Different formulations for solving trim loss problems in a paper-converting mill with ILP

Harjunkoski, Iiro; Westerlund, Tapio; Isaksson, Johnny; Skrifvars, Hans

doi:10.1016/0098-1354(96)00031-2

Cited by 39 publications

(16 citation statements)

References 5 publications

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“…The genetic hybrid algorithm (cf. O È stermark 1999b) combines some key properties of genetic algorithms (GA) with classical (constrained) nonlinear programming methods (cf., e.g., Pettersson 1994;Harjunkoski et al 1996;Westerlund et al 1994;Joines and Houck 1994).…”

Section: A Hybrid Algorithm For Automatic Detection Of Parsimonious Nmentioning

confidence: 97%

“…With few exceptions, the robustness of the downloaded ®les has been improved by some error handling routines for illconditioned problems. The Quasi±Newton library consists of the BFGS-method by Broyden, Fletcher, Goldfarb, and Shanno [19] and crash proof modi®cations of the Steepest descent method with quadratic/cubic linesearch. Possible machine over¯ow is circumvented by safe division procedures: In the case of numerical problems we prefer to extract a poor solution rather than letting the program fail and produce core dump.…”

Section: A Hybrid Algorithm For Automatic Detection Of Parsimonious Nmentioning

confidence: 99%

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Automatic detection of parsimony for heteroskedastic time series processes

Östermark

2002

Soft Computing - A Fusion of Foundations, Methodologies and App

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The paper proposes a new multiple-representation geno-mathematical algorithm for coping with ill-conditioned time series processes through competing nonlinear model formulations. Extensive testing and comparisons to a rigorous statistical time series package indicate that the geno-mathematical search-machine is effective and robust for modelling complicated time series. The new algorithm is used to model a representative set of global asset returns. The diagnostic tests prove that the ARCH-effects of the dif®cult nonlinear processes are annihilated completely in both full and reduced model variants. IntroductionThe present study considers a technique for automatic generation of parsimonious representations for autoregressive conditionally heteroskedastic (ARCH) processes. The topic is important, since numerous economic time series exhibit ARCH-related features. At the same time, the commercially available statistical program packages leave the model speci®cation task to the researcher. Any beautiful theoretical model works as expected with simulated data, when based exactly on the theoretical assumptions. However, when confronted with observed data, the theoretical models usually have to be modi®ed in some suitable way, to cope with unexpected anomalies. Needless to say, estimation of complicated nonlinear time series processes with observed data requires ± almost without exception ± extensive and time consuming testing of numerous alternative model speci®cations, before the ultimate choice can be made. Much of this (non) systematic search can be left to the computer, given suitable software. The empirical researcher should be able to devote his energy to creative work in model speci®cation and interpretation of robust estimation results instead of time-consuming tampering with unreliable statistical packages that frequently produce core dump when applied to ill-conditioned time series.Such packages induce an inherent slow-down of research and require attention on completely irrelevant aspects from a time series modelling viewpoint.Our study represents the intersection of two important research domains: modelling of nonlinear ([X]ARCH) time series and geno-mathematical programming. Our objective is to design and implement a search machine, in which the features of a newly developed genetic hybrid algorithm (O È stermark 1999b, 2001b) are combined with classical maximum likelihood estimation of ARCH-processes. The geno-mathematical programming system has been extensively tested and compared to other techniques in, e.g. O È stermark (1999c, 2000, 2001a).In O È stermark (2001b) we applied a neuro-genetic hybrid algorithm (NGHA) to a dif®cult econometric problem arising from the dynamics of global asset returns. Following Engle (1987a), we initially subjected the global returns database to factor analysis, giving three distinct factors (O È stermark 1997). The time series of the factors were modelled by some rigorous autoregressive conditional heteroskedastic (ARCH)-models suggested in the literature: the self-excit...

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Section: A Hybrid Algorithm For Automatic Detection Of Parsimonious Nmentioning

confidence: 97%

Section: A Hybrid Algorithm For Automatic Detection Of Parsimonious Nmentioning

confidence: 99%

Automatic detection of parsimony for heteroskedastic time series processes

Östermark

2002

Soft Computing - A Fusion of Foundations, Methodologies and App

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“…(5) A nonconvex trim loss problem (Harjunkoski et al, 1996) (6) A neural hard staircase estimation problem (Saxén and Saxén, 1994). …”

Section: Test Problemsmentioning

confidence: 99%

Designing a superstructure for parametric search for optimal search spaces in non‐trivial optimization problems

Östermark

2002

Kybernetes

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In the paper we design a super genetic hybrid algorithm (SuperGHA), an integrated optimization system for simultaneous parametric search and nonlinear optimization. The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimization process. The family of parameter vectors evolves through ordinary genetic operators aimed at producing the best possible parameterization for the underlying optimization problem. In comparison to traditional genetic algorithms, the integrated superstructure involves a twofold ordering of the population of parameter vectors. The first sorting key is provided by the objective function of the optimization problem at issue. The second key is given by the total mesh time absorbed by the parametric setting. In consequence, SuperGHA is geared at solving an optimization problem, using the best feasible parameterization in terms of optimality and time absorbance. The algorithm combines features from classical nonlinear optimization methodology and evolutionary computation utilizing a powerful accelerator technique. The constrained problem can be cast into multiple representations, supporting the integration of different mathematical programming environments. We show by extensive Monte Carlo simulations that SuperGHA extracts suitable parameter vectors for fast solution of complicated nonlinear programming problems.

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“…Recommendations made to modelers (i.e., nonautomatic reformulations) often include: using linear formulations if possible (Harjunkoski et al, 1996); using convex functional forms if possible ; dissaggregating terms (Tawarmalani et al, 2002;Tawarmalani and Sahinidis, 2002b); adding redundant constraints into the model formulation (Karuppiah and Grossmann, 2006;Ahmetović and Grossmann, 2011;Ruiz and Grossmann, 2011b). Any MINLP solution method introducing auxiliary variables is doing automatic reformulations, but it is currently unclear (for the general case) what are the best automatic reformulations.…”

Section: Reformulations and Other Preprocessing Methodsmentioning

confidence: 99%

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

194

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This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained DerivativeFree Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

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Different formulations for solving trim loss problems in a paper-converting mill with ILP

Cited by 39 publications

References 5 publications

Automatic detection of parsimony for heteroskedastic time series processes

Automatic detection of parsimony for heteroskedastic time series processes

Designing a superstructure for parametric search for optimal search spaces in non‐trivial optimization problems

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

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