Result: Chemical equation balancing : An integer programming approach

Title:
Chemical equation balancing : An integer programming approach
Authors:
SEN, S. K, AGARWAL, Hans, SEN, Sagar
Source:
Mathematical and computer modelling. 44(7-8):678-691
Publisher Information:
Oxford: Elsevier Science, 2006.
Publication Year:
2006
Physical Description:
print, 29 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Méthodes de calcul scientifique (y compris calcul symbolique, calcul algébrique), Methods of scientific computing (including symbolic computation, algebraic computation), Algorithme, Algorithm, Algoritmo, Algèbre linéaire numérique, Numerical linear algebra, Algebra lineal numérica, Analyse numérique, Numerical analysis, Análisis numérico, Arithmétique virgule flottante, Floating point arithmetic, Connaissance, Knowledge, Conocimiento, Croissance, Growth, Crecimiento, Défaillance, Failures, Fallo, Fonction objectif, Objective function, Función objetivo, Inversion matrice, Matrix inversion, Inversión matriz, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode directe, Direct method, Método directo, Méthode moindre carré, Least squares method, Método cuadrado menor, Problème NP complet, NP complete problem, Problema NP completo, Programmation en nombres entiers, Integer programming, Programación entera, Programmation linéaire, Linear programming, Programación lineal, Programmation non linéaire, Non linear programming, Programación no lineal, Réaction chimique, Chemical reaction, Reacción química, Système linéaire, Linear system, Sistema lineal, Temps polynomial, Polynomial time, Tiempo polinomial, Unicité solution, Solution uniqueness, Unicidad solución, Solution moindres carrés norme minimum, Minimum-norm least-squares solution, Équation chimique équilibrage, Balancing chemical equation, Balancing chemical equations, Floating-point arithmetic, Integer program, NP-complete problems
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901-6975, United States
Energy Research Center, Lehigh University, 117ATLSS Drive, Bethlehem, PA 18018, United States
Modeling, Simulation and Design Laboratory, School of Computer Science, McGill University, McConnell Engineering Building, Room 202, 3480 University Street, Montreal, Quebec, H3A 2A7, Canada
ISSN:
0895-7177
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18030698
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18030698
Database:
PASCAL Archive

Further Information

Presented here is an integer linear program (ILP) formulation for automatic balancing of a chemical equation. Also described is a integer nonlinear programming (INP) algorithm for balancing. This special algorithm is polynomial time O(n3), unlike the ILP approach, and uses the widely available conventional floating-point arithmetic, obviating the need for both rational arithmetic and multiple modulus residue arithmetic. The rational arithmetic is unsuitable due to intermediate number growth, while the residue arithmetic suffers from the lack of a priori knowledge of the set of prime bases that avoids a possible failure due to division by zero. Further, unlike the floating point arithmetic, both arithmetics are not built-in/standard and hence additional programming effort is needed. The INP algorithm has been tested on several typical chemical equations and found to be very successful for most problems in our extensive balancing experiments. This algorithm also has the capability to determine the feasibility of a new chemical reaction and, if it is feasible, then it will balance the equation and also provide the information if two or more linearly independent balancings exist through the rank information. Any general method to solve the ILP is fail-proof, but it is not polynomial time. Since we have not encountered truly large chemical equations having, say, 1000 products and reactants in a real-world situation, a non-polynomial ILP solver is also useful. A justification for the objective functions for ILP and INP algorithms, each of which produces a unique solution, is provided.