Robust Bicriteria Optimisation


Speaker


Abstract

Optimisation models and techniques are an important and powerful problem solving tool.   However, many challenges arise when modelling and solving real-world problems as mathematical optimisation problems. 

This talk focuses on two of these challenges:

  • uncertainty in the problem parameters, e.g.,  due to unpredictable weather influences, incomplete information, or varying demand,
  • and the presence of several, possibly conflicting goals like profit, customer satisfaction, and impacts on the environment

Both of these challenges have been addressed separately: In stochastic, robust, and online optimisation. Various definitions of solution quality and methods to find 'good' solutions in case of  uncertain problem parameters have been developed.

Multicriteria decision making introduced the concept of efficient (or: Pareto-optimal) solutions to illustrate the trade-off in the compliance of different goals and offers several methods to identify efficient solutions.

However, few attempts have been made to combine both paradigms.

This talk introduces the concept of robust bicriteria optimisation. We illustrate different ways to extend the concept of efficiency to the case of one uncertain objective function using examples from aircraft routing and transportation of hazardous material, discuss relations between the concepts and sketch solution approaches based on methods for multicriteria optimisation.