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2017-04-11
Journal Article
2017-01-9075
Rami Abousleiman, Osamah Rawashdeh, Romi Boimer
Abstract Growing concerns about the environment, energy dependency, and the unstable fuel prices have increased the sales of electric vehicles. Energy-efficient routing for electric vehicles requires novel algorithmic challenges because traditional routing algorithms are designed for fossil-fueled vehicles. Negative edge costs, battery power and capacity limits, vehicle parameters that are only available at query time, alongside the uncertainty make the task of electric vehicle routing a challenging problem. In this paper, we present a solution to the energy-efficient routing problem for electric vehicles using ant colony optimization. Simulation and real-world test results demonstrate savings in the energy consumption of electric vehicles when driven on the generated routes. Real-world test results revealed more than 9% improvements in the energy consumption of the electric vehicle when driven on the recommended route rather than the routes proposed by Google Maps and MapQuest.
2017-04-11
Journal Article
2017-01-9076
Ioannis Karakitsios, Evangelos Karfopoulos, Nikolay Madjarov, Aitor Bustillo, Marc Ponsar, Dionisio Del Pozo, Luca Marengo
Abstract The aim of this paper is to introduce a complete fast dynamic inductive charging infrastructure from the back-office system (EV management system) up to the Electric Vehicle (EV) (inductive power transfer module, positioning mechanism, electric vehicle modifications) and the EV user (User interface). Moreover, in order to assess the impact of the additional demand of inductive charging on the grid operation, an estimation of the 24-hour power profile of dynamic inductive charging is presented considering, apart from the road traffic, the probability of the need for fast charging, as well as the specifications of the proposed solution. In addition, an energy management system is presented enabling the management of the operation of the inductive charging infrastructure, the interaction with the EV users and the provision of demand response services to different stakeholders.
2017-04-11
Journal Article
2017-01-9625
Souhir Tounsi
Abstract In this paper, we present a design and control methodology of an innovated structure of switching synchronous motor. This control strategy is based on the pulse width modulation technique imposing currents sum of a continuous value and a value having a shape varying in phase opposition with respect to the variation of the inductances. This control technology can greatly reduce vibration of the entire system due to the strong fluctuation of the torque developed by the engine, generally characterizing switching synchronous motors. A systemic design and modelling program is developed. This program is validated following the implementation and the simulation of the control model in the simulation environment Matlab-Simulink. Simulation results are with good scientific level and encourage subsequently the industrialization of the global system.
2017-04-11
Journal Article
2017-01-9450
Ali Reza Taherkhani, Carl Gilkeson PhD, Philip Gaskell PhD, Rob Hewson PhD, Vassili Toropov PhD, Amin Rezaienia PhD, Harvey Thompson
Abstract This paper investigates the optimization of the aerodynamic design of a police car, BMW 5-series which is popular police force across the UK. A Bezier curve fitting approach is proposed as a tool to improve the existing design of the warning light cluster in order to reduce drag. A formal optimization technique based on Computational Fluid Dynamics (CFD) and moving least squares (MLS) is used to determine the control points for the approximated curve to cover the light-bar and streamline the shape of the roof. The results clearly show that improving the aerodynamic design of the roofs will offer an important opportunity for reducing the fuel consumption and emissions for police vehicles. The optimized police car has 30% less drag than the non-optimized counter-part.
2017-03-28
Technical Paper
2017-01-0214
Simon O. Omekanda, Rezwanur Rahman, Eric M. Lott, Sadek S. Rahman, Daniel E. Hornback
Designing an efficient transient thermal system model has become a very important task in improving fuel economy. As opposed to steady-state thermal models, part of the difficulty in designing a transient model is optimizing a set of inputs. The first objective in this work is to develop an engine compatible physics-based 1D thermal model for fuel economy and robust control. In order to capture and study the intrinsic thermo-physical nature, both generic “Three Mass” and “Eight Mass” engine model are developed. The models have been correlated heuristically using Simulink and Flowmaster, respectively. In order to extend the lumped mass engine model it also has been extended to Simulink model. In contrast to the complexity of the models the “Heuristic search” of input parameters has been found to be challenging and time consuming.
2017-03-28
Technical Paper
2017-01-1504
Peter Tkacik, Zachary Carpenter, Aaron Gholston, Benjamin James Cobb, Sam Kennedy, Ethan Blankenship, Mesbah Uddin, Surya Phani Krishna Nukala
Wind tunnel aerodynamic testing involving rolling road tire conditions can be expensive and complex to set up. Low cost rolling road testing can be implemented in a 0.3m2 Eiffel wind tunnel by modifying a horizontal belt sander to function as a moving road. This sander is equipped with steel supports to hold a steel plate against the bottom of the wind tunnel to stabilize the entire test section. These supports are bolted directly into the cast iron sander frame to ensure minimal vibrational losses or errors during testing. The wind tunnel design at the beginning of the project was encased in a wooden box which was removed to allow easier access to the test section for installation of the rolling road assembly. The tunnel was also modified to allow observers to view the testing process from various angles.
2017-03-28
Technical Paper
2017-01-0632
Chen Yang, Haiyuan Cheng, Zizhu fan, Jiandong Yin, Yuan Shen
Abstract In recent years, more attention has been focused on environment pollution and energy source issues. As a result, increasingly stringent fuel consumption and emission legislations have been implemented all over the world. For automakers, enhancing engine’s efficiency as a must contributes to lower vehicle fuel consumption. To reach this goal, Geely auto started the development of a 3-cylinder 1.0L turbocharged direct injection (TGDI) gasoline engine to achieve a challenging fuel economy target while maintaining fun-to-drive and NVH performance. Demanding development targets for performance (specific torque 205Nm/L and specific power 100kW/L) and excellent part-load BSFC were defined, which lead to a major challenge for the design of engine systems, especially for combustion system.
2017-03-28
Journal Article
2017-01-0441
Zhenyu Wang, Mei Zhuang
Abstract A numerical study on sunroof noise reduction is carried out. One of the strategies to suppress the noise is to break down the strong vortices impinging upon the trailing edge of the sunroof into smaller eddies. In the current study, a serrated sunroof trailing edge with sinusoidal profiles of wavelengths is investigated for the buffeting noise reduction. A number of combinations of wavelengths and amplitudes of sinusoidal profiles is employed to examine the effects of trailing edge serrations on the noise reduction. A generic vehicle model is used in the study and a straight trailing edge is considered as a baseline. The results indicate that the trailing edge serration has a significant impact on the sound pressure level (SPL) in the vehicle cabin and it can reduce the SPL by up to 10~15 dB for the buffeting frequency.
2017-03-28
Journal Article
2017-01-0437
Bin Li, Subhash Rakheja
Abstract In this paper, a gain-scheduling optimal control approach is proposed to enhance yaw stability of articulated commercial vehicles through active braking of the proper wheel(s). For this purpose, an optimal feedback control is used to design a family of yaw moment controllers considering a broad range of vehicle velocities. The yaw moment controller is designed such that the instantaneous tractor yaw rate and articulation angle responses are forced to track the target values at each specific vehicle velocity. A gain scheduling mechanism is subsequently constructed via interpolations among the controllers. Furthermore, yaw moments derived from the proposed controller are realized by braking torque distribution among the appropriate wheels. The effectiveness of the proposed yaw stability control scheme is evaluated through software-in-the-loop (SIL) co-simulations involving Matlab/Simulink and TruckSim under lane change maneuvers.
2017-03-28
Technical Paper
2017-01-0438
Zhenhai Gao, Tianjun Sun, Lei He
Abstract A multitude of recent studies are suggestive of the EV as a paramount representative of the NEV, its development direction is transformed from “individuals adapt to vehicles” to “vehicles serve for occupants”. The multi-mode drive control technology is relatively mature in traditional auto control sphere, however, a host of EV continues to use a single control strategy, which lacks of flexibility and diversity, little if nothing interprets the vehicle performances. Furthermore, due to the complex road environment and peculiarity of vehicle occupants that different requirement has been made for vehicle performance.
2017-03-28
Technical Paper
2017-01-0436
Tianjun Zhu, Bin Li
Abstract A new extended planar model for multi-axle articulated vehicle with nonlinear tire model is presented. This nonlinear multi-axle articulated vehicle model is specifically intended for improving the model performance in operating regimes where tire lateral force is near the point of saturation, and it has the potential to extend the specific axles model to any representative configuration of articulated vehicle model. At the same time, the extended nonlinear vehicle model can reduce the model's sensitivity to the tire cornering coefficients. Firstly, a nonlinear tire model is used in conjunction with the 6-axle planar articulated vehicle model to extend the ranges of the original linear model into the nonlinear regimes of operation. Secondly, the performance analysis of proposed nonlinear vehicle model is verified through the double lane change maneuver on different road adhesion coefficients using TruckSim software.
2017-03-28
Technical Paper
2017-01-0479
Soichi Hareyama, Ken-ichi Manabe, Makoto Nakashima, Takayuki Shimodaira, Akio Hoshi
Abstract This investigation describes a method for estimating the absolute lock effect in bolted joint. Observation results of loosening phenomenon in industrial vehicle are analyzed for the linear relation by the proposed regression formula. Based on the relation, in early stages of the development test, the rate of clamping force decrease can be estimated accurately after prolonged operation by measuring the clamping force behavior. The tendency to decrease is observed about the depression type and working load type loosening. For evaluation design bases, the residual clamping force estimation chart is established. The L-N (Loosening Lifetime - Number of Cycles to Loosening N) diagram is proposed for the loosening lifetime prediction for working load type loosening also. Using the loosening damage (cumulative decrease of clamping force) and L-N diagram, the lifetime to loosening failure can be predicted accurately for the locking device and method as an absolute evaluation.
2017-03-28
Technical Paper
2017-01-0522
Jianning Zhao, Antonio Sciarretta
Abstract Fuel consumption is an essential factor that requires to be minimized in the design of a vehicle powertrain. Simple energy models can be of great help - by clarifying the role of powertrain dimensioning parameters and reducing the computation time of complex routines aiming at optimizing these parameters. In this paper, a Fully Analytical fuel Consumption Estimation (FACE) is developed based on a novel GRaphical-Analysis-Based fuel Energy Consumption Optimization (GRAB-ECO), both of which predict the fuel consumption of light- and heavy-duty series hybrid-electric powertrains that is minimized by an optimal control technique. When a drive cycle and dimensioning parameters (e.g. vehicle road load, as well as rated power, torque, volume of engine, motor/generators, and battery) are considered as inputs, FACE predicts the minimal fuel consumption in closed form, whereas GRAB-ECO minimizes fuel consumption via a graphical analysis of vehicle optimal operating modes.
2017-03-28
Technical Paper
2017-01-0520
Gianluca Montenegro, Augusto Della Torre, Tarcisio Cerri, Angelo Onorati, Lorenzo Nocivelli, Marco Fiocco
Abstract In this work an integration between a 1D code (Gasdyn) with a CFD code (OpenFOAM®) has been applied to improve the performance of a Moto3 engine. The four-stroke, single cylinder S.I. engine was modeled, in order to predict the wave motion in the intake and exhaust systems and to study how it affects the cylinder gas exchange process. The engine considered was characterized by having an air induction system with integrated filter cartridge, air-box and intake runner, including two fuel injectors, resulting in a complex air-path from the intake mouth to the intake valves, which presents critical aspects when a 1D modeling is addressed. The exhaust and intake systems have been optimized form the point of view of the wave action. However, due to the high revolution speed reached by this type of engine, the interaction between the gas stream and the fuel spray becomes a key aspect to be addressed in order to achieve the best performance at the desired operating condition.
2017-03-28
Journal Article
2017-01-0153
Dipankar Sahoo, Adam Kotrba, Tom Steiner, Greg Swift
Abstract Nearly a third of the fuel energy is wasted through the exhaust of a vehicle. An efficient waste heat recovery process will undoubtedly lead to improved fuel efficiency and reduced greenhouse gas (GHG) emissions. Currently, there are multiple waste heat recovery technologies that are being investigated in the auto industry. One innovative waste heat recovery approach uses Thermoacoustic Converter (TAC) technology. Thermoacoustics is the field of physics related to the interaction of acoustic waves (sonic power) with heat flows. As in a heat engine, the TAC produces electric power where a temperature differential exists, which can be generated with engine exhaust (hot side) and coolant (cold side). Essentially, the TAC converts exhaust waste heat into electricity in two steps: 1) the exhaust waste heat is converted to acoustic energy (mechanical) and 2) the acoustic energy is converted to electrical energy.
2017-03-28
Technical Paper
2017-01-0171
Quansheng Zhang, Yan Meng, Christopher Greiner, Ciro Soto, William Schwartz, Mark Jennings
Abstract In this paper, the tradeoff relationship between the Air Conditioning (A/C) system performance and vehicle fuel economy for a hybrid electric vehicle during the SC03 drive cycle is presented. First, an A/C system model was integrated into Ford’s HEV simulation environment. Then, a system-level sensitivity study was performed on a stand-alone A/C system simulator, by formulating a static optimization problem which minimizes the total energy use of actuators, and maintains an identical cooling capacity. Afterwards, a vehicle-level sensitivity study was conducted with all controllers incorporated in sensitivity analysis software, under three types of formulations of cooling capacity constraints. Finally, the common observation from both studies, that the compressor speed dominates the cooling capacity and the EDF fan has a marginal influence, is explained using the thermodynamics of a vapor compression cycle.
2017-03-28
Technical Paper
2017-01-0190
Neelakandan Kandasamy, Steve Whelan
Abstract The range of Plug-In Electric Vehicles (EVs) is highly influenced by the electric power consumed by various sub systems, the major part of the power being used for vehicle climate control strategies in order to ensure an acceptable level of thermal comfort for the passengers. Driving range decreases with low temperatures in particular because cabin heating system requires significant amount of electric power. Range also decreases with high ambient temperatures because of the air conditioning system with electrically-driven compressor. Both thermal systems reduce EV driving range under real life operating cycles, which can be a barrier against market penetration. The structure of a vehicle is capable of absorbing a significant amount of heat when exposed to hot climate conditions. 50-70% of this heat penetrates through the glazing and raises both the internal cabin air temperature and the interior trim surface temperature.
2017-03-28
Technical Paper
2017-01-0186
Cory J. Kreutzer, John Rugh, Jeff Tomerlin
Abstract Increased market penetration of electric drive vehicles (EDVs) requires overcoming a number of hurdles, including limited vehicle range and the elevated cost in comparison to conventional vehicles. Climate control loads have a significant impact on range, cutting it by over 50% in both cooling and heating conditions. To minimize the impact of climate control on EDV range, the National Renewable Energy Laboratory has partnered with Hyundai America and key industry partners to quantify the performance of thermal load reduction technologies on a Hyundai Sonata plug-in hybrid electric vehicle. Technologies that impact vehicle cabin heating in cold weather conditions and cabin cooling in warm weather conditions were evaluated. Tests included thermal transient and steady-state periods for all technologies, including the development of a new test methodology to evaluate the performance of occupant thermal conditioning.
2017-03-28
Technical Paper
2017-01-0189
Song Lan, Cedric Rouaud, Richard Stobart, Rui Chen, Zhijia Yang, Dezong Zhao
Abstract This paper reports on an investigation into the potential for a thermoelectric generator (TEG) to improve the fuel economy of a mild hybrid vehicle. A simulation model of a parallel hybrid vehicle equipped with a TEG in the exhaust system is presented. This model is made up by three sub-models: a parallel hybrid vehicle model, an exhaust model and a TEG model. The model is based on a quasi-static approach, which runs a fast and simple estimation of the fuel consumption and CO2 emissions. The model is validated against both experimental and published data. Using this model, the annual fuel saving, CO2 reduction and net present value (NPV) of the TEG’s life time fuel saving are all investigated. The model is also used as a flexible tool for analysis of the sensitivity of vehicle fuel consumption to the TEG design parameters. The analysis results give an effective basis for optimization of the TEG design.
2017-03-28
Technical Paper
2017-01-0188
Yoichiro Higuchi, Hiroyuki Kobayashi, Zhiwei Shan, Mikiharu Kuwahara, Yoshiharu Endo, Yuha Nakajima
Abstract As vehicle emission regulations become increasingly rigorous, the automotive industry is accelerating the development of electrified vehicle platforms such as Battery Electric Vehicles (BEV) and Plug-in Hybrid Electric Vehicles (PHEV). Since the available waste heat from these vehicles is limited, additional heat sources such as electric heaters are needed for cabin heating operation. The use of a heat pump system is one of the solutions to improve EV driving range at cold ambient conditions. In this study, an efficient gas-injection heat pump system has been developed, which achieves high cabin heating performance at low ambient temperature and dehumidification operation without the assistance of electric heaters in ’17 model year Prius Prime.
2017-03-28
Technical Paper
2017-01-0184
Miyoko Oiwake, Ozeki Yoshiichi, Sogo Obata, Hideaki Nagano, Itsuhei Kohri
Abstract In order to develop various parts and components for hybrid electric vehicles, understanding the effect of their structure and thermal performance on their fuel consumption and cruising distance is essential. However, this essential information is generally not available to suppliers of vehicle parts and components. In this report, following a previous study of electric vehicles, a simple method is proposed as the first step to estimate the algorithm of the energy transmission and then the cruising performance for hybrid electric vehicles. The proposed method estimates the cruising performance using only the published information given to suppliers, who, in general, are not supplied with more detailed information. Further, an actual case study demonstrating application of the proposed method is also discussed.
2017-03-28
Technical Paper
2017-01-0183
Mingyu Wang, Timothy Craig, Edward Wolfe, Tim J LaClair, Zhiming Gao, Michael Levin, Danrich Demitroff, Furqan Shaikh
Abstract It is widely recognized in the automotive industry that, in very cold climatic conditions, the driving range of an Electric Vehicle (EV) can be reduced by 50% or more. In an effort to minimize the EV range penalty, a novel thermal energy storage system has been designed to provide cabin heating in EVs and Plug-in Hybrid Electric Vehicles (PHEVs) by using an advanced phase change material (PCM). This system is known as the Electrical PCM-based Thermal Heating System (ePATHS) [1, 2]. When the EV is connected to the electric grid to charge its traction battery, the ePATHS system is also “charged” with thermal energy. The stored heat is subsequently deployed for cabin comfort heating during driving, for example during commuting to and from work. The ePATHS system, especially the PCM heat exchanger component, has gone through substantial redesign in order to meet functionality and commercialization requirements.
2017-03-28
Technical Paper
2017-01-0263
Krishnaraj Udayachalam, Manan Trivedi, Ziliang Zheng, Amit Shrestha, Naeim Henein
Abstract SASOL IPK is a low cetane number synthetic fuel formed from coal by the Fischer-Tropsch process which can be used as an extender to JP8, currently used in military ground vehicles. This paper presents two surrogates developed considering the following criteria: (a) availability of kinetic combustion models for each component, (b) smallest number of components to reduce computation time and cost, (c) matching the following properties of target fuel DCN, distillation curve, density, LHV, MW and H/C ratio. The autoignition and combustion characteristics of the surrogates were validated in IQT according to ASTM D6890-10a. Surrogate formulation strategy involves an equation to calculate DCN of the surrogate mixture from the DCN of each component. The linear equation commonly used for such calculations was modified to include a multiplier, based on regression analysis, for each component to produces DCN values that agree well with the measured DCN in the IQT.
2017-03-28
Technical Paper
2017-01-0261
Randolph Jones, Robert Marinier III, Frank Koss, Robert Bechtel, John A. Sauter
Abstract When evaluating new vehicle designs, modeling and simulation offer techniques to predict parameters such as maximum speed, fuel efficiency, turning radius, and the like. However, the measure of greatest interest is the likelihood of mission success. One approach to assessing the likelihood of mission success in simulation is to build behavior models, operating at the human decision-making level, that can execute realistic missions in simulation. This approach makes it possible to not only measure changes in mission success rates, but also to analyze the causes of mission failures. Layering behavior modeling and simulation on underlying models of equipment and components enables measurement of more conventional parameters such as time, fuel efficiency under realistic conditions, distance traveled, equipment used, and survivability.
2017-03-28
Technical Paper
2017-01-0260
Yuanying Wang, Heath Hofmann, Denise Rizzo, Scott Shurin
Abstract This paper presents a computationally-efficient model of heat convection due to air circulation produced by rotor motion in the air gap of an electric machine. The model calculates heat flux at the boundaries of the rotor and stator as a function of the rotor and stator temperatures and rotor speed. It is shown that, under certain assumptions, this mapping has the homogeneity property. This property, among others, is used to pose a structure for the proposed model. The coefficients of the model are then determined by fitting the model to the results of a commercial Computational Fluid Dynamics (CFD) simulation program. The accuracy of the new model is compared to the CFD results, shown an error of less than 0.3% over the studied operating range.
2017-03-28
Journal Article
2017-01-0267
Tomasz Haupt, Gregory Henley, Angela Card, Michael S. Mazzola, Matthew Doude, Scott Shurin, Christopher Goodin
Abstract The Powertrain Analysis and Computational Environment (PACE) is a powertrain simulation tool that provides an advanced behavioral modeling capability for the powertrain subsystems of conventional or hybrid-electric vehicles. Due to its origins in Argonne National Lab’s Autonomie, PACE benefits from the reputation of Autonomie as a validated modeling tool capable of simulating the advanced hardware and control features of modern vehicle powertrains. However, unlike Autonomie that is developed and executed in Mathwork’s MATLAB/Simulink environment, PACE is developed in C++ and is targeted for High-Performance Computing (HPC) platforms. Indeed, PACE is used as one of several actors within a comprehensive ground vehicle co-simulation system (CRES-GV MERCURY): during a single MERCURY run, thousands of concurrent PACE instances interact with other high-performance, distributed MERCURY components.
2017-03-28
Journal Article
2017-01-0268
Venkatesh Babu, Richard Gerth
Abstract The aim of this analysis was to model the effect of adding stiffening ribs in structural aluminum components by friction stir processing (FSP) Nano material into the aluminum matrix. These stiffening ribs could dampen, redirect, or otherwise alter the transmission of energy waves created from automotive, ballistic, or blast shocks to improve noise, vibration, and harshness (NVH) and structural integrity (reduced joint stress) response. Since the ribs are not created by geometry changes they can be space efficient and deflect blast / ballistic energy better than geometry ribbing, resulting in a lighter weight solution. The blast and ballistic performance of different FSP rib patterns in AL 5182 and AL 7075 were simulated and compared to the performance of an equivalent weight of RHA plate FSP helps to increase localized strength and stiffness of the base metal, while achieving light weighting of the base metal.
2017-03-28
Technical Paper
2017-01-0264
Venkatesh Babu, Ravi Thyagarajan, Jaisankar Ramalingam
Abstract In this paper, the capability of three methods of modelling detonation of high explosives (HE) buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) (2) Structured - Arbitrary Lagrangian-Eulerian (S-ALE), and (3) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The ALE method of modeling the effects of buried charges in soil is well known and widely used in blast simulations today [1]. Due to high computational costs, inconsistent robustness and long run times, alternate modeling methods such as Smoothed Particle Hydrodynamics (SPH) [2, 9] and DEM are gaining more traction. In all these methods, accuracy of the analysis relies not only on the fidelity of the soil and high explosive models but also on the robustness of fluid-structure interaction. These high-fidelity models are also useful in generating fast running models (FRM) useful for rapid generation of blast simulation results of acceptable accuracy.
2017-03-28
Journal Article
2017-01-0271
Robert Jane, Gordon G. Parker, Wayne Weaver, Ronald Matthews, Denise Rizzo, Michael Cook
Abstract This paper considers optimal power management during the establishment of an expeditionary outpost using battery and vehicle assets for electrical generation. The first step in creating a new outpost is implementing the physical protection and barrier system. Afterwards, facilities that provide communications, fires, meals, and moral boosts are implemented that steadily increase the electrical load while dynamic events, such as patrols, can cause abrupt changes in the electrical load profile. Being able to create a fully functioning outpost within 72 hours is a typical objective where the electrical power generation starts with batteries, transitions to gasoline generators and is eventually replaced by diesel generators as the outpost matures.
2017-03-28
Journal Article
2017-01-0272
Andrej Ivanco
Abstract Military vehicles experience a wide range of duty cycles depending on the place and purpose of their deployment. Vehicle fuel consumption directly depends on those use cases, which are ranging from patrolling during peace keeping operations to direct engagements in hostiles areas. Vehicle design should accommodate this wide range of operation modes to maximize the vehicle practicality during their service life. This paper aims to quantify the sensitivity of the powerpack design for a notional 15-ton series hybrid electric vehicle for two highly dynamic military drive cycles. The optimal design for a powerpack (engine coupled with a generator) will be separately determined for each of the use cases through a previously developed optimization routine that use the Genetic Algorithm. For each iteration of the Genetic Algorithm a design benchmarking was incorporated by using Dynamic Programming.
Viewing 1 to 30 of 12739

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