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Numerical experience with lower bounds for MIQP branchandbound
, 1995
"... The solution of convex Mixed Integer Quadratic Programming (MIQP) problems with a general branchandbound framework is considered. It is shown how lower bounds can be computed efficiently during the branchandbound process. Improved lower bounds such as the ones derived in this paper can reduc ..."
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Cited by 66 (0 self)
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The solution of convex Mixed Integer Quadratic Programming (MIQP) problems with a general branchandbound framework is considered. It is shown how lower bounds can be computed efficiently during the branchandbound process. Improved lower bounds such as the ones derived in this paper can reduce the number of QP problems that have to be solved. The branchandbound approach is also shown to be superior to other approaches to solving MIQP problems. Numerical experience is presented which supports these conclusions. Key words : Integer Programming, Mixed Integer Quadratic Programming, BranchandBound AMS subject classification: 90C10, 90C11, 90C20 1 Introduction One of the most successful methods for solving mixedinteger nonlinear problems is branchandbound. Land and Doig [16] first introduced a branchandbound algorithm for the travelling salesman problem. Dakin [3] introduced the now common branching dichotomy and was the first to realize that it is possible to so...
Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
 SIAM Journal on Optimization
, 2004
"... A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for gene ..."
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Cited by 55 (6 self)
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A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictate what can be proved about certain limit points generated by the algorithm. To demonstrate the usefulness of the algorithm, the algorithm is applied to the design of a loadbearing thermal insulation system. We believe this is the first algorithm with provable convergence results to directly target this class of problems.
Integrating SQP and branchandbound for Mixed Integer Nonlinear Programming
 Computational Optimization and Applications
, 1998
"... This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving ..."
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Cited by 45 (1 self)
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This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branchandbound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branchandbound is presented and a factor of about 3 improvement over branchandbound is observed...
EVBDDbased algorithms for integer linear programming, spectral transformation, and function decomposition
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1994
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STATEOFTHEART REVIEW OF OPTIMIZATION METHODS FOR SHORTTERM SCHEDULING OF BATCH PROCESSES
, 2005
"... There has been significant progress in the area of shortterm scheduling of batch processes, including the solution of industrialsized problems, in the last 20 years. The main goal of this paper is to provide an uptodate review of the stateoftheart in this challenging area. Main features, stre ..."
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Cited by 30 (9 self)
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There has been significant progress in the area of shortterm scheduling of batch processes, including the solution of industrialsized problems, in the last 20 years. The main goal of this paper is to provide an uptodate review of the stateoftheart in this challenging area. Main features, strengths and limitations of existing modeling and optimization techniques as well as other available major solution methods are examined through this paper. We first present a general classification for scheduling problems of batch processes as well as for the corresponding optimization models. Subsequently, the modeling of representative optimization approaches for the different problem types are introduced in detail, focusing on both discrete and continuous time models. A comparison of effectiveness and efficiency of these models is given for two benchmarking examples from the literature. We also discuss two realworld applications of scheduling problems that cannot be readily accommodated using existing methods. For the sake of completeness, other alternative solution methods applied in the field of scheduling are also reviewed, followed by a discussion related to solving largescale problems through rigorous optimization approaches. Finally, we list available academic and commercial software and briefly address the issue of rescheduling capabilities of the various optimization approaches.
Practical Problem Solving with Cutting Plane Algorithms in Combinatorial Optimization
, 1994
"... Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many p ..."
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Cited by 24 (5 self)
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Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane algorithms from an implementor's point of view. Special emphasis is given to control and data structures used in practically successful implementations of branch and cut algorithms. We also address the issue of parallelization. Finally, we point out that in important applications branch and cut algorithms are not only able to produce optimal solutions but also approximations to the optimum with certified good quality in moderate computation times. We close with an overview of successful practical applications in the literature.
Global Optimization in Control System Analysis and Design
 CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS
, 1992
"... Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are ..."
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Cited by 15 (2 self)
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Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are known only to within a certain accuracy, or vary depending on operating conditions etc. Frequently asked questions here deal with performance issues: "How bad can a certain performance measure of the system be over all possible values of the parameters?" Another example is parametric controller design, where the parameters represent degrees of freedom available to the control system designer. A typical question here would be: "What is the best choice of parameters, one that optimizes a certain design objective?" Many of the questions above may be directly restated as optimization problems: If q denotes the vector of parameters, Q
Automatically improve software architecture models for performance, reliability, and cost using evolutionary algorithms
 In Proc. first joint WOSP/SIPEW international conference on Performance engineering
"... Quantitative prediction of quality properties (i.e. extrafunctional properties such as performance, reliability, and cost) of software architectures during design supports a systematic software engineering approach. Designing architectures that exhibit a good tradeoff between multiple quality crite ..."
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Cited by 15 (2 self)
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Quantitative prediction of quality properties (i.e. extrafunctional properties such as performance, reliability, and cost) of software architectures during design supports a systematic software engineering approach. Designing architectures that exhibit a good tradeoff between multiple quality criteria is hard, because even after a functional design has been created, many remaining degrees of freedom in the software architecture span a large, discontinuous design space. In current practice, software architects try to find solutions manually, which is timeconsuming, can be errorprone and can lead to suboptimal designs. We propose an automated approach to search the design space for good solutions. Starting with a given initial architectural model, the approach iteratively modifies and evaluates architectural models. Our approach applies a multicriteria genetic algorithm to software architectures modelled with the Palladio Component Model. It supports quantitative performance, reliability, and cost prediction and can be extended to other quantitative quality criteria of software architectures. We validate the applicability of our approach by applying it to an architecture model of a componentbased business information system and analyse its quality criteria tradeoffs by automatically investigating more than 1200 alternative design candidates.