Category Optimization

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Journal Articles

Robust strategies for managing rangelands with multiple stable attractors

Janssen, M.A., J.M. Anderies and B.H. Walker

2004 Journal of Environmental Economics and Management 47(1):140-162.


Savanna rangelands are characterized by dynamic interactions between grass, shrubs, fire and livestock driven by highly variable rainfall. When the livestock are grazers (only or preferentially eating grass) the desirable state of the system is dominated by grass, with scattered trees and shrubs. However, the system can have multiple stable attractors and a perturbation such as a drought can cause it to move from such a desired configuration into one that is dominated by shrubs with very little grass. In this paper, using the rangelands of New South Wales in Australia as an example, we provide a methodology to find robust management strategies in the context of this complex ecological system driven by stochastic rainfall events. The control variables are sheep density and the degree of fire suppression. By comparing the optimal solution where it is assumed the manager has perfect knowledge and foresight of rainfall conditions with one where the rainfall variability is ignored, we found that rainfall variability and the related uncertainty lead to a reduction of the possible expected returns from grazing activity by 33%. Using a genetic algorithm, we develop robust management strategies for highly variable rainfall that more than doubles expected returns compared to those obtained under variable rainfall using an optimal solution based on average rainfall (i.e., where the manager ignores rainfall variability).

Our analysis suggests some key features of a robust strategy. The robust strategy is precautionary and is forced by rainfall variability. It is less reactive with respect to grazing pressure changes and more reactive with respect to fire suppression than is an optimum strategy based on a deterministic system (no rainfall variability). Finally, the costs associated with implementing a robust strategy are far less than the expected economic losses when uncertainty is not taken into account.

Keywords: Rangelands; Multiple stable states; Robust management; Genetic algorithms


Sequential optimization of integrated climate change models

Janssen, M.A.

2001 Mathematics and Computers in Simulation 54(6): 477-489.


A sequential optimization approach is applied to optimize the behavior of a complex dynamical system. It sequentially solves a large set of mathematical equations and next optimizes the behavior of a reduced-system, fixing certain variables of the larger original problem. These two steps are repeated till convergence occurs. The approach is applied to the problem of identifying response strategies for climate change caused by antropogenic emissions of different trace gases. The convergence properties are analyzed for this example.

Keywords: Sequential optimization; Sequential reduced-system programming; Dynamical system.


Climate change policy targets and the role of technological change

Janssen, M.A. and H.J.M. de Vries

2000 Climatic Change 46 (1/2): 1-28.


In this paper, we present results of simulationexperiments with the TIME-model on the issue ofmitigation strategies with regard to greenhouse gases.The TIME-model is an integrated system dynamics worldenergy model that takes into account the fact that the systemhas an inbuilt inertia and endogenouslearning-by-doing dynamics, besides the more commonelements of price-induced demand response and fuelsubstitution. First, we present four scenarios tohighlight the importance of assumptions on innovationsin energy technology in assessing the extent to whichCO2 emissions have to be reduced. The inertia ofthe energy system seems to make a rise ofCO2 emissions in the short term almostunavoidable. It is concluded that for the populationand economic growth assumptions of the IPCC IS92ascenario, only a combination of supply- anddemand-side oriented technological innovations incombination with policy measures can bring the targetof CO2-concentration stabilization at 550 ppmv bythe year 2100 within reach. This will probably beassociated with a temporary increase in the overallenergy expenditures in the world economy. Postponingthe policy measures will be more disadvantageous,and less innovation in energy technology will happen.


Optimization of a non-linear dynamical system for global climate change

Janssen, M.A.

1997 European Journal of Operations Research 99(2): 322-335.


We regard the global climate system as a controlled dynamic system, with controls corresponding to economic activities causing emissions of greenhouse gases. Previous optimization studies for climate change have used descriptions of the environmental system which are found to be too unrepresentative of what is known in the scientific community. In this paper an approach is applied which tries to include a more sophisticated model of the environmental system. The resulting continuous dynamic control problem is solved by the application of a set of non-linear optimization techniques to find optimal response strategies to maximize the discounted sum of future consumption while adhering to certain environmental constraints.

Keywords: Non-linear optimization; CO2; Climate change.


Climate change: optimization of response strategies

Janssen, M.A., J. Rotmans, and O.J. Vrieze

1995 International Transactions in Operational Research 2(1): 1-15.


The development of climate change response strategies is expected to remain an important issue in the next few decades. The use of optimization techniques might serve as a helpful guide in this process. Although, in recent years, a number of studies have focused on optimization techniques, the optimization models do not fully employ the dynamics of climatic and economic systems. In this paper a heuristic is introduced that combines an integrated simulation model and an optimization technique (local search). This approach may be considered as a first step towards a more comprehensive and systematic analysis of climate change response strategies in a dynamic setting described by a simulation model. Results of a number of experiments in which the heuristic is applied to the integrated global assessment model TARGETS are discussed.


Book Chapters

An application of optimization to the problem of climate change

Filar, J.A., P.S. Gaertner and M.A. Janssen

1996 In State of the Art in Global Optimization: Computational Methods and Applications, edited by C.A. Floudas and P.M. Pardalos, pp. 475-498, Kluwer Academic Publishers, Dordrecht/Boston/London.


The objective of this paper is to demonstrate a methodology whereby reductions of greenhouse gas emissions can be allocated on a regional level with minimal deviation from the “business as usual emission scenario”. The methodology developed employs a two stage optimization process utilizing techniques of mathematical programming. The stage one process solves a world emission reduction problem producing an optimal emission reduction strategy for the world by maximizing an economic utility function. Stage two addresses a regional emission reduction allocation problem via the solution of an auxiliary optimization problem minimizing disruption from the above business as usual emission strategies. Our analysis demonstrates that optimal CO2 emission reduction strategies are very sensitive to the targets placed on CO2 concentrations, in every region of the world. It is hoped that the optimization analysis will help decision-makers narrow their debate to realistic environmental targets.



Allocating CO2-Emissions by Using Equity Rules and Optimization

Janssen, M.A., M.G.J. den Elzen and J. Rotmans
1992 RIVM, Report nr. 222901012, Bilthoven, The Netherlands.


In order to reduce the risks of climate change, a major problem in developing an effective international policy is the allocation of the responsibility for reducing green­ house gas emissions among regions.

This report presents two approaches to provide for the allocation problem of emission reductions in the most important greenhouse gas C02. The first deals with a description of the emission debt concept. We use an equity rule by which all past and future dwellers on earth are permitted to emit an equal C02 quotum per year. Furthermore, the level of the equal emission quotum is dependent on the policy-related C02-equivalent concentration targets. The regional emission debt is the amount of C02, based on an equal share per capita, emitted in a region in the past exceeding the amount allowed. The resulting initial allocation of emission rights may be used as a start for a concept of tradable emission rights.

In the second approach, the allocation problem is formulated as an optimization problem. This contains an ‘optimal’ trade-off between rough estimates for social and economic consequences of reducing fossil C02-emissions in order to meet policy targets, as expressed in a C02-equivalent concentration level. The optimization algorithm developed is a first attempt in solving the optimization problem, where restrictions are dependent on simulation runs with IMAGE (an Integrated Model to Assess the Greenhouse Effect). The algorithm is used to find an allocation of regional fossil C02-emissions in order to maximize the welfare of future generations, given a maximum allowable concentration level.

Results of both approaches indicate that if the world community is to accept constraints on C02-emissions, industrialized regions will have to take the main responsibility in reducing C02-emissions either by reducing emissions in their own regions and in developing regions.


Historical and Future Regional Emission Paths of Carbon Dioxide: Allocation and Optimization Mechanisms

Janssen, M.A.
1992 Master Thesis, Department of Operations Research, Erasmus University of Rotterdam.

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