Optimization as an Analysis Tool for Human Complex Problem Solving

Abstract

Abstract. We present a problem class of mixed-integer nonlinear programs (MINLPs) with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving. In a round-based scenario participants hold an executive function. A posteriori a performance indicator is calculated and correlated to personal measures such as intelligence, working memory, or emotion regulation. Altogether, we investigate 2088 optimization problems that differ in size and initial conditions, based on real-world experimental data from 12 rounds of 174 participants. The goals are twofold. First, from the optimal solutions we gain additional insight into a complex system, which facilitates the analysis of a participant's performance in the test. Second, we propose a methodology to automatize this process by providing a new criterion based on the solution of a series of optimization problems. By providing a mathematical optimization model and this methodology, we disprove the assumption that the "fruit fly of complex problem solving," the Tailorshop scenario that has been used for dozens of published studies, is not mathematically accessible-although it turns out to be extremely challenging even for advanced state-of-the-art global optimization algorithms and we were not able to solve all instances to global optimality in reasonable time in this study. The publicly available computational tool Tobago [TOBAGO web site https://sourceforge.net/ projects/tobago] can be used to automatically generate problem instances of various complexity, contains interfaces to AMPL and GAMS, and is hence ideally suited as a testbed for different kinds of algorithms and solvers. Computational practice is reported with respect to the influence of integer variables, problem dimension, and local versus global optimization with different optimization codes.

A decomposition approach for a new test-scenario in complex problem solving

“…Based on the experience with the original Tailorshopmicroworld described in [13] with modeling oddities, bugs, and other undesirable properties, we decided to continue our work with a mathematical model developed from scratch.…”

“…To measure performance within the Tailorshop microworld, different indicator functions have been proposed in the literature, see [11] for a recent review. In [12,13] the question how to get a reliable performance indicator for the Tailorshop microworld has been addressed. Because all previously used indicators have unknown reliability and validity, decisions are compared to mathematically optimal solutions.…”

“…The result can be used in different ways to cope with questions like how to measure performance in complex environments in an objective way and how to determine decisions which were critical for the overall performance of a participant. This technique is described in detail in [13].…”

“…However, solving (1) to proven global optimality is already a challenging task. The novel methodological approach has also been combined with experimental studies [6,7,13].…”

“…To our knowledge, a systematic development of CPS microworlds based on a mathematical model, sensitivity analysis, and eventually optimization methods to choose parameters that lead to a wanted behavior of the complex system for all possible trajectories has not yet been applied. As an example for the need to do this, the mathematical modeling of the Tailorshop microworld in [13] led to the discovery of a priori unwanted and unrealistic winning strategies (e.g., the vans bug).…”