Mathematical Programming Techniques for Optimization under Uncertainty and Their Application in Process Systems Engineering

Grossmann, Ignacio E.; Apap, Robert M.; Calfa, Bruno A.; García-Herreros, Pablo; Zhang, Qi

doi:10.1134/s0040579517060057

Cited by 34 publications

(19 citation statements)

References 19 publications

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“…Solving optimization problems is the norm in almost all disciplines of engineering [1,2] and science [3,4], and the need for more robust solutions is ever increasing. This means, we need plausible algorithms that can fit the intricate nature of such up-to-date scientific and engineering challenges.…”

Section: Introductionmentioning

confidence: 99%

A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves

Braik

Ryalat

Al-Zoubi

2021

Neural Comput & Applic

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This paper presents a novel meta-heuristic algorithm called Ali Baba and the forty thieves (AFT) for solving global optimization problems. Recall the famous tale of Ali Baba and the forty thieves, where Ali Baba once saw a gang of forty thieves enter a strange cave filled with all kinds of treasures. The strategies pursued by the forty thieves in the search for Ali Baba inspired us to design ideas and underlie the basic concepts to put forward the mathematical models and implement the exploration and exploitation processes of the proposed algorithm. The performance of the AFT algorithm was assessed on a set of basic benchmark test functions and two more challenging benchmarks called IEEE CEC-2017 and IEEE CEC-C06 2019 benchmark test functions. These benchmarks cover simple and complex test functions with various dimensions and levels of complexity. An extensive comparative study was performed between the AFT algorithm and other well-studied algorithms, and the significance of the results was proved by statistical test methods. To study the potential performance of AFT, its further development is discussed and carried out from five aspects. Finally, the applicability of the AFT algorithm was subsequently demonstrated in solving five engineering design problems. The results in both benchmark functions and engineering problems show that the AFT algorithm has stronger performance than other competitors' algorithms.

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Section: Introductionmentioning

confidence: 99%

A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves

Braik

Ryalat

Al-Zoubi

2021

Neural Comput & Applic

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“…The optimization problem is reformulated into its robust counterpart optimization problem with uncertain parameters without any historical knowledge of parametric behaviour. Applications of such formulations are evident in various aspects related to process systems engineering, in the context of process systems engineering, Grossmann et al (2017) presented the review of such mathematical programming techniques for optimization under uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Robust resource targeting in continuous and batch process

Kumawat

Chaturvedi

2021

Clean Techn Environ Policy

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Water is considered a significant resource in process industries. It is essential for planners to target and optimize the use of water as an external resource for industrial operations. Such optimization problems account for uncertainties related to internal resources and must be handled to provide solutions for real plants of industrial relevance. In this paper, these parametric uncertainties are addressed, while targeting resources for continuous and flexible schedule batch process. The proposed robust counterpart formulations include resource minimization constraints for continuous and batch processes to satisfy the demand. Three different robust optimization methodologies are adapted and extended to handle parametric uncertainties associated with internal resources. Assuming bounded and known uncertainty, the resultant formulations are then implemented to literature examples and the results are compared with the deterministic formulation. The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for the defined problem because it preserves the linearity and provides a mechanism to control the degree of conservatism, guaranteeing feasibility. This model will assist the planner to decide the resource requirement under uncertain conditions. Thus, immune the process against uncertainties to satisfy demands.

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“…Other authors have developed mathematical frameworks that include uncertainty as an effective tool to evaluate the effect of variability of parameters on the system performance. On this subject, one can distinguish two approaches to include uncertainty in an optimization model, a robust optimization approach (Ben-Tal et al, 2011;Zhang et al, 2016;Saeedi et al, 2019) and a two-stage stochastic approach (Grossmann et al, 2017). The first one consists of finding a feasible solution for every uncertain scenario, while the second approach optimizes the expected value over the possible realizations considered within a set of uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Design of Sustainable Renewable-Based Utility Plants in the Face of Uncertainty

2021

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This work presents the formulation of a two-stage stochastic mixed-integer linear programming (MILP) model to include uncertainty in the design of renewable-based utility plants. The model is based on a superstructure that integrates technologies to process biomass, waste, solar radiation, and wind and considers uncertainty in availability of the renewable resources and on the utility demands. The uncertain parameter space is calculated based on a monthly probability density function for each uncertain parameter and discretized into different levels. It is shown that as uncertainty is considered in the model formulation, design flexibility improves with respect to the deterministic-based designs, although the flexibility is achieved at the expense of higher underused facilities and therefore unused investment cost.

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Mathematical Programming Techniques for Optimization under Uncertainty and Their Application in Process Systems Engineering

Cited by 34 publications

References 19 publications

A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves

A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves

Robust resource targeting in continuous and batch process

Design of Sustainable Renewable-Based Utility Plants in the Face of Uncertainty

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