Handling practicalities in agricultural policy optimization for water quality improvements

Bilevel and multi-objective optimization methods are often useful to spatially target agri-environmental policy throughout a watershed. This type of problem is complex and is comprised of a number of practicalities: (i) a large number of decision variables, (ii) at least two inter-dependent levels of optimization between policy makers and policy followers, and (iii) uncertainty in decision variables and problem parameters. Given agricultural and economic data from the Raccoon watershed in central Iowa, we formulate a bilevel multi-objective optimization problem that accommodates objectives of both policy makers and farmers. The solution procedure then explicitly accounts for the nested nature of farm-level management decisions in response to agri-environmental policy incentives constructed by policy makers. We specifically examine the spatial targeting of a fertilizer-reduction incentive policy while seeking to maximize farm-level productivity while generating mandated water quality improvements using this framework. We test three different evolutionary optimization algorithms - m-BLEAQ, NSGA-II, and SPEA2 - and show that m-BLEAQ is well suited for handling the bilevel optimization problems and the considered practicalities.

[1]  P. Marcotte,et al.  A bilevel model of taxation and its application to optimal highway pricing , 1996 .

[2]  Kalyanmoy Deb,et al.  Transportation policy formulation as a multi-objective bilevel optimization problem , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[3]  Jerome Bracken,et al.  Mathematical Programs with Optimization Problems in the Constraints , 1973, Oper. Res..

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  Manoj K. Jha,et al.  The Allocation of Nutrient Load Reduction Across a Watershed: Assessing Delivery Coefficients As an Implementation Tool , 2006 .

[6]  L. Kurkalova,et al.  Land use change in a biofuels hotspot: The case of Iowa, USA , 2011 .

[7]  Helio J. C. Barbosa,et al.  Differential Evolution assisted by a surrogate model for bilevel programming problems , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[8]  G. Anandalingam,et al.  A penalty function approach for solving bi-level linear programs , 1993, J. Glob. Optim..

[9]  J. Morgan,et al.  Existence of Solutions to Bilevel Variational Problems in Banach Spaces , 2001 .

[10]  Miles G. Nicholls,et al.  Aluminum Production Modeling - A Nonlinear Bilevel Programming Approach , 1995, Oper. Res..

[11]  J. Wilen,et al.  Natural Resource Economics and Conservation: Contributions of Agricultural Economics and Agricultural Economists , 2010 .

[12]  Arthur W. Westerberg,et al.  Bilevel programming for steady-state chemical process design—I. Fundamentals and algorithms , 1990 .

[13]  Kalyanmoy Deb,et al.  Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping , 2017, Eur. J. Oper. Res..

[14]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[15]  Philip W. Gassman,et al.  Water Quality Modeling for the Raccoon River Watershed Using SWAT , 2006 .

[16]  E. J. Sadler,et al.  The Conservation Effects Assessment Project benchmark watersheds: Synthesis of preliminary findings , 2008, Journal of Soil and Water Conservation.

[17]  Todd Campbell,et al.  Nonpoint-source pollution reduction for an Iowa watershed: an application of evolutionary algorithms. , 2010 .

[18]  Marc Parizeau,et al.  DEAP: evolutionary algorithms made easy , 2012, J. Mach. Learn. Res..

[19]  Lawrence M. Wein,et al.  OR Forum - Homeland Security: From Mathematical Models to Policy Implementation: The 2008 Philip McCord Morse Lecture , 2009, Oper. Res..

[20]  Peter Värbrand,et al.  A global optimization approach for the linear two-level program , 1993, J. Glob. Optim..

[21]  Philip W Gassman,et al.  Assessment of total maximum daily load implementation strategies for nitrate impairment of the Raccoon River, Iowa. , 2010, Journal of environmental quality.

[22]  Lyubov A. Kurkalova,et al.  Cost‐Effective Placement of Best Management Practices in a Watershed: Lessons Learned from Conservation Effects Assessment Project , 2015 .

[23]  K. Deb,et al.  Real-coded evolutionary algorithms with parent-centric recombination , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  J. Pang,et al.  Existence of optimal solutions to mathematical programs with equilibrium constraints , 1988 .

[25]  Gerald G. Brown,et al.  A Two-Sided Optimization for Theater Ballistic Missile Defense , 2005, Oper. Res..

[26]  John R. Williams,et al.  LARGE AREA HYDROLOGIC MODELING AND ASSESSMENT PART I: MODEL DEVELOPMENT 1 , 1998 .

[27]  Martine Labbé,et al.  A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network , 2000, Transp. Sci..

[28]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[29]  Kalyanmoy Deb,et al.  Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization , 2013, ArXiv.

[30]  Arthur W. Westerberg,et al.  Bilevel programming for steady-state chemical process design , 1990 .

[31]  Silvia Secchi,et al.  Least-cost control of agricultural nutrient contributions to the Gulf of Mexico hypoxic zone. , 2010, Ecological applications : a publication of the Ecological Society of America.

[32]  Nicolas Prcovic,et al.  Parallel Optimisation in the SCOOP Library , 1998, IPPS/SPDP Workshops.

[33]  Stephan Dempe,et al.  Necessary Optimality Conditions and a New Approach to Multiobjective Bilevel Optimization Problems , 2012, J. Optim. Theory Appl..

[34]  J. Morgan,et al.  Topological existence and stability for stackelberg problems , 1995 .

[35]  William R. Smith,et al.  Chemical Reaction Equilibrium Analysis: Theory and Algorithms , 1982 .

[36]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[37]  Yafeng Yin,et al.  Genetic-Algorithms-Based Approach for Bilevel Programming Models , 2000 .

[38]  E. G. Bekele,et al.  Multiobjective management of ecosystem services by integrative watershed modeling and evolutionary algorithms , 2005 .

[39]  Kalyanmoy Deb,et al.  Multi-objective Stackelberg game between a regulating authority and a mining company: A case study in environmental economics , 2013, 2013 IEEE Congress on Evolutionary Computation.

[40]  Athanasios Migdalas,et al.  Bilevel programming in traffic planning: Models, methods and challenge , 1995, J. Glob. Optim..

[41]  Jonathan F. Bard,et al.  A Branch and Bound Algorithm for the Bilevel Programming Problem , 1990, SIAM J. Sci. Comput..

[42]  L. Lachmann,et al.  Capital, expectations, and the market process : essays on the theory of the market economy , 1978 .

[43]  Jacqueline Morgan,et al.  Weak via strong Stackelberg problem: New results , 1996, J. Glob. Optim..

[44]  Rolf Färe,et al.  A hybrid genetic algorithm for multiobjective problems with activity analysis-based local search , 2009, Eur. J. Oper. Res..

[45]  J. Outrata.  Necessary optimality conditions for Stackelberg problems , 1993 .

[46]  Kalyanmoy Deb,et al.  An improved bilevel evolutionary algorithm based on Quadratic Approximations , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[47]  Kalyanmoy Deb,et al.  Towards Understanding Bilevel Multi-objective Optimization with Deterministic Lower Level Decisions , 2015, EMO.

[48]  Steven T. Bednarz,et al.  LARGE AREA HYDROLOGIC MODELING AND ASSESSMENT PART II: MODEL APPLICATION 1 , 1998 .

[49]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[50]  Catherine L. Kling,et al.  Economic Incentives to Improve Water Quality in Agricultural Landscapes: Some New Variations on Old Ideas , 2011 .

[51]  Gabriele Eichfelder,et al.  Multiobjective bilevel optimization , 2010, Math. Program..

[52]  R. Färe,et al.  Valuing water quality tradeoffs at different spatial scales: An integrated approach using bilevel optimization , 2015 .

[53]  Kalyanmoy Deb,et al.  An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm , 2010, Evolutionary Computation.

[54]  Kalyanmoy Deb,et al.  Solving optimistic bilevel programs by iteratively approximating lower level optimal value function , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[55]  Kalyanmoy Deb,et al.  Solving Bilevel Multicriterion Optimization Problems With Lower Level Decision Uncertainty , 2016, IEEE Transactions on Evolutionary Computation.