A heuristic for solving the irregular strip packing problem with quantum optimization

We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal pieces within a fixed-height, rectangular container to minimize waste. Traditional methods heavily rely on manual optimization by specialists, highlighting the complexity and computational difficulty of achieving quasi-optimal layouts. The proposed algorithm employs a quantum-inspired heuristic that decomposes the strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem. This strategy facilitates a novel application of quantum computing to industrial optimization, aiming to minimize waste and enhance material efficiency. Experimental evaluations using both classical and quantum computational methods demonstrate the algorithm's efficacy. We evaluate the algorithm's performance using the quantum approximate optimization algorithm and the quantum alternating operator ansatz, through simulations and real quantum computers, and compare it to classical approaches.Comment: 30 pages, 12 figure

A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results

Optimal Packing of Irregular 3D Objects For Transportation and Disposal

This research developed algorithms, platforms, and workflows that can optimize the packing of 3D irregular objects while guaranteeing an acceptable processing time for real-life problems, including but not limited to nuclear waste packing optimization. Many nuclear power plants (NPPs) are approaching their end of intended design life, and approximately half of existing NPPs will be shut down in the next two decades. Since decommissioning and demolition of these NPPs will lead to a significant increase in waste inventory, there is an escalating demand for technologies and processes that can efficiently manage the decommissioning and demolition (D&D) activities, especially optimal packing of NPP waste. To minimize the packing volume of NPP waste, the objective is to arrange irregular-shaped waste objects into one or a set of containers such that container volume utilization is maximized, or container size is minimized. Constraints also include weight and radiation limits per container imposed by transportation requirements and the waste acceptance requirements of storage facilities and repositories. This problem falls under the theoretical realm of cutting and packing problems, precisely, the 3D irregular packing problem. Despite its broad applications and substantial potential, research on 3D irregular cutting and packing problems is still nascent, and largely absent in construction and civil engineering. Finding good solutions for real-life problems, such as the one mentioned above, through current approaches is computationally expensive and time-consuming. New algorithms and technologies, and processes are required. This research adopted 3D scanning as a means of geometry acquisition of as-is 3D irregular objects (e.g., nuclear waste generated from decommissioning and demolition of nuclear power plants), and a metaheuristics-based packing algorithm is implemented to find good packing configurations. Given the inefficiency of fully autonomous packing algorithms, a virtual reality (VR) interactive platform allowing human intervention in the packing process was developed to decrease the time and computation power required, while potentially achieving better outcomes. The VR platform was created using the Unity® game engine and its physics engine to mimic real-world physics (e.g., gravity and collision). Validation in terms of feasibility, efficiency, and rationality of the presented algorithms and the VR platform is achieved through functional demonstration with case studies. Different optimal packing workflows were simulated and evaluated in the VR platform. Together, these algorithms, the VR platform, and workflows form a rational and systematic framework to tackle the optimal packing of 3D irregular objects in civil engineering and construction. The overall framework presented in this research has been demonstrated to effectively provide packing configurations with higher packing efficiency in an adequate amount of time compared to conventional methods. The findings from this research can be applied to numerous construction and manufacturing activities, such as optimal packing of prefabricated construction assemblies, facility waste management, and 3D printing

Metaheuristics For Solving Real World Employee Rostering and Shift Scheduling Problems

Optimising resources and making considerate decisions are central concerns in any responsible organisation aiming to succeed in efficiently achieving their goals. Careful use of resources can have positive outcomes in the form of fiscal savings, improved service levels, better quality products, improved awareness of diminishing returns and general output efficiency, regardless of field. Operational research techniques are advanced analytical tools used to improve managerial decision-making. There have been a variety of case studies where operational research techniques have been successfully applied to save millions of pounds. Operational research techniques have been successfully applied to a multitude of fields, including agriculture, policing, defence, conservation, air traffic control, and many more. In particular, management of resources in the form of employees is a challenging problem --- but one with the potential for huge improvements in efficiency. The problem this thesis tackles can be divided into two sub-problems; the personalised shift scheduling & employee rostering problem, and the roster pattern problem. The personalised shift scheduling & employee rostering problem involves the direct scheduling of employees to hours and days of week. This allows the creation of schedules which are tailored to individuals and allows a fine level over control over the results, but with at the cost of a large and challenging search space. The roster pattern problem instead takes existing patterns employees currently work, and uses these as a pool of potential schedules to be used. This reduces the search space but minimises the number of changes to existing employee schedules, which is preferable for personnel satisfaction. Existing research has shown that a variety of algorithms suit different problems and hybrid methods are found to typically outperform standalone ones in real-world contexts. Several algorithmic approaches for solving variations of the employee scheduling problem are considered in this thesis. Initially a VNS approach was used with a Metropolis-Hastings acceptance criterion. The second approach utilises ER&SR controlled by the EMCAC, which has only been used in the field of exam timetabling, and has not before been used within the domain of employee scheduling and rostering. ER&SR was then hybridised with our initial approach, producing ER&SR with VNS. Finally, ER&SR was hybridised into a matheuristic with Integer Programming and compared to the hybrid's individual components. A contribution of this thesis is evidence that the algorithm ER&SR has merit outside of the original sub-field of exam scheduling, and can be applied to shift scheduling and employee rostering. Further, ER&SR was hybridised and schedules produced by the hybridisations were found to be of higher quality than the standalone algorithm. In the literature review it was found that hybrid algorithms have become more popular in real-world problems in recent years, and this body of work has explored and continued this trend. Problem formulations in this thesis provide insight into creating constraints which satisfy the need for minimising employee dissatisfaction, particularly in regards to abrupt change. The research presented in this thesis has positively impacted a multinational and multibillion dollar field service operations company. This has been achieved by implementing a variety of techniques, including metaheuristics and a matheuristic, to schedule shifts and roster employees over a period of several months. This thesis showcases the research outputs by this project, and highlights the real-world impact of this research

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order