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23 pages, 5256 KiB

Open AccessArticle

Assembly Function Recognition in Embedded Systems as an Optimization Problem

by Matan Avitan, Elena V. Ravve and Zeev Volkovich

Mathematics 2024, 12(5), 658; https://doi.org/10.3390/math12050658 - 23 Feb 2024

Viewed by 537

Abstract

Many different aspects of software system development and verification rely on precise function identification in binary code. Recognition of the source Assembly functions in embedded systems is one of the fundamental challenges in binary program analysis. While numerous approaches assume that the functions [...] Read more.

Many different aspects of software system development and verification rely on precise function identification in binary code. Recognition of the source Assembly functions in embedded systems is one of the fundamental challenges in binary program analysis. While numerous approaches assume that the functions are given a priori, correct identification of the functions in binaries remains a great issue. This contribution addresses the problem of uncertainty in binary code in identification of functions, which were optimized during compilation. This paper investigates the difference between debug and optimized functions via modeling of these functions. To do so, we introduce an extensible model-centred hands-on approach for examining similarities between binary functions. The main idea is to model each function using a set of predetermined, experimentally discovered features, and then find a suitable weight vector that could give impact factor to each such a feature. After finding the weight vector, the introduced models of such desired functions can be identified in binary software packages. It means that we reduce the similarity identification problem of the models to a classical version of optimization problems with one optimization criterion. Using our implementation, we found that the proposed approach works smoothly for functions, which contain at least ten Assembly instructions. Our tool guarantees success at a very high level. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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19 pages, 3608 KiB

Open AccessArticle

A Multi-Stage Methodology for Long-Term Open-Pit Mine Production Planning under Ore Grade Uncertainty

by Enrique Jelvez, Julian Ortiz, Nelson Morales Varela, Hooman Askari-Nasab and Gonzalo Nelis

Mathematics 2023, 11(18), 3907; https://doi.org/10.3390/math11183907 - 14 Sep 2023

Cited by 1 | Viewed by 2757

Abstract

The strategic planning of open pit operations defines the best strategy for extraction of the mineral deposit to maximize the net present value. The process of strategic planning must deal with several sources of uncertainty; therefore, many authors have proposed models to incorporate [...] Read more.

The strategic planning of open pit operations defines the best strategy for extraction of the mineral deposit to maximize the net present value. The process of strategic planning must deal with several sources of uncertainty; therefore, many authors have proposed models to incorporate it at each of its stages: Computation of the ultimate pit, optimization of pushbacks, and production scheduling. However, most works address it at each level independently, with few aiming at the whole process. In this work, we propose a methodology based on new mathematical optimization models and the application of conditional simulation of the deposit for addressing the geological uncertainty at all stages. We test the method in a real case study and evaluate whether incorporating uncertainty increases the quality of the solutions. Moreover, we benefit from our integrated framework to evaluate the relative impact of uncertainty at each stage. This could be used by decision-makers as a guide for detecting risks and focusing efforts. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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33 pages, 8896 KiB

Open AccessArticle

Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm

by Wanida Limmun, Boonorm Chomtee and John J. Borkowski

Mathematics 2023, 11(16), 3558; https://doi.org/10.3390/math11163558 - 17 Aug 2023

Viewed by 753

Abstract

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture [...] Read more.

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture designs that remain robust in the face of missing observation. Our algorithm prioritizes designs that exhibit superior D-efficiency while maintaining a high minimum D-efficiency due to missing observations. The focus on D-efficiency stems from its ability to minimize the impact of missing observations on parameter estimates, ensure reliability across the experimental space, and maximize the utility of available data. We study problems with three mixture components where the experimental region is an irregularly shaped polyhedral within the simplex. Our designs have proven to be D-optimal designs, demonstrating exceptional performance in terms of D-efficiency and robustness to missing observations. We provide a well-distributed set of optimal designs derived from the Pareto front, enabling experimenters to select the most suitable design based on their priorities using the desirability function. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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15 pages, 2797 KiB

Open AccessArticle

Inverse Optimization Method for Safety Resource Allocation and Inferring Cost Coefficient Based on a Benchmark

by Lili Zhang and Wenhao Guo

Mathematics 2023, 11(14), 3207; https://doi.org/10.3390/math11143207 - 21 Jul 2023

Viewed by 786

Abstract

Due to cost-push inflation, the trade-off between safety costs and risk prevention (safety) has become difficult worldwide. Most companies experience the difficulty of safety cost overruns and allocate safety resource inefficiently. In this paper, a forward model maximizing safety input is formulated. Because [...] Read more.

Due to cost-push inflation, the trade-off between safety costs and risk prevention (safety) has become difficult worldwide. Most companies experience the difficulty of safety cost overruns and allocate safety resource inefficiently. In this paper, a forward model maximizing safety input is formulated. Because there is a wide range of variation of safety resource cost coefficient parameters, it is hard to determine safety resource cost coefficients in the forward model, to make the decisions on which types of safety resources are allocated to which potentially risky locations with what prices, and to ensure total input is as close to the benchmark as possible. Taking allocation, themes, resources, and cost coefficient parameters as new decision variables, the inverse optimization model is formulated based on a bi-level model. With consideration of quaternion decision, bi-level programming, and NP-hard problem, based on the comparison of exact penalty algorithm and an improved PSO algorithm, in which the inertia weight is adaptively changing with the number of iterations, the PSO is suitable for solving the specific inverse model. Numerical experiments demonstrated the effectiveness of the PSO algorithm, proving that it can allocate the right amount and types of safety resources with the right prices at the right places. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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19 pages, 695 KiB

Open AccessArticle

Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions

by Linas Stripinis and Remigijus Paulavičius

Mathematics 2023, 11(13), 2920; https://doi.org/10.3390/math11132920 - 29 Jun 2023

Cited by 3 | Viewed by 930

Abstract

This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential [...] Read more.

This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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22 pages, 497 KiB

Open AccessArticle

The Set Covering and Other Problems: An Empiric Complexity Analysis Using the Minimum Ellipsoidal Width

by Ivan Derpich, Juan Valencia and Mario Lopez

Mathematics 2023, 11(13), 2794; https://doi.org/10.3390/math11132794 - 21 Jun 2023

Cited by 1 | Viewed by 664

Abstract

This research aims to explain the intrinsic difficulty of Karp’s list of twenty-one problems through the use of empirical complexity measures based on the ellipsoidal width of the polyhedron generated by the constraints of the relaxed linear programming problem. The variables used as [...] Read more.

This research aims to explain the intrinsic difficulty of Karp’s list of twenty-one problems through the use of empirical complexity measures based on the ellipsoidal width of the polyhedron generated by the constraints of the relaxed linear programming problem. The variables used as complexity measures are the number of nodes visited by the

B & B

and the CPU time spent solving the problems. The measurements used as explanatory variables correspond to the Dikin ellipse eigenvalues within the polyhedron. Other variables correspond to the constraint clearance with respect to the analytical center used as the center of the ellipse. The results of these variables in terms of the number of nodes and CPU time are particularly satisfactory. They show strong correlations, above 60%, in most cases. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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16 pages, 287 KiB

Open AccessArticle

A Matheuristic Approach to the Integration of Three-Dimensional Bin Packing Problem and Vehicle Routing Problem with Simultaneous Delivery and Pickup

by Ana Moura, Telmo Pinto, Cláudio Alves and José Valério de Carvalho

Mathematics 2023, 11(3), 713; https://doi.org/10.3390/math11030713 - 31 Jan 2023

Cited by 7 | Viewed by 1916

Abstract

This work presents a hybrid approach to solve a distribution problem of a Portuguese company in the automotive industry. The objective is to determine the minimum cost for daily distribution operations, such as collecting and delivering goods to multiple suppliers. Additional constraints are [...] Read more.

This work presents a hybrid approach to solve a distribution problem of a Portuguese company in the automotive industry. The objective is to determine the minimum cost for daily distribution operations, such as collecting and delivering goods to multiple suppliers. Additional constraints are explicitly considered, such as time windows and loading constraints due to the limited capacity of the fleet in terms of weight and volume. An exhaustive review of the state of the art was conducted, presenting different typology schemes from the literature for the pickup and delivery problems in the distribution field. Two mathematical models were integrated within a matheuristic approach. One model reflects the combination of the Vehicle Routing Problem with Simultaneous Delivery and Pickup with the Capacitated Vehicle Routing Problem with Time Windows. The second one aims to pack all the items to be delivered onto the pallets, reflecting a three-dimensional single bin size Bin Packing Problem. Both formulations proposed—a commodity-flow model and a formulation of the Three-Dimensional Packing Problem must be solved within the matheuristic. All the approaches were tested using real instances from data provided by the company. Additional computational experiments using benchmark instances were also performed. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

18 pages, 750 KiB

Open AccessArticle

Experimental Study of Excessive Local Refinement Reduction Techniques for Global Optimization DIRECT-Type Algorithms

by Linas Stripinis and Remigijus Paulavičius

Mathematics 2022, 10(20), 3760; https://doi.org/10.3390/math10203760 - 12 Oct 2022

Cited by 4 | Viewed by 1181

Abstract

This article considers a box-constrained global optimization problem for Lipschitz continuous functions with an unknown Lipschitz constant. The well-known derivative-free global search algorithm DIRECT (DIvide RECTangle) is a promising approach for such problems. Several studies have shown that recent two-step (global and local) [...] Read more.

This article considers a box-constrained global optimization problem for Lipschitz continuous functions with an unknown Lipschitz constant. The well-known derivative-free global search algorithm DIRECT (DIvide RECTangle) is a promising approach for such problems. Several studies have shown that recent two-step (global and local) Pareto selection-based algorithms are very efficient among all DIRECT-type approaches. However, despite its encouraging performance, it was also observed that the candidate selection procedure has two possible shortcomings. First, there is no limit on how small the size of selected candidates can be. Secondly, a balancing strategy between global and local candidate selection is missing. Therefore, it may waste function evaluations by over-exploring the current local minimum and delaying finding the global one. This paper reviews and employs different strategies in a two-step Pareto selection framework (1-DTC-GL) to overcome these limitations. A detailed experimental study has revealed that existing strategies do not always improve and sometimes even worsen results. Since 1-DTC-GL is a DIRECT-type algorithm, the results of this paper provide general guidance for all DIRECT-type algorithms on how to deal with excessive local refinement more efficiently. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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34 pages, 5666 KiB

Open AccessArticle

A Line Planning Optimization Model for High-Speed Railway Network Merging Newly-Built Railway Lines

by Wenliang Zhou, Yujun Huang, Naijie Chai, Bo Li and Xiang Li

Mathematics 2022, 10(17), 3174; https://doi.org/10.3390/math10173174 - 03 Sep 2022

Cited by 2 | Viewed by 1236

Abstract

This paper is devoted to developing a line-planning approach for high-speed railway networks merging newly built railway lines, which result in the change of the network’s original structure and some passengers’ travel routes. In order to exactly describe the choice of time-varying passengers [...] Read more.

This paper is devoted to developing a line-planning approach for high-speed railway networks merging newly built railway lines, which result in the change of the network’s original structure and some passengers’ travel routes. In order to exactly describe the choice of time-varying passengers and the operation of the trains, a passenger travel network with time information is constructed based on the pre-generated candidate train set. Following this, a line-planning optimization model for optimizing trains on both the existing railway network and the merged new railway line is established under the considered constraints, such as transportation resources on the network. It does not aim to only provide higher service level for passengers and increase revenue of railway enterprise, but also to ensure the continuity of the existing trains to facilitates passengers and train organization. A framework of the Simulated Annealing Algorithm is designed to solve the proposed model by combining the neighboring solution search strategies with evaluation method based on the allocation of passengers. The case of a partial high-speed railway network in China is studied to test the practicability and validity of the proposed approach. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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24 pages, 3361 KiB

Open AccessArticle

Design and Operation of Multipurpose Production Facilities Using Solar Energy Sources for Heat Integration Sustainable Strategies

by Pedro Simão, Miguel Vieira, Telmo Pinto and Tânia Pinto-Varela

Mathematics 2022, 10(11), 1941; https://doi.org/10.3390/math10111941 - 06 Jun 2022

Viewed by 1574

Abstract

Industrial production facilities have been facing the requirement to optimise resource efficiency, while considering sustainable goals. This paper addresses the introduction of renewable energies in production by exploring the combined design and scheduling of a multipurpose batch facility, with innovative consideration of direct/indirect [...] Read more.

Industrial production facilities have been facing the requirement to optimise resource efficiency, while considering sustainable goals. This paper addresses the introduction of renewable energies in production by exploring the combined design and scheduling of a multipurpose batch facility, with innovative consideration of direct/indirect heat integration using a solar energy source for thermal energy storage. A mixed-integer linear programming model is formulated to support decisions on scheduling and design selection of storage and processing units, heat exchange components, collector systems, and energy storage units. The results show the minimisation of utilities consumption, with an increase in the operational profit using combined heat integration strategies for the production schedule. A set of illustrative case-study examples highlight the advantages of the solar-based heat storage integration, assessing optimal decision support in the strategic and operational management of these facilities. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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18 pages, 654 KiB

Open AccessArticle

An Integrated Two-Level Integer Linear Program (ILP) Model for Elective Surgery Scheduling: A Case Study in an Italian Hospital

by Rafael L. Patrão, Reinaldo C. Garcia and João M. da Silva

Mathematics 2022, 10(11), 1901; https://doi.org/10.3390/math10111901 - 01 Jun 2022

Cited by 1 | Viewed by 2180

Abstract

The urban population is increasing worldwide. This demographic shift generates great pressure over public services, especially those related to health-care. One of the most expensive health-care services is surgery, and in order to contain this growing cost of providing better services, the efficiency [...] Read more.

The urban population is increasing worldwide. This demographic shift generates great pressure over public services, especially those related to health-care. One of the most expensive health-care services is surgery, and in order to contain this growing cost of providing better services, the efficiency of surgical centers must be improved. This work proposes an integer linear programming model (ILP) considering the case-mix planning (CMP) and the master surgical scheduling (MSS) problems. The case-mix planning problem deals with the planning of the number of operating rooms to be assigned to surgical specialties. The master surgical scheduling is related to when to assign the rooms to the different specialties. The developed model uses a data set from a hospital of the city of Turin, Italy. The results are very promising, showing a reduction from 240 weeks to 144 weeks to empty the surgical waiting list (WL). Moreover, if changes to the hospital situation are implemented, including the introduction of two new surgical teams into one of the hospital’s specialties, the time to empty the surgical WL could decrease to 79 weeks. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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12 pages, 602 KiB

Open AccessArticle

Shifted Brownian Fluctuation Game

by Song-Kyoo (Amang) Kim

Mathematics 2022, 10(10), 1735; https://doi.org/10.3390/math10101735 - 19 May 2022

Cited by 2 | Viewed by 1319

Abstract

This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict the turning points of a stochastic [...] Read more.

This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict the turning points of a stochastic process. This compound process evolves until it reaches one step prior to the turning point. The Shifted Brownian Fluctuation Game has been constructed based on this new process to find the optimal moment of actions. Analytically tractable results are obtained by using the fluctuation theory and the mixed strategy game theory. The joint functional of the Shifted Brownian Fluctuation Process is targeted for transformation of the first passage time and its index. These results enable us to predict the moment of a turning point and the moment of actions to obtain the optimal payoffs of a game. This research adapts the theoretical framework to implement an autonomous trader for value assets including stocks and cybercurrencies. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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19 pages, 1416 KiB

Open AccessArticle

Integrated Order Picking and Multi-Skilled Picker Scheduling in Omni-Channel Retail Stores

by Shandong Mou

Mathematics 2022, 10(9), 1484; https://doi.org/10.3390/math10091484 - 29 Apr 2022

Cited by 7 | Viewed by 1856

Abstract

Utilizing local brick-and-mortar stores for same-day order fulfillment is becoming prominent in omni-channel retailing. Efficient in-store order picking is critical to providing timely value-added omni-channel delivery services. Despite numerous studies on order picking in traditional logistics warehouses and distribution centers, there is scant [...] Read more.

Utilizing local brick-and-mortar stores for same-day order fulfillment is becoming prominent in omni-channel retailing. Efficient in-store order picking is critical to providing timely value-added omni-channel delivery services. Despite numerous studies on order picking in traditional logistics warehouses and distribution centers, there is scant research focusing on in-store order fulfillment with the multi-skilled workforce in omni-channel retail stores. We studied the integrated Order Picking and Heterogeneous Picker Scheduling Problem (OPPSP-Het) in omni-channel retail stores. We characterized the OPPSP-Het in a mixed-integer linear optimization model with the objective of the minimization of total tardiness of all customer orders. A hybrid heuristic combining the genetic algorithm and variable neighborhood descent was designed to obtain effective solutions. Extensive experiments were conducted to validate the performance of the proposed approach relative to existing algorithms in recent literature. We further numerically showed the effects of order size and heterogeneous workforce on order fulfillment performance. We lastly emphasized the importance of workforce flexibility as a cost-effective approach to improving in-store order fulfillment performance. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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26 pages, 4977 KiB

Open AccessArticle

Robust Optimization of High-Speed Railway Train Plan Based on Multiple Demand Scenarios

by Wenliang Zhou, Jing Kang, Jin Qin, Sha Li and Yu Huang

Mathematics 2022, 10(8), 1278; https://doi.org/10.3390/math10081278 - 12 Apr 2022

Cited by 5 | Viewed by 1571

Abstract

The optimization of train plans is highly dependent on the space–time distribution of passenger demand in high-speed railway systems. A train plan usually needs to be implemented on multiple operation days, and obviously the amount and space–time distribution of demand over these days [...] Read more.

The optimization of train plans is highly dependent on the space–time distribution of passenger demand in high-speed railway systems. A train plan usually needs to be implemented on multiple operation days, and obviously the amount and space–time distribution of demand over these days has noteworthy differences. To ensure the same train plan is able to be implemented on multiple operation days while effectively satisfying the different levels of demand on those days, a novel robust optimization of a high-speed railway train plan based on multiple demand scenarios is performed in this research. Firstly, the passenger demand of each operation day is described as a demand scenario, and a candidate train set is generated that is able to satisfy the multiple demand scenarios. Then, a regret value corresponding to the total cost, including the train operation cost and passenger travel expense, is proposed to measure the deviation in the costs generated between the robust and the optimal train plan under each demand scenario. Then a robust optimization model for a high-speed railway train plan is constructed to minimize the maximum regret value. Moreover, a simulated annealing algorithm for solving the model is designed by constructing some neighborhood solution search strategies for multiple demand scenarios. Finally, the validity and feasibility of the proposed robust optimization method for train planning are verified on the Shijiazhuang–Jinandong high-speed railway line in China. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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15 pages, 5035 KiB

Open AccessArticle

Multi-UAV Coverage Path Planning Based on Hexagonal Grid Decomposition in Maritime Search and Rescue

by Sung-Won Cho, Jin-Hyoung Park, Hyun-Ji Park and Seongmin Kim

Mathematics 2022, 10(1), 83; https://doi.org/10.3390/math10010083 - 27 Dec 2021

Cited by 21 | Viewed by 4401

Abstract

In the event of a maritime accident, surveying the maximum area efficiently in the least amount of time is crucial for rescuing survivors. Increasingly, unmanned aerial vehicles (UAVs) are being used in search and rescue operations. This study proposes a method to generate [...] Read more.

In the event of a maritime accident, surveying the maximum area efficiently in the least amount of time is crucial for rescuing survivors. Increasingly, unmanned aerial vehicles (UAVs) are being used in search and rescue operations. This study proposes a method to generate a search path that covers all generated nodes in the shortest amount of time with multiple heterogeneous UAVs. The proposed model, which is a mixed-integer linear programming (MILP) model based on a hexagonal grid-based decomposition method, was verified through a simulation analysis based on the performance of an actual UAV. This study presents both the optimization technique’s calculation time as a function of the search area size and the various UAV routes derived as the search area grows. The results of this study can have wide-ranging applications for emergency search and rescue operations. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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13 pages, 460 KiB

Open AccessArticle

A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

by Saeid Jafarzadeh Ghoushchi, Elnaz Osgooei, Gholamreza Haseli and Hana Tomaskova

Mathematics 2021, 9(22), 2937; https://doi.org/10.3390/math9222937 - 18 Nov 2021

Cited by 12 | Viewed by 2207

Abstract

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut [...] Read more.

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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Review

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26 pages, 1245 KiB

Open AccessReview

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

by Mohammad Asghari, Amir M. Fathollahi-Fard, S. M. J. Mirzapour Al-e-hashem and Maxim A. Dulebenets

Mathematics 2022, 10(2), 283; https://doi.org/10.3390/math10020283 - 17 Jan 2022

Cited by 68 | Viewed by 12807

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Operations Research and Optimization)

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