Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey

Mohammad Asghari, Amir M. Fathollahi-Fard, S. M. J. Mirzapour Al-e-hashem and Maxim A. Dulebenets
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Mohammad Asghari: Department of Industrial Engineering, Dalhousie University, 5269 Morris Street, Halifax, NS B3H 4R2, Canada
Amir M. Fathollahi-Fard: Department of Electrical Engineering, École de Technologie Supérieure, University of Québec, Montréal, QC H3C 1K3, Canada
S. M. J. Mirzapour Al-e-hashem: Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15875-4413, Iran
Maxim A. Dulebenets: Department of Civil & Environmental Engineering, College of Engineering, Florida A&M University-Florida State University (FAMU-FSU), 2525 Pottsdamer Street, Building A, Suite A124, Tallahassee, FL 32310-6046, USA

Mathematics, 2022, vol. 10, issue 2, 1-26

Abstract: To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.

Keywords: linearization techniques; operations research analytics; transformation process; approximation; linear programming relaxation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

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