A Field-Based Benchmark

Abstract

The definition of test problems is important for the development of methods and algorithms for field inversion. In the middle nineties of last century a first group of benchmarks was proposed, focusing on inverse magnetostatics (e.g. SMES device, and Die press by the TEAM Workshop series (www-igte.tu-graz.ac.at/team), Loney solenoid by the University of Pavia (Di Barba et al. 1995). All these benchmarks were characterised by either a single objective or by the scalar formulation of a two-objective problem; consequently, the application of numerical procedures gave rise to a single solution, that was supposed to be the optimum. An attempt to introduce Paretian optimality in the TEAM benchmark about SMES device optimisation can be found in (Alotto et al. 2008).

In general, comparison among various algorithms is obtained in terms of classical indicators of performance; they include runtime, number of local minima identified, value of the global minimum found numerically, number of function evaluations, stopping criteria, success rate and so forth (Locatelli and Wood 2005; Khompatraporn et al. 2005). Some less obvious indicators of performance refer to the tuning parameters featuring the optimisation algorithm (e.g. the mutation rate in genetic algorithms). Nevertheless, a discussion about, e.g. the dual role of objective and constraints, the effect of their exchange on the solution, or the importance of ‘hidden’ objectives like sensitivity of the minimum found, is usually overlooked.