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Related Concept Videos

Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Lagrange Multipliers: One Constraint01:29

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...
Lagrange Multipliers: Problem Solving01:30

Lagrange Multipliers: Problem Solving

A silo with a cylindrical base, flat bottom, and hemispherical roof is a common design in agricultural and industrial storage due to its structural efficiency and ease of construction. Optimizing its dimensions to maximize storage capacity for a given amount of material—i.e., a fixed surface area—is a classic problem in applied calculus and engineering design. The key parameters are the radius r of the base and the height h of the cylindrical section.The total volume of the silo is obtained by...
Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures enhance...
Two-Dimensional Force System: Problem Solving01:29

Two-Dimensional Force System: Problem Solving

Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...

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Related Experiment Video

Updated: Jun 12, 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

Soft constraints-based multiobjective framework for flux balance analysis.

Deepak Nagrath1, Marco Avila-Elchiver, François Berthiaume

  • 1Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.

Metabolic Engineering
|June 18, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for multi-objective optimization in metabolic modeling. It addresses limitations in current methods, enabling better analysis of complex biological systems like liver functions.

Related Experiment Videos

Last Updated: Jun 12, 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:

  • Metabolic Engineering
  • Computational Biology
  • Systems Biology

Background:

  • Flux Balance Analysis (FBA) traditionally uses single objective functions, limiting its application to complex biological systems.
  • Mammalian systems exhibit diverse functions, necessitating multiobjective optimization for accurate flux distribution analysis.
  • Existing multiobjective methods lack clarity on objective prioritization and combination for truly optimal solutions.

Purpose of the Study:

  • To develop a novel framework for multiobjective optimization in FBA using soft constraints and linear physical programming.
  • To address limitations in current methods regarding objective selection, combination, and prioritization.
  • To enable the computation of truly optimal flux distributions in complex metabolic networks.

Main Methods:

  • Developed a soft constraints-based linear physical programming-based flux balance analysis (LPPFBA) framework.
  • Applied LPPFBA to compute multiobjective optimal solutions for hepatocyte functions (urea, albumin, NADPH, glutathione synthesis).
  • Performed simultaneous analysis of multiple objectives and simulated bioartificial liver systems.

Main Results:

  • Successfully computed a set of multiobjective optimal solutions for key hepatocyte functions.
  • Demonstrated the framework's ability to analyze simultaneous objectives and improve simulated hepatic functions.
  • Validated the LPPFBA framework for optimizing complex metabolic networks.

Conclusions:

  • The LPPFBA framework provides a robust method for multiobjective optimization in metabolic networks.
  • This approach enhances the understanding and optimization of complex biological systems, including bioartificial liver systems.
  • The quantitative and visualization framework is broadly applicable to large-scale metabolic network analysis.