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Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

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Updated: Jun 20, 2026

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
11:53

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

Inexact rough-interval two-stage stochastic programming for conjunctive water allocation problems.

Hongwei Lu1, Guohe Huang, Li He

  • 1EVSE, Faculty of Engineering and Applied Science, University of Regina, Regina, SK, Canada.

Journal of Environmental Management
|September 22, 2009
PubMed
Summary
This summary is machine-generated.

An inexact rough-interval two-stage stochastic programming (IRTSP) method optimizes conjunctive water allocation. This approach effectively handles complex parameters, providing reliable allocation schemes for water resource management.

Related Experiment Videos

Last Updated: Jun 20, 2026

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
11:53

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

Area of Science:

  • Water Resource Management
  • Operations Research
  • Environmental Engineering

Background:

  • Conjunctive water allocation problems involve complex, dual-layer information from decision-makers.
  • Traditional stochastic programming models may not fully capture the uncertainty and imprecision inherent in these parameters.
  • Existing methods struggle to represent the most reliable and possible variation ranges of critical input data.

Purpose of the Study:

  • To develop an Inexact Rough-Interval Two-Stage Stochastic Programming (IRTSP) method for conjunctive water allocation.
  • To incorporate rough intervals (RIs) into the modeling framework to address dual-layer information.
  • To derive an interactive solution method and validate the model with a conjunctive water-allocation system.

Main Methods:

  • Development of the Inexact Rough-Interval Two-Stage Stochastic Programming (IRTSP) model.
  • Integration of rough intervals (RIs), a concept from rough sets, to handle parameter uncertainty.
  • Derivation of an interactive solution algorithm and application to a conjunctive water allocation system.

Main Results:

  • The IRTSP method yields a detailed optimal allocation scheme in a rough-interval form.
  • A total allocation range of [[1048.83, 2078.29]:[1482.26, 2020.60]] was obtained under pre-regulated inputs.
  • Comparisons show IRTSP's optimal objective function values and decision variables are more consistently within reliable ranges than conventional TSP and Interval TSP (ITSP).

Conclusions:

  • The proposed IRTSP method reliably handles conjunctive water allocation problems with imprecise parameters.
  • Rough intervals effectively capture dual-layer information and identify reliable variation ranges for complex inputs.
  • IRTSP offers a more robust approach compared to traditional two-stage stochastic programming models for water resource allocation.