Uncertainty, probability and information-gaps

Ben‐Haim, Yakov

doi:10.1016/j.ress.2004.03.015

Cited by 125 publications

(61 citation statements)

References 10 publications

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“…Each individual in the population is first evaluated to obtain its nominal fitness. Subsequently, each individual undergoes a sequence of nested searches to establish the uncertainty or maximum variations in design parameters for the given maximum performance degradation tolerable, in the spirit of InfoGap theory [6][7][8]. In particular, we solve a sequence of constrained optimization subproblems for each chromosome of the form:…”

Section: Begin Ea (For Maximization Problem)mentioning

confidence: 99%

“…Various classifications of uncertainty in design optimization have been suggested over recent years [2][3][4][5][6][7][8]. In [2], four types of uncertainty were described.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, epistemic uncertainty is caused by incomplete knowledge about the designs to be optimized and should be reducible if more knowledge can be acquired. In [6][7][8], uncertainty is defined as the gap between known and unknown facts. In this paper, we follow the categorization of uncertainty in [2] and [3].…”

Section: Introductionmentioning

confidence: 99%

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Inverse multi-objective robust evolutionary design

Lim

Ong

Jin

et al. 2006

Genet Program Evolvable Mach

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Abstract. In this paper, we present an Inverse Multi-Objective Robust Evolutionary (IMORE) design methodology that handles the presence of uncertainty without making assumptions about the uncertainty structure. We model the clustering of uncertain events in families of nested sets using a multi-level optimization search. To reduce the high computational costs of the proposed methodology we proposed schemes for 1) adapting the step-size in estimating the uncertainty, and 2) trimming down the number of calls to the objective function in the nested search. Both offline and online adaptation strategies are considered in conjunction with the IMORE design algorithm. Design of Experiments (DOE) approaches further reduce the number of objective function calls in the online adaptive IMORE algorithm. Empirical studies conducted on a series of test functions having diverse complexities show that the proposed algorithms converge to a pareto set of design solutions with non-dominated nominal and robustness performances efficiently.

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Section: Begin Ea (For Maximization Problem)mentioning

confidence: 99%

“…Various classifications of uncertainty in design optimization have been suggested over recent years [2][3][4][5][6][7][8]. In [2], four types of uncertainty were described.…”

Section: Introductionmentioning

confidence: 99%

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Inverse multi-objective robust evolutionary design

Lim

Ong

Jin

et al. 2006

Genet Program Evolvable Mach

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“…In the design of engineering structures, uncertain factors always exist in their material properties, load conditions, geometrical dimensions, and so on, and these uncertain factors must be taken into consideration in the design process since they will result in fluctuation of the mechanical properties of structures (Ben-Haim, 2004;Verhaeghe et al, 2013;Wu et al, 2015b;Xia et al, 2015). Reliability-based design optimization is frequently conducted to enhance the reliability of engineering structures and reduce the chance of function failure under potentially critical conditions.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the limitations of probabilistic methods in the process of reliability-based design optimization, scholars have gradually turned to nonprobabilistic methods for handling uncertainties since non-probabilistic models have advantages such as low requirements for sample data and simplicity of calculation (Ben-Haim, 1994;1995;Elishakoff et al, 1994;Qiu et al, 1995;2004;Elishakoff and Elettro, 2014). Ben-Haim (1994) first proposed the concept of non-probabilistic reliability based on convex set theory, where non-probabilistic convex models of uncertainty were utilized to formulate reliability in terms of acceptable system performance given an uncertain operating environment or uncertain geometrical imperfections.…”

Section: Introductionmentioning

confidence: 99%

Direct reliability-based design optimization of uncertain structures with interval parameters

Cheng

Tang

Liu

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.

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Beyond optimality: Multistakeholder robustness tradeoffs for regional water portfolio planning under deep uncertainty

Herman

Zeff

Reed

et al. 2014

Water Resources Research

190

139

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While optimality is a foundational mathematical concept in water resources planning and management, ''optimal'' solutions may be vulnerable to failure if deeply uncertain future conditions deviate from those assumed during optimization. These vulnerabilities may produce severely asymmetric impacts across a region, making it vital to evaluate the robustness of management strategies as well as their impacts for regional stakeholders. In this study, we contribute a multistakeholder many-objective robust decision making (MORDM) framework that blends many-objective search and uncertainty analysis tools to discover key tradeoffs between water supply alternatives and their robustness to deep uncertainties (e.g., population pressures, climate change, and financial risks). The proposed framework is demonstrated for four interconnected water utilities representing major stakeholders in the ''Research Triangle'' region of North Carolina, U.S. The utilities supply well over one million customers and have the ability to collectively manage drought via transfer agreements and shared infrastructure. We show that water portfolios for this region that compose optimal tradeoffs (i.e., Pareto-approximate solutions) under expected future conditions may suffer significantly degraded performance with only modest changes in deeply uncertain hydrologic and economic factors. We then use the Patient Rule Induction Method (PRIM) to identify which uncertain factors drive the individual and collective vulnerabilities for the four cooperating utilities. Our framework identifies key stakeholder dependencies and robustness tradeoffs associated with cooperative regional planning, which are critical to understanding the tensions between individual versus regional water supply goals. Cooperative demand management was found to be the key factor controlling the robustness of regional water supply planning, dominating other hydroclimatic and economic uncertainties through the 2025 planning horizon. Results suggest that a modest reduction in the projected rate of demand growth (from approximately 3% per year to 2.4%) will substantially improve the utilities' robustness to future uncertainty and reduce the potential for regional tensions. The proposed multistakeholder MORDM framework offers critical insights into the risks and challenges posed by rising water demands and hydrological uncertainties, providing a planning template for regions now forced to confront rapidly evolving water scarcity risks.

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Uncertainty, probability and information-gaps

Cited by 125 publications

References 10 publications

Inverse multi-objective robust evolutionary design

Inverse multi-objective robust evolutionary design

Direct reliability-based design optimization of uncertain structures with interval parameters

Beyond optimality: Multistakeholder robustness tradeoffs for regional water portfolio planning under deep uncertainty

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