Solving difficult mixed integer and disjunctive non-linear problems on single and parallel processors

Östermark, Ralf

doi:10.1016/j.asoc.2014.07.018

Cited by 3 publications

(3 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the area of computational biology, parallel methods have already shown promising results in non-linear optimization problems ([ 36 , 37 ]). For the case of mixed-integer nonlinear programming, a few researchers have considered the development of parallel methods [ 38 – 40 ], but there is a lack of studies in the case of the mixed-integer nonlinear dynamic optimization problems considered here.…”

Section: Introductionmentioning

confidence: 99%

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

et al. 2017

View full text Add to dashboard Cite

BackgroundWe consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs).MethodsWe present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems.ResultsWe illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores).ConclusionsThese results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

show abstract

Section: Introductionmentioning

confidence: 99%

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Floudas, 1995;Grossmann and Biegler, 2004;Exler et al, 2011;Abhishek et al, 2010;Bussieck and Vigerske, 2010;Bonami et al, 2012;Lee and Leyffer, 2012). The most powerful algorithms for large-scale convex non-linear programming problems currently available are the active-set SQP methods and interior point methods (Nocedal and Wright, 2006;Östermark, 2014a). The established algorithms mostly yield at least a feasible mixed-integer non-linear programming (MINLP) solution also in difficult problems (cf.…”

Section: Introductionmentioning

confidence: 99%

“…A huge disjunctive programming problem is solved by parallel processors using finite element approximation. The local LP-problems are solved via the MINLP-switchboard of GHA using the primal-dual simplex algorithm (Maros, 2003;Östermark, 2014a). Section 5 concludes.…”

mentioning

confidence: 99%

A parallel algorithm for optimizing the capital structure contingent on maximum value at risk

Östermark

2015

Kybernetes

Self Cite

View full text Add to dashboard Cite

Purpose -The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation. Design/methodology/approach -Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper. Findings -Parallel processing and mathematical modeling provide a fruitful basis for solving ultrascale non-convex general disjunctive programming (GDP) problems, where the computational challenge in direct mixed-integer non-linear programming (MINLP) formulations or single processor algorithms would be insurmountable.Research limitations/implications -The test is limited to a single firm in an experimental setting. Repeating the test on large sample of firms in future research will indicate the general validity of Monte-Carlo-based VAR estimation. Practical implications -The authors show that the risk surface of the firm can be approximated by integrated use of accounting logic, corporate finance, mathematical programming, stochastic simulation and parallel processing. Originality/value -Parallel processing has potential to simplify large-scale MINLP and GDP problems with non-convex, multi-modal and discontinuous parameter generating functions and to solve them faster and more reliably than conventional approaches on single processors.

show abstract

Massively parallel processing of recursive multi-period portfolio models

Östermark

2017

European Journal of Operational Research

View full text Add to dashboard Cite

Solving difficult mixed integer and disjunctive non-linear problems on single and parallel processors

Cited by 3 publications

References 67 publications

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

A parallel algorithm for optimizing the capital structure contingent on maximum value at risk

Massively parallel processing of recursive multi-period portfolio models

Contact Info

Product

Resources

About