New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractOptimal control of dynamic econometric models has a wide variety of applications including economic policy relevant issues. There are several algorithms extending the basic case of a linear-quadratic optimization and taking nonlinearity and stochastics into account, but being still limited in a variety of ways, e.g., symmetry of the objective function and identical data frequencies of control variables. To overcome these problems, an alternative approach based on heuristics is suggested. To this end, we apply a 'classical' algorithm (OPTCON) and a heuristic approach (Differential Evolution) to three different econometric models and compare their performance. In this paper we consider scenarios of symmetric and asymmetric quadratic objective functions. Results provide a strong support for the heuristic approach encouraging its further application to optimum control problems.

Optimal policy identification: Insights from the German electricity market

“…37 Our ABM is written in R. A single restart of the ABM for the parameter setting stated requires from 6 to 30 seconds using R 3.1.1 and Pentium IV 3.3 GHz (depending on the policy mix and planning DE is a population-based optimisation technique for continuous objective functions and only few tuning parameters to initialise (Blueschke et al, 2013). In short, starting with an initial population of random solutions (line 2 in Algorithm 1), DE updates this population by linear combination (line 7) and crossover (line 9) of four different solution vectors into one, and selects the fittest solutions among the original and the updated population.…”

“…Based on the tuning exercise described in (Blueschke et al, 2013, p. 825-826), p = 10 × K, the shrinkage parameter F is set to 0.8, while the crossover rate CR = 0.3. A detailed discussion on how DE can be applied and tuned for optimal control problems is provided in Blueschke et al (2013).…”

“…Again, in line with Blueschke et al (2013), we set an upper limit on the number of DE generations to be performed within one restart (G max equal to 500), but at the same time control for convergence within the population by looking on the candidates' objective values. In particular, DE algorithm stops if 50% of solutions in the population reach a deviation less then 10 −9 from the best solution available.…”

Solving Nonlinear Stochastic Optimal Control Problems Using Evolutionary Heuristic Optimization

“…In a recent work by Blueschke et al (2013a) a new way of handling optimal control problems is analyzed. The authors test an evolutionary (so-called heuristic) approach for this purpose, namely Differential Evolution (DE, Storn and Price (1997)), which does not rely on LQ framework.…”

“…In particular, some better approximations of the targets stated by policy makers are achieved. However, the work by Blueschke et al (2013a) is designed to deterministic problems only. The present study extends this methodology and analyses the application of DE for stochastic problems.…”