Applied Soft Computing 5 (2004) 35–44 Solving nonconvex climate control problems: pitfalls and algorithm performances Carmen G. Moles a , Julio R. Banga a,∗ , Klaus Keller b a Process Engineering Group, Instituto de Investigaciones, Marinas (CSIC), 36208 Vigo, Spain b Department of Geosciences, The Pennsylvania State University, 16802-2714 University Park, PA, USA Received 20 January 2003; received in revised form 17 March 2004; accepted 23 March 2004 Abstract Global optimization can be used as the main component for reliable decision support systems. In this contribution, we explore numerical solution techniques for nonconvex and nondifferentiable economic optimal growth models. As an illustrative example, we consider the optimal control problem of choosing the optimal greenhouse gas emissions abatement to avoid or delay abrupt and irreversible climate damages. We analyze a number of selected global optimization methods, including adaptive stochastic methods, evolutionary computation methods and deterministic/hybrid techniques. Differential evolution (DE) and one type of evolution strategy (SRES) arrived to the best results in terms of objective function, with SRES showing the best convergence speed. Other simple adaptive stochastic techniques were faster than those methods in obtaining a local optimum close to the global solution, but mis-converged ultimately. © 2004 Elsevier B.V. All rights reserved. Keywords: Global optimization; Optimal control; Climate thresholds 1. Introduction The optimization of dynamic systems is an impor- tant class of problems arising in most scientific and engineering areas. In fact, optimal control problems are the subject of many research efforts in fields such as economics, physics, and virtually all engineering branches, with problems ranging from optimal tra- jectory determination for spaceships to the computa- tion of optimal operating policies for chemical plants. The objective of optimal control is to find a set of control variables (which are functions of time) in or- ∗ Corresponding author. Fax: +34-98-629-2762. E-mail addresses: cmoles@iim.csic.es (C.G. Moles), julio@iim.csic.es (J.R. Banga), kkeller@geosc.psu.edu (K. Keller). der to maximize the performance of a given dynamic system, as measured by some functional, and all this subject to a set of path constraints. The dynamics of most systems are usually described in terms of dif- ferential equations or, as in this paper, equations in differences. The task of identifying an economically efficient cli- mate policy has been interpreted as an optimal control problem [31,26]. In this framework, an optimal cli- mate policy is interpreted as a schedule of investments into reducing (abating) carbon dioxide emissions that maximized the net benefits. Unabated carbon diox- ide (CO 2 ) emissions cause global climate change that, in turn, results in economic damages. Abating carbon dioxide emissions reduces global climate change and the resulting economic damages. The task of the opti- 1568-4946/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2004.03.011