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Safe bounds in linear and mixedinteger linear programming
 MATH. PROGRAMMING
, 2004
"... Current mixedinteger linear programming solvers are based on linear programming routines that use floatingpoint arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many stateo ..."
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Cited by 15 (0 self)
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oftheart MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre and postprocessing of the linear programs arising in a branchandcut framework can guarantee that no solution is lost, at least for mixedinteger programs in which all variables can be bounded
Safe Bounds in Linear and MixedInteger Programming
 MATH. PROG
, 2002
"... Current mixedinteger linear programming solvers are based on linear programming routines that use floating point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. It is shown how, using directed rounding ..."
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Cited by 32 (2 self)
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rounding and interval arithmetic, cheap pre and postprocessing of the linear programs arising in a branchandcut framework can guarantee that no solution is lost, at least for mixedinteger programs in which all variables can be bounded rigorously by bounds of reasonable size.
Duality for mixedinteger linear programs
 The International Journal of Operations Research
, 2007
"... AbstractThe theory of duality for linear programs is welldeveloped and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixedinteger linear programs, but this has proven difficult, in part because dua ..."
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Cited by 3 (1 self)
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AbstractThe theory of duality for linear programs is welldeveloped and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixedinteger linear programs, but this has proven difficult, in part because
MILP: MixedInteger Linear Programming
"... This paper investigates the feasibility of electrolytic hydrogen production for the transport sector during offpeak periods in Ontario. This analysis is based on the existing electricity system infrastructure and its planned future development up to 2025. First, a simplified but realistic zonal bas ..."
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This paper investigates the feasibility of electrolytic hydrogen production for the transport sector during offpeak periods in Ontario. This analysis is based on the existing electricity system infrastructure and its planned future development up to 2025. First, a simplified but realistic zonal based model for Ontario’s electricity transmission network is developed. Then, based on Ontario’s Integrated Power System Plan (IPSP), a zonal pattern of generation capacity procurement in Ontario from 2008 to 2025 is proposed, specifying the total effective generation capacity in each zone that contributes to baseload energy. Finally, an optimization model is developed to find the optimal size of hydrogen production plants to be developed in different zones, as well as optimal hydrogen transportation routes to achieve a feasible hydrogen economy penetration in Ontario up to 2025. The proposed model is shown to be an effective planning tool for electrolysis based hydrogen economy studies. The results of the present study demonstrate that the present and projected electricity grid in Ontario can be optimally exploited for hydrogen production, achieving 1.2 % to 2.8 % levels of hydrogen economy penetration by 2025 without any additional grid or power generation investments beyond those currently planned.
Mixing MixedInteger Inequalities
 MATHEMATICAL PROGRAMMING
, 1998
"... Mixedinteger rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixedinteger programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixedinteger region S and a coll ..."
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Cited by 23 (2 self)
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Mixedinteger rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixedinteger programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixedinteger region S and a
An exact rational mixedinteger programming solver
, 2010
"... We present an exact rational solver for mixedinteger linear programming which avoids the numerical inaccuracies inherent in the floatingpoint computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where corr ..."
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Cited by 8 (1 self)
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We present an exact rational solver for mixedinteger linear programming which avoids the numerical inaccuracies inherent in the floatingpoint computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where
Analyzing Infeasible MixedInteger and Integer Linear Programs
, 1999
"... Algorithms and computerbased tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixedinteger or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isola ..."
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Cited by 10 (0 self)
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Algorithms and computerbased tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixedinteger or integer linear programs. One approach that has proven especially useful for infeasible linear programs
Automatic Discovery of Linear Restraints Among Variables of a Program
, 1978
"... The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs. ..."
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Cited by 733 (47 self)
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The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs.
Review of nonlinear mixedinteger and disjunctive programming techniques
 Optimization and Engineering
, 2002
"... This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are ex ..."
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Cited by 94 (22 self)
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This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, OuterApproximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems
Genetic Programming
, 1997
"... Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring ..."
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Cited by 1051 (12 self)
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Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring
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