Deep Optimisation:Solving Combinatorial Optimisation Problems using Deep Neural Networks

Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully applied to classification, regression, decision and generative tasks and in this paper we extend its application to solving optimisation problems. Model Building Optimisation Algorithms (MBOAs), a branch of evolutionary algorithms, have been successful in combining machine learning methods and evolutionary search but, until now, they have not utilised DNNs. DO is the first algorithm to use a DNN to learn and exploit the problem structure to adapt the variation operator (changing the neighbourhood structure of the search process). We demonstrate the performance of DO using two theoretical optimisation problems within the MAXSAT class. The Hierarchical Transformation Optimisation Problem (HTOP) has controllable deep structure that provides a clear evaluation of how DO works and why using a layerwise technique is essential for learning and exploiting problem structure. The Parity Modular Constraint Problem (MCparity) is a simplistic example of a problem containing higher-order dependencies (greater than pairwise) which DO can solve and state of the art MBOAs cannot. Further, we show that DO can exploit deep structure in TSP instances. Together these results show that there exists problems that DO can find and exploit deep problem structure that other algorithms cannot. Making this connection between DNNs and optimisation allows for the utilisation of advanced tools applicable to DNNs that current MBOAs are unable to use

Holistic, data-driven, service and supply chain optimisation: linked optimisation.

The intensity of competition and technological advancements in the business environment has made companies collaborate and cooperate together as a means of survival. This creates a chain of companies and business components with unified business objectives. However, managing the decision-making process (like scheduling, ordering, delivering and allocating) at the various business components and maintaining a holistic objective is a huge business challenge, as these operations are complex and dynamic. This is because the overall chain of business processes is widely distributed across all the supply chain participants; therefore, no individual collaborator has a complete overview of the processes. Increasingly, such decisions are automated and are strongly supported by optimisation algorithms - manufacturing optimisation, B2B ordering, financial trading, transportation scheduling and allocation. However, most of these algorithms do not incorporate the complexity associated with interacting decision-making systems like supply chains. It is well-known that decisions made at one point in supply chains can have significant consequences that ripple through linked production and transportation systems. Recently, global shocks to supply chains (COVID-19, climate change, blockage of the Suez Canal) have demonstrated the importance of these interdependencies, and the need to create supply chains that are more resilient and have significantly reduced impact on the environment. Such interacting decision-making systems need to be considered through an optimisation process. However, the interactions between such decision-making systems are not modelled. We therefore believe that modelling such interactions is an opportunity to provide computational extensions to current optimisation paradigms. This research study aims to develop a general framework for formulating and solving holistic, data-driven optimisation problems in service and supply chains. This research achieved this aim and contributes to scholarship by firstly considering the complexities of supply chain problems from a linked problem perspective. This leads to developing a formalism for characterising linked optimisation problems as a model for supply chains. Secondly, the research adopts a method for creating a linked optimisation problem benchmark by linking existing classical benchmark sets. This involves using a mix of classical optimisation problems, typically relating to supply chain decision problems, to describe different modes of linkages in linked optimisation problems. Thirdly, several techniques for linking supply chain fragmented data have been proposed in the literature to identify data relationships. Therefore, this thesis explores some of these techniques and combines them in specific ways to improve the data discovery process. Lastly, many state-of-the-art algorithms have been explored in the literature and these algorithms have been used to tackle problems relating to supply chain problems. This research therefore investigates the resilient state-of-the-art optimisation algorithms presented in the literature, and then designs suitable algorithmic approaches inspired by the existing algorithms and the nature of problem linkages to address different problem linkages in supply chains. Considering research findings and future perspectives, the study demonstrates the suitability of algorithms to different linked structures involving two sub-problems, which suggests further investigations on issues like the suitability of algorithms on more complex structures, benchmark methodologies, holistic goals and evaluation, processmining, game theory and dependency analysis

Problem-Based Learning Of Heuristic Methods For Decision Problems In Mathematics, Computer Science And Industrial Engineering

In a digitalized world, most processes can be formalised, measured and described mathematically. The use of analytical methods to optimise such models and decisions constitutes operational research (OR), developing new methods for a specific problem and analysing them are part of discrete optimisation (DO). However, there is limited research on OR and application driven DO in higher education. Furthermore, neither is well integrated into engineering education research. In this work, we present a case study of an interdisciplinary Master’s course on heuristic methods in the context of OR and DO. We discuss to what extent wellestablished approaches from engineering education practice, such as ProblemBased Learning, are applicable. Furthermore, we introduce two practical cases and argue that due to its application-oriented nature, OR and DO specifically stimulate independent student work. Results from evaluations, minute papers and student coursework indicate that the teaching approach successfully contributed to students’ achievement of the intended learning outcomes. To further foster discussion, we not only provide the lecture notes publicly, but also all tutorial and project case data to instructors upon request under a CC BY-NC license