directions for hyper-heuristic research

Modelling and Optimisation of Space Allocation and layout Problems

This thesis investigates the development of optimisation-based, decision-making frameworks for allocation problems related to manufacturing, warehousing, logistics, and retailing. Since associated costs with these areas constitute significant parts to the overall supply chain cost, mathematical models of enhanced fidelity are required to obtain optimal decisions for i) pallet loading, ii) assortment, and iii) product shelf space, which will be the main research focus of this thesis. For the Manufactures Pallet loading problems (MPLP), novel single- and multi-objective Mixed Integer Linear Programming (MILP) models have been proposed, which generate optimal layouts of improved 2D structure based on a block representation. The approach uses a Complexity Index metric, which aids in comparing 2 pallet layouts that share the same pallet size and number of boxes loaded but with different box arrangements. The proposed algorithm has been tested against available data-sets in literature. In the area of Assortments (optimal 2D packing within given containers) , an iterative MILP algorithm has been developed to provide a diverse set of solutions within pre-specified range of key performance metrics. In addition, a basic software prototype, based on AIMMS platform, has been developed using a user-friendly interface so as to facilitate user interaction with a visual display of the solutions obtained. In Shelf- Space Allocation (SSAP) problem, the relationship between the demand and the retailer shelf space allocated to each item is defined as space elasticity. Most of existing literature considers the problem with stationary demand and fixed space elasticities. In this part of the thesis, a dynamic framework has been proposed to forecast space elasticities based on historical data using standard time-series methodologies. In addition, an optimisation mathematical model has been implemented using the forecasted space elasticities to provide the retailer with optimal shelf space thus resulting into closer match between supply and demand and increased profitability. The applicability and effectiveness of the proposed framework is demonstrated through a number of tests and comparisons against literature data-sets