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14
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 that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
Probe Backtrack Search for Minimal Perturbation in Dynamic Scheduling
, 1999
"... This paper describes an algorithm designed to minimally recongure schedules in response to a changing environment. External factors have caused an existing schedule to become invalid, perhaps due to the withdrawal of resources, or because of changes to the set of scheduled activities. The total shi ..."
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Cited by 90 (14 self)
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This paper describes an algorithm designed to minimally recongure schedules in response to a changing environment. External factors have caused an existing schedule to become invalid, perhaps due to the withdrawal of resources, or because of changes to the set of scheduled activities. The total shift in the start and end times of already scheduled activities should be kept to a minimum. This optimization requirement may be captured using a linear optimization function over linear constraints. However, the disjunctive nature of the resource constraints impairs traditional mathematical programming approaches. The unimodular probing algorithm interleaves constraint programming and linear programming. The linear programming solver handles only a controlled subset of the problem constraints, to guarantee that the values returned are discrete. Using probe backtracking, a complete, repairbased method for search, these values are simply integrated into constraint programming. Unimodular p...
Statespace Planning by Integer Optimization
 In Proceedings of the Sixteenth National Conference on Artificial Intelligence
, 1999
"... This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can ..."
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Cited by 65 (0 self)
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This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand bound IP solvers and efficient new integer local search algorithms. ILPPLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving statespace planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...
Minimal Perturbation in Dynamic Scheduling
, 1998
"... . This paper describes an algorithm, unimodular probing, conceived to optimally reconfigure schedules in response to a changing environment. In the problems studied, resources may become unavailable, and scheduled activities may change. The total shift in the start and end times of activities shoul ..."
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Cited by 21 (2 self)
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. This paper describes an algorithm, unimodular probing, conceived to optimally reconfigure schedules in response to a changing environment. In the problems studied, resources may become unavailable, and scheduled activities may change. The total shift in the start and end times of activities should be kept to a minimum. This requirement is captured in terms of a linear optimization function over linear constraints. However, the disjunctive nature of many scheduling problems impedes traditional mathematical programming approaches. The unimodular probing algorithm interleaves constraint programming and linear programming. The linear programming solver is applied to a dynamically controlled subset of the problem constraints, to guarantee that the values returned are discrete. Using a repair strategy, these values are naturally integrated into the constraint programming search. We explore why the algorithm is effective and discuss its applicability to a wider class of problems. It appear...
Logic, Optimization, and Constraint Programming
 INFORMS Journal on Computing
, 2000
"... Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use ..."
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Cited by 16 (2 self)
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Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in di#erent ways, and how these ways can be combined. It sketches the intellectual background for recent e#orts at integration. In particular, it traces the history of logicbased methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications. Optimization and constraint programming are beginning to converge, despite their very di#erent origins. Optimization is primarily associated with mathematics and engineering, while constraint programming developed much more recently in the computer science an...
Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions
 ANNALS OF OPERATIONS RESEARCH
, 2000
"... ... Knapsack Problems to fix some variables to zero and to separate the rest into two groups those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem w ..."
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Cited by 12 (5 self)
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... Knapsack Problems to fix some variables to zero and to separate the rest into two groups those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computational testing, including the set of problems in the ORlibrary and our own set of difficult problems, shows our approach helps to solve difficult problems in a reasonable amount of time and, in most cases, with a fewer number of nodes in the search tree than leading commercial software. ______________________________________________________________________________________
Systematic Modeling of DiscreteContinuous Optimization Models through Generalized Disjunctive Programming
"... This article is dedicated to the memory of Professor Neil Amundsen, who pioneered the application of mathematical modeling and analysis in chemical engineering. Discretecontinuous optimization problems in process systems engineering are commonly modeled in algebraic form as mixedinteger linear or ..."
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Cited by 7 (5 self)
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This article is dedicated to the memory of Professor Neil Amundsen, who pioneered the application of mathematical modeling and analysis in chemical engineering. Discretecontinuous optimization problems in process systems engineering are commonly modeled in algebraic form as mixedinteger linear or nonlinear programming models. Since these models can often be formulated in different ways, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models, particularly their continuous relaxations. This paper describes a modeling framework, Generalized Disjunctive Programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. We provide an overview of major research results that have emerged in this area. Basic concepts are emphasized as well as major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixedinteger optimization models that exhibit strong continuous relaxations. 1.
Unimodular Probing for Minimal Perturbance in Dynamic Resource Feasibility Problems
, 1997
"... . This paper describes unimodular probing  a new technique that has been used to solve a class of dynamic scheduling problems. In benchmarks a unimodular probing algorithm has outperformed two wellestablished approaches: backtrack search with local consistency and specialised heuristics, and mixed ..."
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Cited by 6 (3 self)
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. This paper describes unimodular probing  a new technique that has been used to solve a class of dynamic scheduling problems. In benchmarks a unimodular probing algorithm has outperformed two wellestablished approaches: backtrack search with local consistency and specialised heuristics, and mixed integer programming (MIP). The problems amenable to unimodular probing involve disjunctive constraints, discrete variables, and a linear optimisation function. In addition, some of the constraints should be totally unimodular  for example, temporal precedence and distance constraints. Problems in this class are difficult for CSP techniques because of the optimisation requirement, and for MIP because of the number of discrete (integer) variables. Our studies have focussed on DCSPs, with an optimisation criterion of minimal perturbance to an existing solution. Unimodular probing builds on an ordinary backtracking repair algorithm with constraint propagation. However, by contrast with previo...
E.: Logicbased Outer Approximation for Globally Optimal Synthesis of Process Networks
 Computers and Chemical Engineering
, 1914
"... Process network problems can be formulated as Generalized Disjunctive Programs where a logicbased representation is used to deal with the discrete and continuous decisions. A new deterministic algorithm for the global optimization of process networks is presented in this work. The proposed algorithm ..."
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Cited by 6 (1 self)
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Process network problems can be formulated as Generalized Disjunctive Programs where a logicbased representation is used to deal with the discrete and continuous decisions. A new deterministic algorithm for the global optimization of process networks is presented in this work. The proposed algorithm, which does not rely on spatial branchandbound, is based on the LogicBased Outer Approximation that exploits the special structure of flowsheet synthesis models. The method is capable of considering nonconvexities, while guaranteeing globality in the solution of an optimal synthesis of process network problem. This is accomplished by solving iteratively reduced NLP subproblems to global optimality and MILP master problems, which are valid outer approximations of the original problem. Piecewise linear under and overestimators for bilinear and concave terms have been constructed with the property of having zero gap in a finite set of points. The global optimization of the reduced NLP may be performed either with a suitable global solver or using the inner optimization strategy that is proposed in this work. Theoretical properties are discussed as well as several alternatives for implementing the proposed algorithm. Several examples were successfully solved with this algorithm. Results show that only few
Applying Integer Programming to AI Planning
 Knowledge Engineering Review
, 2000
"... Despite the historical di#erence in focus between AI planning techniques and Integer Programming (IP) techniques, recent research has shown that IP techniques show significant promise in their ability to solve AI planning problems. This paper provides approaches to encode AI planning problems as ..."
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Cited by 4 (0 self)
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Despite the historical di#erence in focus between AI planning techniques and Integer Programming (IP) techniques, recent research has shown that IP techniques show significant promise in their ability to solve AI planning problems. This paper provides approaches to encode AI planning problems as IP problems, describes some of the more significant issues that arise in using IP for AI planning, and discusses promising directions for future research. 1 Introduction AI planning is concerned with developing automated methods for generating and reasoning about sequences of actions to perform certain tasks or achieve certain goals. Planning problems are similar but in some sense more general than scheduling problems, which have received longstanding attention in the Operations Research community. What separates AI planning from scheduling is that solving a planning problem typically involves determining both what actions to do and when to do those actions. Scheduling problems on other h...