Robust multi-objective optimization in networks
(Topic B.3)
– The usage of wood is diverse: building material, cellulose, energy,... What to produce out of a piece of wood considering different (conflicting) objectives while quality and demands are uncertain? –
The utilization possibilities of wood are diverse, including its use as a raw material and as a source for energy or for chemical substances like cellulose. The development of new processing methods, for example to combine wood with plastic to wood plastic composites, and improvements in recycling processes lead to even more utilization options. One possibility to try to maximize the resource efficiency is to apply cascading utilization, in which wood is for example first used as a building material and later as an energy source. But which processing steps should a piece of wood go through for a "best possible" utilization, regarding resource efficiency, environmental friendliness and profitability?
One aspect of this doctoral project is to develop a network model in which the utilization of wood resources can be optimized regarding different objectives, particularly the ones mentioned above: the amount of consumed resources, the environmental impact and the profitability for the involved companies. Since multiple objectives are to consider and aspects like production costs, demands and the amount and quality of the available resources are uncertain, this will lead to an uncertain multi-objective network problem.
In multi-objective optimization several objective functions are considered, which may contradict each other. The aim is to find so called Pareto optimal solutions, where no objective can be improved without worsening another one. Robust optimization is, beside stochastic optimization, one way to consider uncertainties given in constraints or objective functions of an optimization problem. It aims to hedge against all possible scenarios without assuming any information on the stochastic distribution.
Only recently have concepts of those two fields been combined to multi-objective robust optimization and different notions of multi-objective robustness have been developed.
In this doctoral project network problems like the shortest path problem and the minimum cost flow problem are considered for multiple objectives and given uncertainties. Its purpose is to analyze their multi-objective robust counterparts, to develop solution approaches and to apply those to the resource utilization model described above. We consider different concepts of multi-object robustness and different types of uncertainty sets. We analyze, if algorithms for the multi-objective cases without uncertainties and for the one-criterial robust counterparts can be enhanced to find robust solutions for multiple objectives and search also for new methods.
For the application of the developed methods on resource utilization networks a close cooperation with experts on forestry and economics is important. Uncertain and multi-objective problems also occur in other projects of this research training group and might be further applications for our concepts and solution approaches.