SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems

Müller, Juliane; Shoemaker, Christine A.; Piché, Robert

doi:10.1016/j.cor.2012.08.022

Cited by 168 publications

(109 citation statements)

References 56 publications

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“…The computation time of the objective function can also be a problem, since it can be prohibitive high (subrogate models are sometimes useful in these cases [18]). In addition, the structure of the problem cannot be exploited in the majority of BBOP cases, and sometimes, BBOPs involve some kind of noise in the objective function or their parameters, that make the optimization even more complicated [17].…”

Section: Black-box Optimization Problems In Reinsurancementioning

confidence: 99%

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An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

et al. 2013

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Black-box optimization problems (BBOP) are defined as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the field of insurance, and more specifically in reinsurance problems. In this area, the complexity of the models and assumptions considered to define the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

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Section: Black-box Optimization Problems In Reinsurancementioning

confidence: 99%

“…Evolutionary-based search algorithms have been traditionally applied to solve these problems, with excellent results [17,18].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

et al. 2013

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“…Ierapetritou (2013, 2014) employ kriging approximations for the objective function and the lumped feasibility-based criterion which aims to represent the feasible space of the problem through a single function. Recent work of Müller et al (2013) extends the capabilities of the radial-basis function based black-box method for mixed-integer problems, under the assumption of continuity of the objective and constraints surfaces with respect to the discrete variables.…”

Section: Surrogate Model Based Methodsmentioning

confidence: 99%

“…This is an aspect which has not been discussed in the literature significantly, since typically local solvers are used to optimize the formulated surrogate model which may in turn be nonconvex and exhibit multiplicity of local optima. The majority of the developed algorithms guarantee asymptotic convergence in the limit of infinite samples (Jones, 2001;Forrester and Keane, 2009;Jakobsson et al, 2010;Jones et al, 1998;Müller et al, 2013).…”

Section: Surrogate Model Based Methodsmentioning

confidence: 99%

“…Conejo et al (2013) develop a method which uses local quadratic models of the objective function for problems with a known convex feasible region. General constrained CDFO problems have been studied by Caballero and Grossmann (2008) and Sankaran et al (2010) using local kriging models for the objective and constraints; Powell (1994Powell ( , 2013a developed the COBYLA algorithm which uses local linear approximations for the unknown objective and the unknown constraints which is an approach revisited recently by March and Willcox (2012); Conn and Le Digabel (2013) employ quadratic models for the objective and constraints; Müller et al (2013) use radial-basis function models; and finally Müller and Shoemaker (2014) use an ensemble of various surrogate-models to best fit the objective and constraints of the problem. A recent extension of the BOBYQA algorithm for mixed variable programming has been published which uses quadratic approximations and local integer search, with guaranteed identification of locally optimal points (Newby and Ali, 2014).…”

Section: Model-based Methodsmentioning

confidence: 99%

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

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

193

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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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Global change and the groundwater management challenge

Gorelick

Chen

2015

Water Resources Research

329

142

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With rivers in critical regions already exploited to capacity throughout the world and groundwater overdraft as well as large-scale contamination occurring in many areas, we have entered an era in which multiple simultaneous stresses will drive water management. Increasingly, groundwater resources are taking a more prominent role in providing freshwater supplies. We discuss the competing fresh groundwater needs for human consumption, food production, energy, and the environment, as well as physical hazards, and conflicts due to transboundary overexploitation. During the past 50 years, groundwater management modeling has focused on combining simulation with optimization methods to inspect important problems ranging from contaminant remediation to agricultural irrigation management. The compound challenges now faced by water planners require a new generation of aquifer management models that address the broad impacts of global change on aquifer storage and depletion trajectory management, land subsidence, groundwater-dependent ecosystems, seawater intrusion, anthropogenic and geogenic contamination, supply vulnerability, and long-term sustainability. The scope of research efforts is only beginning to address complex interactions using multiagent system models that are not readily formulated as optimization problems and that consider a suite of human behavioral responses.

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SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems

Cited by 168 publications

References 56 publications

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

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

Global change and the groundwater management challenge

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