Design and Experimental Analysis of Novel Integrated Optimization Methods

Efficient transportation and logistics are important in today?s society. Freight transport contributes to around 10% of the world?s CO2-emissions, and it is not unusual that transportation makes up more than 10% of the product cost. One important factor for achieving more efficient logistics is to select resources and to schedule tasks in the best way possible. Operations research is the field where we study quantitative methods for solving such problems. Mathematical optimization is the most important tool. Decision-making tools for various planning problems are already improving the efficiency of transport and logistics. In AXIOM, strong research groups at NTNU, Molde University College, and SINTEF have collaborated on designing integrated methods combining elements from exact optimization methods, advanced heuristics and heterogeneous computing for solving complex discrete optimization problems. As a main case, we studied the inventory routing problem (IRP). The IRP is very complex, which makes it suitable for the type of design and analyses made in AXIOM. It is also highly relevant industrially, as it merges decision processes of transportation routing and inventory management that traditionally are managed separately. Previous methods have not been sufficient to solve real-life applications of the integrated problem. In Axiom, three PhD Candidates and a postdoctoral researcher have worked full time on developing new integrated solution methods based on mathematical programming, mainly aimed at solving the IRP. The methods developed in AXIOM have produced "world records" on 8 instances of the capacitated vehicle routing problem, more than 200 problem instances from the literature on the IRP, and more than 400 ?world records? on the even more general production routing problem. Further, a new set of benchmark instances for the IRP has been developed, that will enable researchers to benchmark their methods on a richer and more varied instance set for the IRP, than what was previously available. The project has resulted in more than 35 papers in internationally recognized peer reviewed journals, where 16 of them are at the prestigious UHR level 2. The work within the project has also led to more than 25 presentations at scientific conferences world-wide. When exploited by users in industry and the public sector, the optimization methods developed in AXIOM will lead to better efficiency and timeliness in the management of supply chains, and especially those who mix inventory management with distribution by vehicles. Further details regarding the project, its members, and an overview of published papers and results may be found at the project website: http://axiomresearchproject.com/

Through AXIOM, NTNU, HIMOLDE and SINTEF have strengthened their already strong expertise on combinatorial optimization, in particular on rich vehicle routing problems, such as the inventory routing problem (IRP) and the production routing problem. AXIOM designed new, very powerful, solution methods for many variants of the Vehicle Routing Problem. These methods will benefit the research community as the methods developed has raised the bar for the solution quality obtainable by optimization methods for these problems. Further, a new set of benchmark instances for the IRP that will enable researchers to benchmark their methods on a richer and more varied instance set for the problem. When exploited by users in industry and the public sector, the optimization methods developed in AXIOM will lead to better efficiency and timeliness in the management of supply chains, and especially those who mix inventory management with distribution by vehicles.

Our main goal is to move the research frontier considerably in design of novel integrated methods for solving complex discrete optimization problems. The cornerstones are the partners' deep knowledge in exact methods, metaheuristics, and heterogeneous computing. The expected results are innovative methods combining elements from these areas. AXIOM has four workpackages (WPs). WP1 starts from exact methods and analyzes how these methods can be extended and improved using heuristics. WP2 investigates how exact methods are best utilized within a metaheuristic framework. WP3 develops algorithms that fully utilize all processing elements of modern PCs and are flexible and scalable. In WP4 experimental data are collected, analyzed, and synthesized into new knowledge and understanding. The expected methods will be generic, but the inventory routing problem (IRP) is our main case. The IRP is a very complex and challenging problem with many degrees of freedom, which makes it suitable for the type of analyses and developments in AXIOM. It is also highly relevant industrially, as it merges decision processes that traditionally are managed separately. Current methods are not sufficient to solve real-life applications. To increase the benefits of decision support systems, richer problems must be analyzed and solved more efficiently by new methods. The groups at NTNU, Molde University College and SINTEF have a long track record of developing advanced methods to solve real-life optimization problems. They have collaborated in several successful research projects and organized international conferences together. The partners are already world leaders in operations research within maritime transport and form a nationally outstanding group on discrete optimization. Through AXIOM, we shall further strengthen and integrate our work. 3 PhDs and 1 postdoc will be recruited. International networks will be enhanced through workshops, visiting researchers, and joint publication.