Kuban Altinel - Academia.edu (original) (raw)

Papers by Kuban Altinel

Computers & Operations Research, 2015

This paper is concerned with the minimization of a function whose closed-form analytical expressi... more This paper is concerned with the minimization of a function whose closed-form analytical expression is unknown, subject to well-defined and differentiable constraints. We assume that there is available data to train a multi-layer perceptron, which can be used for estimating the gradient of the objective function. We combine this estimate with the gradients of the constraints to approximate the reduced gradient, which is ultimately used for determining a feasible descent direction. We call this variant of the reduced gradient method as the Neural Reduced Gradient algorithm. We evaluate its performance on a large set of constrained convex and nonconvex test problems. We also provide an interesting and important application of the new method in the minimization of shear stress for drag reduction in the control of turbulence.

Environmentally Conscious Manufacturing IV, 2004

ABSTRACT Product line selection and pricing are two crucial decisions for the profitability of a ... more ABSTRACT Product line selection and pricing are two crucial decisions for the profitability of a manufacturing firm. Remanufacturing, on the other hand, may be a profitable strategy that captures the remaining value in used products. In this paper we develop a mixed-integer nonlinear programming model form the perspective of an original equipment manufacturer (OEM). The objective of the OEM is to select products to manufacture and remanufacture among a set of given alternatives and simultaneously determine their prices so as to maximize its profit. It is assumed that the probability a customer selects a product is proportional to its utility and inversely proportional to its price. The utility of a product is an increasing function of its perceived quality. In our base model, products are discriminated by their unit production costs and utilities. We also analyze a case where remanufacturing is limited by the available quantity of collected remanufacturable products. We show that the resulting problem is decomposed into the pricing and product line selection subproblems. Pricing problem is solved by a variant of the simplex search procedure which can also handle constraints, while complete enumeration and a genetic algorithm are used for the solution of the product line selection problem. A number of experiments are carried out to identify conditions under which it is economically viable for the firm to sell remanufactured products. We also determine the optimal utility and unit production cost values of a remanufactured product, which maximizes the total profit of the OEM.

Operations Research/Computer Science Interfaces Series, 2000

... Planning in a Refinery MURAT DRAMAN, i. KUBAN ALTINEL, NUAZ BAJGORIC, ALI TAMER ONAL, AND BUR... more ... Planning in a Refinery MURAT DRAMAN, i. KUBAN ALTINEL, NUAZ BAJGORIC, ALI TAMER ONAL, AND BURAK BIRGOREN Department of ... its components, and finally, internally generates and solves the mathematical programming model without any interaction with the user. ...

Neural Networks, 1999

In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporatin... more In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporating Explicit Statistics (KNIES) that is based on Kohonen's Self-Organizing Map (SOM). The primary difference between the SOM and the KNIES is the fact that every iteration in the training phase includes two distinct modules-the attracting module and the dispersing module. As a result of the newly introduced dispersing module the neurons maintain the overall statistical properties of the data points. Thus, although in SOM the neurons individually find their places both statistically and topologically, in KNIES they collectively maintain their mean to be the mean of the data points, which they represent. Although the scheme as it is currently implemented maintains the mean as its invariant, the scheme can easily be generalized to maintain higher order central moments as invariants. The new scheme has been used to solve the Euclidean Travelling Salesman Problem (TSP). Experimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSPLIB-A travelling salesman problem library. ORSA Journal on Computing, 3, pp. 376-384] indicate that it is a very accurate NN strategy for the TSP-probably the most accurate neural solutions available in the literature.

Naval Research Logistics, 2007

In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, square... more In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, squared Euclidean, and pdistances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient.

Journal of Waterway, Port, Coastal, and Ocean Engineering, 2013

Vessels arriving at a port wait for an available berth at the quay to load/unload. The ability to... more Vessels arriving at a port wait for an available berth at the quay to load/unload. The ability to provide a berthing space for a vessel without delay is a major managerial concern. Thus, there is an optimal resource-allocation problem, in which the resource is the length of the quay allocated dynamically over the vessels according to an arrival process. Unfortunately, quay length cannot be changed arbitrarily because of the construction and operating costs, which are increasing functions of the quay length. This paper's concern is the determination of the optimal quay length, and this problem is formulated using a variant of the stochastic knapsack problem. This method is primarily intended to estimate the length of a single quay. After introducing the mathematical formulation for the model, it is applied to a number of case studies built based on the real data obtained for several ports. Next, a sensitivity analysis of the model is presented with a wide range of arrival and service parameters drawn from real-life data. The paper concludes with a practical approach to estimating the quay lengths roughly.

Industrial Management & Data Systems, 2002

An application development framework for a software project based on fusion as an object‐oriented... more An application development framework for a software project based on fusion as an object‐oriented application development method is presented. An object‐oriented approach has been adopted for the design and implementation of the prototype interactive visual modelling system for building a visual presentation of a refinery process and creation of linear programming model for optimizing production decision variables. The main reason for this selection is the consideration of object‐oriented programming (OOP) as an obvious vehicle for the development of complex visual interactive modelling systems. The main dimensions of the framework are as follows: OO approach, fusion method, computer‐aided software engineering (CASE) tool, application development tool, GUI development tool, and C++ as an implementation language.

IIE Transactions, 2013

ABSTRACT This work considers the capacitated multi-facility Weber problem, which is concerned wit... more ABSTRACT This work considers the capacitated multi-facility Weber problem, which is concerned with locating m facilities and allocating their limited capacities to n customers in order to satisfy their demand at minimum total transportation cost. This is a nonconvex optimization problem and difficult to solve. Therefore, we propose new approximate solution methods. Some of them are based on the relaxation of the capacity constraints and apply the subgradient algorithm. The resulting Lagrangean subproblem is a variant of the well-known Multi-facility Weber Problem and can be solved using column generation and branch-and-price on a variant of the set covering formulation. Others are based on the approximating mixed integer linear programming formulations obtained by exploiting norm properties and the alternate solution of the discrete location and transportation problems. The results of a detailed computational analysis are also reported. Supplementary materials are available for this article. Go to the publisher’s online edition of IIE Transaction, datasets, additional tables, detailed proofs, etc.

IIE Transactions, 2001

We consider the component testing problem of a series system with redundant subsystems where all ... more We consider the component testing problem of a series system with redundant subsystems where all components fail exponentially. The main feature of our model is that the component failure rates are not constant parameters, but in fact change in a dynamic fashion with respect to time. The optimal component testing problem is formulated as a semi-in®nite linear program. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.

European Journal of Operational Research, 1998

An unrealistic and very restrictive assumption of component testing models in the literature is t... more An unrealistic and very restrictive assumption of component testing models in the literature is the stochastic independence of the components. The independence assumption is hardly true for a complex system where all components operate under the same environmental conditions which may change randomly in time. We consider such a model where stochastic dependence is due to the common environment that

European Journal of Operational Research, 1996

European Journal of Operational Research, 2008

In this paper, we consider the balanced unidirectional cyclic layout problem (BUCLP) arising in t... more In this paper, we consider the balanced unidirectional cyclic layout problem (BUCLP) arising in the determination of workstation locations around a closed loop conveyor system, in the allocation of cutting tools on the sites around a turret, in the positioning of stations around a unidirectional single loop AGV path. BUCLP is known to be NP-Complete. One important property of this

European Journal of Operational Research, 2010

A wireless sensor network is a network consisting of distributed autonomous electronic devices ca... more A wireless sensor network is a network consisting of distributed autonomous electronic devices called sensors. In this work, we develop a mixed-integer linear programming model to maximize the network lifetime by optimally determining locations of sensors and sinks, sensor-to-sink data flows, and activity schedules of the deployed sensors subject to coverage, flow conservation, energy consumption and budget constraints. Since solving this model is difficult except for very small instances, we propose a heuristic method which works on a reformulation of the problem. In the first phase of this heuristic, the linear programming relaxation of the reformulation is solved by column generation. The second phase consists of constructing a feasible solution for the original problem using the columns obtained in the first phase. Computational experiments conducted on a set of test instances indicate that both the accuracy and the efficiency of the proposed heuristic is quite promising.

European J. of Industrial Engineering, 2013

Sensors form an effective wireless network for the surveillance of a region. Ensuring coverage is... more Sensors form an effective wireless network for the surveillance of a region. Ensuring coverage is an important issue in wireless sensor network design. This paper focuses on an application where sensors are used to detect intruders. The defender wants to determine the best locations of the sensors to maximise the point coverage in the area with the anticipation that an intruder will attack and destroy some of the sensors to reduce the coverage. This sequential game between the defender and the intruder is modelled using bilevel programming. Two models are formulated: a bilevel pure integer linear programme (BPILP) where an attacked sensor is destroyed completely and a bilevel mixed integer linear programme (BMILP) where a damaged sensor continues to operate at a reduced capacity. Since BPILP and BMILP models are difficult to solve exactly, solution methods based on local search and tabu search are proposed, which are hybridised with an exact method. [

Computers & Operations Research, 2000

Unlike its cousin, the Euclidean Traveling Salesman Problem (TSP), to the best of our knowledge, ... more Unlike its cousin, the Euclidean Traveling Salesman Problem (TSP), to the best of our knowledge, there has been no documented all-neural solution to the Euclidean Hamiltonian Path Problem (HPP). The reason for this is the fact that the heuristics which map the cities onto the neurons “lose their credibility” because the underlying cyclic property of the order of the neurons

Computers & Operations Research, 2012

We address the problem of locating new facilities of a firm or franchise that enters a market whe... more We address the problem of locating new facilities of a firm or franchise that enters a market where a competitor operates existing facilities. The goal of the new entrant firm is to decide the location and attractiveness of its new facilities that maximize its profit. The competitor can react by opening new facilities, closing existing ones, and adjusting the attractiveness levels of its existing facilities, with the aim of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the new facilities of both the firm and the competitor can be located at predetermined candidate sites. We employ the gravity-based rule in modeling the behavior of the customers where the probability that a customer visits a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. We propose heuristics that combine tabu search with exact solution methods.

Computers & Operations Research, 2012

... top of page AUTHORS. Search for M. Hakan Akyüz Search for Temel Öncan Search for İ. ... [4]. ... more ... top of page AUTHORS. Search for M. Hakan Akyüz Search for Temel Öncan Search for İ. ... [4]. Al-Loughani L. Algorithmic approaches for solving the Euclidean distance location-allocation problems. PhD thesis, Virginia Polytechnic Institute and State University, USA; 1997. ...

Computers & Chemical Engineering, 1999

In this work, the mixed integer linear programming (MILP) model developed in Orçun et. al 1996 fo... more In this work, the mixed integer linear programming (MILP) model developed in Orçun et. al 1996 for optimal planning and scheduling of batch process plants under uncertain operating conditions is further improved to deal also with discrete probability functions. Furthermore, the logic behind integrating the processing uncertainties within the MILP model is implemented on the variations in the production volumes

Computers & Chemical Engineering, 1996

In this work, a mathematical programming model for optimal scheduling of the operations of a batc... more In this work, a mathematical programming model for optimal scheduling of the operations of a batch processing chemical plant is developed. The model is capable to handle all possible deterministic variations in the set-up and operation times of batch operations, and the model is sufficiently general to include the uncertainties introduced by the probabilistic behavior of set-up and operation times

Computer Networks, 2008

... Wireless sensor networks are based on the collaborative effort of a very large number of low-... more ... Wireless sensor networks are based on the collaborative effort of a very large number of low-power, low-cost, multi ... point coverage models based on set covering formulations do not seem to have a direct concern with efficient energy usage, Yang et al.'s work provides a ...

Computers & Operations Research, 2015

This paper is concerned with the minimization of a function whose closed-form analytical expressi... more This paper is concerned with the minimization of a function whose closed-form analytical expression is unknown, subject to well-defined and differentiable constraints. We assume that there is available data to train a multi-layer perceptron, which can be used for estimating the gradient of the objective function. We combine this estimate with the gradients of the constraints to approximate the reduced gradient, which is ultimately used for determining a feasible descent direction. We call this variant of the reduced gradient method as the Neural Reduced Gradient algorithm. We evaluate its performance on a large set of constrained convex and nonconvex test problems. We also provide an interesting and important application of the new method in the minimization of shear stress for drag reduction in the control of turbulence.

Environmentally Conscious Manufacturing IV, 2004

ABSTRACT Product line selection and pricing are two crucial decisions for the profitability of a ... more ABSTRACT Product line selection and pricing are two crucial decisions for the profitability of a manufacturing firm. Remanufacturing, on the other hand, may be a profitable strategy that captures the remaining value in used products. In this paper we develop a mixed-integer nonlinear programming model form the perspective of an original equipment manufacturer (OEM). The objective of the OEM is to select products to manufacture and remanufacture among a set of given alternatives and simultaneously determine their prices so as to maximize its profit. It is assumed that the probability a customer selects a product is proportional to its utility and inversely proportional to its price. The utility of a product is an increasing function of its perceived quality. In our base model, products are discriminated by their unit production costs and utilities. We also analyze a case where remanufacturing is limited by the available quantity of collected remanufacturable products. We show that the resulting problem is decomposed into the pricing and product line selection subproblems. Pricing problem is solved by a variant of the simplex search procedure which can also handle constraints, while complete enumeration and a genetic algorithm are used for the solution of the product line selection problem. A number of experiments are carried out to identify conditions under which it is economically viable for the firm to sell remanufactured products. We also determine the optimal utility and unit production cost values of a remanufactured product, which maximizes the total profit of the OEM.

Operations Research/Computer Science Interfaces Series, 2000

... Planning in a Refinery MURAT DRAMAN, i. KUBAN ALTINEL, NUAZ BAJGORIC, ALI TAMER ONAL, AND BUR... more ... Planning in a Refinery MURAT DRAMAN, i. KUBAN ALTINEL, NUAZ BAJGORIC, ALI TAMER ONAL, AND BURAK BIRGOREN Department of ... its components, and finally, internally generates and solves the mathematical programming model without any interaction with the user. ...

Neural Networks, 1999

In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporatin... more In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporating Explicit Statistics (KNIES) that is based on Kohonen's Self-Organizing Map (SOM). The primary difference between the SOM and the KNIES is the fact that every iteration in the training phase includes two distinct modules-the attracting module and the dispersing module. As a result of the newly introduced dispersing module the neurons maintain the overall statistical properties of the data points. Thus, although in SOM the neurons individually find their places both statistically and topologically, in KNIES they collectively maintain their mean to be the mean of the data points, which they represent. Although the scheme as it is currently implemented maintains the mean as its invariant, the scheme can easily be generalized to maintain higher order central moments as invariants. The new scheme has been used to solve the Euclidean Travelling Salesman Problem (TSP). Experimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSPLIB-A travelling salesman problem library. ORSA Journal on Computing, 3, pp. 376-384] indicate that it is a very accurate NN strategy for the TSP-probably the most accurate neural solutions available in the literature.

Naval Research Logistics, 2007

In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, square... more In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, squared Euclidean, and pdistances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient.

Journal of Waterway, Port, Coastal, and Ocean Engineering, 2013

Vessels arriving at a port wait for an available berth at the quay to load/unload. The ability to... more Vessels arriving at a port wait for an available berth at the quay to load/unload. The ability to provide a berthing space for a vessel without delay is a major managerial concern. Thus, there is an optimal resource-allocation problem, in which the resource is the length of the quay allocated dynamically over the vessels according to an arrival process. Unfortunately, quay length cannot be changed arbitrarily because of the construction and operating costs, which are increasing functions of the quay length. This paper's concern is the determination of the optimal quay length, and this problem is formulated using a variant of the stochastic knapsack problem. This method is primarily intended to estimate the length of a single quay. After introducing the mathematical formulation for the model, it is applied to a number of case studies built based on the real data obtained for several ports. Next, a sensitivity analysis of the model is presented with a wide range of arrival and service parameters drawn from real-life data. The paper concludes with a practical approach to estimating the quay lengths roughly.

Industrial Management & Data Systems, 2002

An application development framework for a software project based on fusion as an object‐oriented... more An application development framework for a software project based on fusion as an object‐oriented application development method is presented. An object‐oriented approach has been adopted for the design and implementation of the prototype interactive visual modelling system for building a visual presentation of a refinery process and creation of linear programming model for optimizing production decision variables. The main reason for this selection is the consideration of object‐oriented programming (OOP) as an obvious vehicle for the development of complex visual interactive modelling systems. The main dimensions of the framework are as follows: OO approach, fusion method, computer‐aided software engineering (CASE) tool, application development tool, GUI development tool, and C++ as an implementation language.

IIE Transactions, 2013

ABSTRACT This work considers the capacitated multi-facility Weber problem, which is concerned wit... more ABSTRACT This work considers the capacitated multi-facility Weber problem, which is concerned with locating m facilities and allocating their limited capacities to n customers in order to satisfy their demand at minimum total transportation cost. This is a nonconvex optimization problem and difficult to solve. Therefore, we propose new approximate solution methods. Some of them are based on the relaxation of the capacity constraints and apply the subgradient algorithm. The resulting Lagrangean subproblem is a variant of the well-known Multi-facility Weber Problem and can be solved using column generation and branch-and-price on a variant of the set covering formulation. Others are based on the approximating mixed integer linear programming formulations obtained by exploiting norm properties and the alternate solution of the discrete location and transportation problems. The results of a detailed computational analysis are also reported. Supplementary materials are available for this article. Go to the publisher’s online edition of IIE Transaction, datasets, additional tables, detailed proofs, etc.

IIE Transactions, 2001

We consider the component testing problem of a series system with redundant subsystems where all ... more We consider the component testing problem of a series system with redundant subsystems where all components fail exponentially. The main feature of our model is that the component failure rates are not constant parameters, but in fact change in a dynamic fashion with respect to time. The optimal component testing problem is formulated as a semi-in®nite linear program. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.

European Journal of Operational Research, 1998

An unrealistic and very restrictive assumption of component testing models in the literature is t... more An unrealistic and very restrictive assumption of component testing models in the literature is the stochastic independence of the components. The independence assumption is hardly true for a complex system where all components operate under the same environmental conditions which may change randomly in time. We consider such a model where stochastic dependence is due to the common environment that

European Journal of Operational Research, 1996

European Journal of Operational Research, 2008

In this paper, we consider the balanced unidirectional cyclic layout problem (BUCLP) arising in t... more In this paper, we consider the balanced unidirectional cyclic layout problem (BUCLP) arising in the determination of workstation locations around a closed loop conveyor system, in the allocation of cutting tools on the sites around a turret, in the positioning of stations around a unidirectional single loop AGV path. BUCLP is known to be NP-Complete. One important property of this

European Journal of Operational Research, 2010

A wireless sensor network is a network consisting of distributed autonomous electronic devices ca... more A wireless sensor network is a network consisting of distributed autonomous electronic devices called sensors. In this work, we develop a mixed-integer linear programming model to maximize the network lifetime by optimally determining locations of sensors and sinks, sensor-to-sink data flows, and activity schedules of the deployed sensors subject to coverage, flow conservation, energy consumption and budget constraints. Since solving this model is difficult except for very small instances, we propose a heuristic method which works on a reformulation of the problem. In the first phase of this heuristic, the linear programming relaxation of the reformulation is solved by column generation. The second phase consists of constructing a feasible solution for the original problem using the columns obtained in the first phase. Computational experiments conducted on a set of test instances indicate that both the accuracy and the efficiency of the proposed heuristic is quite promising.

European J. of Industrial Engineering, 2013

Sensors form an effective wireless network for the surveillance of a region. Ensuring coverage is... more Sensors form an effective wireless network for the surveillance of a region. Ensuring coverage is an important issue in wireless sensor network design. This paper focuses on an application where sensors are used to detect intruders. The defender wants to determine the best locations of the sensors to maximise the point coverage in the area with the anticipation that an intruder will attack and destroy some of the sensors to reduce the coverage. This sequential game between the defender and the intruder is modelled using bilevel programming. Two models are formulated: a bilevel pure integer linear programme (BPILP) where an attacked sensor is destroyed completely and a bilevel mixed integer linear programme (BMILP) where a damaged sensor continues to operate at a reduced capacity. Since BPILP and BMILP models are difficult to solve exactly, solution methods based on local search and tabu search are proposed, which are hybridised with an exact method. [

Computers & Operations Research, 2000

Unlike its cousin, the Euclidean Traveling Salesman Problem (TSP), to the best of our knowledge, ... more Unlike its cousin, the Euclidean Traveling Salesman Problem (TSP), to the best of our knowledge, there has been no documented all-neural solution to the Euclidean Hamiltonian Path Problem (HPP). The reason for this is the fact that the heuristics which map the cities onto the neurons “lose their credibility” because the underlying cyclic property of the order of the neurons

Computers & Operations Research, 2012

We address the problem of locating new facilities of a firm or franchise that enters a market whe... more We address the problem of locating new facilities of a firm or franchise that enters a market where a competitor operates existing facilities. The goal of the new entrant firm is to decide the location and attractiveness of its new facilities that maximize its profit. The competitor can react by opening new facilities, closing existing ones, and adjusting the attractiveness levels of its existing facilities, with the aim of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the new facilities of both the firm and the competitor can be located at predetermined candidate sites. We employ the gravity-based rule in modeling the behavior of the customers where the probability that a customer visits a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. We propose heuristics that combine tabu search with exact solution methods.

Computers & Operations Research, 2012

... top of page AUTHORS. Search for M. Hakan Akyüz Search for Temel Öncan Search for İ. ... [4]. ... more ... top of page AUTHORS. Search for M. Hakan Akyüz Search for Temel Öncan Search for İ. ... [4]. Al-Loughani L. Algorithmic approaches for solving the Euclidean distance location-allocation problems. PhD thesis, Virginia Polytechnic Institute and State University, USA; 1997. ...

Computers & Chemical Engineering, 1999

In this work, the mixed integer linear programming (MILP) model developed in Orçun et. al 1996 fo... more In this work, the mixed integer linear programming (MILP) model developed in Orçun et. al 1996 for optimal planning and scheduling of batch process plants under uncertain operating conditions is further improved to deal also with discrete probability functions. Furthermore, the logic behind integrating the processing uncertainties within the MILP model is implemented on the variations in the production volumes

Computers & Chemical Engineering, 1996

In this work, a mathematical programming model for optimal scheduling of the operations of a batc... more In this work, a mathematical programming model for optimal scheduling of the operations of a batch processing chemical plant is developed. The model is capable to handle all possible deterministic variations in the set-up and operation times of batch operations, and the model is sufficiently general to include the uncertainties introduced by the probabilistic behavior of set-up and operation times

Computer Networks, 2008

... Wireless sensor networks are based on the collaborative effort of a very large number of low-... more ... Wireless sensor networks are based on the collaborative effort of a very large number of low-power, low-cost, multi ... point coverage models based on set covering formulations do not seem to have a direct concern with efficient energy usage, Yang et al.'s work provides a ...