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Multiple-criteria landscapes with valleys and hills

Computer scientists from Leiden University and the University of Münster describe a new theoretical starting point for approaching difficult optimization problems. They can take into account several criteria simultaneously, instead of just one at a time.

Skip expensive trial-and-error

In any industry it is a fact: you cannot optimize all the aspects of your product or production process. You will have to compromise in one way or another. Through trial-and-error, you will find out what works best for you. It might take years, of course. Wouldn’t it be great if a computer could do all kinds of calculations and enable you to skip this long and expensive try-out phase?

Mathematical basis

Theoretical computer scientists from Leiden University are working on the mathematical basis of problems like these, in collaboration with colleagues from Münster. PhD-students Pascal Kerschke from Münster and Hao Wang from the Leiden Institute of Advanced Computer Science (LIACS) presented their research at the most important conference in their field, last week in Edinburgh. Kerschke and Wang won the Best Paper Award.

Defining the features

In their article, Kerschke and Wang elaborate on the landscape of multiple-objective optimization problems, as you would call it in math’s terms. Several optimization criteria are handled at the same time, instead of just one. For the first time, the authors define the features of such problems formally, like the trade-offs and geometrical properties of the search landscape. The high standard of the publication makes it a starting point for future research.

Pareto fronts

A graphical representation of their work looks like an overlay slide of several landscapes with valleys and hills. Each colour represents a multi-peak function with several optima (hills). The hills of different functions are connected by lines, which visualize the trade-offs, or Pareto fronts, that are being considered by the model.

Hao Wang from LIACS: ‘This is mainly theoretical work. We are not proposing new algorithms, instead we focus on understanding fundamental characteristics of such optimization problems. This work is important because it will provide a basis for the design of optimization methods, which you will need once you are in the phase of applications.’

Tata Steel and BMW

Wang’s research is being jointly funded by NWO, Tata Steel and BMW. Wang: ‘There is always something to be improved. For instance, in the process of car parts production, there are typically multiple optimization criteria that are of concern to industrial partners. Like the minimization of production defects and the maximization of throughput.’

Most important conference in the field

Hao Wang and his German colleague presented their paper on the most important conference in their field, the Parallel Problem Solving from Nature 2016. It was held in Edinburgh last month.