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

被引:89
|
作者
Asghari, Mohammad [1 ]
Fathollahi-Fard, Amir M. [2 ]
Mirzapour Al-e-hashem, S. M. J. [3 ]
Dulebenets, Maxim A. [4 ]
机构
[1] Dalhousie Univ, Dept Ind Engn, 5269 Morris St, Halifax, NS B3H 4R2, Canada
[2] Univ Quebec, Dept Elect Engn, Ecole Technol Super, Montreal, PQ H3C 1K3, Canada
[3] Amirkabir Univ Technol, Dept Ind Engn & Management Syst, Tehran Polytech, Tehran 158754413, Iran
[4] Florida State Univ FAMU FSU, Florida A&M Univ, Coll Engn, Dept Civil & Environm Engn, Pottsdamer St,Bldg A,Suite A124, Tallahassee, FL 32310 USA
关键词
linearization techniques; operations research analytics; transformation process; approximation; linear programming relaxation; PIECEWISE-LINEAR-APPROXIMATION; VESSEL SCHEDULING PROBLEM; SUPERIOR REPRESENTATION METHOD; GLOBAL OPTIMIZATION; BINARY VARIABLES; SHIPPING ROUTE; SUPPLY CHAIN; ALGORITHM; FORMULATIONS; RELAXATIONS;
D O I
10.3390/math10020283
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
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页数:26
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