Energy-Efficient Timely Transportation of Long-Haul Heavy-Duty Trucks

Transcription

1 Energy-Efficient Timely Transportation of Long-Haul Heavy-Duty Trucks Lei Deng 1 Mohammad H. Hajiesmaili 1 Minghua Chen 1 Haibo Zeng 2 1 Department of Information Engineering The Chinese University of Hong Kong, Hong Kong 2 Department of Electrical and Computer Engineering Virginia Tech, Blacksburg, VA, USA June 23, 2016 Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

2 Heavy-Duty Trucks Are Energy Hungry Medium trucks: 5% Others: 12% Repair & Maintenance: 9% Others: 9% Heavy trucks: 18% (4% vehicle popu.) Air: 8% Driver Benefits: 8% Truck Lease/Purchase Payments: 13% Fuel Costs: 34% Driver Wages: 27% Light vehicles: 58% Transportation energy use (US 2013, source: US DOE) Operational costs of trucking (US 2014, source: ATRI) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

3 Truck Operation Centers around Timely Delivery Perishable goods Amazon SLA (source: Internet) Logistic role in a supply chain Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

4 Truck Operation Centers around Timely Delivery Perishable goods Amazon SLA (source: Internet) Logistic role in a supply chain As estimated by US FHWA, unexpected delay can increase freight cost by 50% to 250% Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

5 How to Reduce Fuel Consumption in Timely Transportation? Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

6 How to Reduce Fuel Consumption in Timely Transportation? Use more fuel-efficient heavy-duty trucks Designs better engines, drivetrains, aerodynamics and tires, etc. Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

7 How to Reduce Fuel Consumption in Timely Transportation? Use more fuel-efficient heavy-duty trucks Designs better engines, drivetrains, aerodynamics and tires, etc. Operate heavy-duty trucks more economically Reduce idling energy consumption Platoon more than one trucks Route planning Speed planning etc. Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

8 Route Planning Fuel-related factors: mileages congestions road grades surface types etc. Different routes from Dallas to New York (source: Google Map) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

9 Speed Planning Fuel economy (mpg) speed (mph) Fuel economy v.s. speed for a 36-ton truck (source: ADVISOR) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

10 Our Problem and Contributions Our Problem Objective: minimize the energy consumption of a heavy-duty truck Constraint: a hard delay constraint Design Space: both route planning and speed planning Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

11 Our Problem and Contributions Our Problem Objective: minimize the energy consumption of a heavy-duty truck Constraint: a hard delay constraint Design Space: both route planning and speed planning This study generalizes previous works by considering both route planning and speed planning. Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

12 Our Problem and Contributions Our Problem Objective: minimize the energy consumption of a heavy-duty truck Constraint: a hard delay constraint Design Space: both route planning and speed planning This study generalizes previous works by considering both route planning and speed planning. Our Contributions Formulate the problem and prove that it is NP-Complete Propose an FPTAS with complexity O( mn2 ɛ 2 ) Propose a heuristic algorithm with complexity O(m + n log n) Use extensive simulations over real-world US highway networks to show our solutions achieve up to 17% fuel consumption reduction than the fastest/shortest path algorithm Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

13 System Model Highway Network: G = (V, E) with n = V, m = E 1 2 s {D e,re lb,r ub e,f e } d 3 4 Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

14 System Model 1 2 Highway Network: G = (V, E) with n = V, m = E Road/Edge Distance: D e (miles) s {D e,re lb,r ub e,f e } d 3 4 Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

15 System Model Highway Network: G = (V, E) with n = V, m = E s 1 2 e,f e } {D e,re lb,r ub d Road/Edge Distance: D e (miles) Min/Max Speed: Re lb /Re ub (mph) 3 4 Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

16 System Model Highway Network: G = (V, E) with n = V, m = E s 1 2 e,f e } {D e,re lb,r ub 3 4 d Road/Edge Distance: D e (miles) Min/Max Speed: Re lb /Re ub (mph) Fuel-Rate-Speed Function: f e f e (x) is the (instantaneous) fuel consumption rate (gallons per hour, gph) when the truck runs x mph on e Road-dependent Assume f e ( ) is polynomial and strictly convex over [Re lb, Re ub ] Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

17 System Model Highway Network: G = (V, E) with n = V, m = E s 1 2 e,f e } {D e,re lb,r ub 3 4 d Road/Edge Distance: D e (miles) Min/Max Speed: Re lb /Re ub (mph) Fuel-Rate-Speed Function: f e f e (x) is the (instantaneous) fuel consumption rate (gallons per hour, gph) when the truck runs x mph on e Road-dependent Assume f e ( ) is polynomial and strictly convex over [Re lb, Re ub ] (Source, Dest, Hard Delay): (s, d, T ) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

18 Problem Formulation Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

19 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

20 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Speed Optimization (Speed Planning) t e > 0 : Edge-e travel time { } T t : t lb e t e t ub e, e : speed limits Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

21 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Speed Optimization (Speed Planning) t e > 0 : Edge-e travel time { } T t : t lb e t e t ub e, e : speed limits Fuel Consumption Travel Time: t e Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

22 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Speed Optimization (Speed Planning) t e > 0 : Edge-e travel time { } T t : t lb e t e t ub e, e : speed limits Fuel Consumption Travel Time: t e Travel Speed: De t e Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

23 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Speed Optimization (Speed Planning) t e > 0 : Edge-e travel time { } T t : t lb e t e t ub e, e : speed limits Fuel Consumption Travel Time: t e Travel Speed: De t e Fuel Consumption Rate: f e ( De t e ) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

24 Problem Formulation Path Selection (Route Planning) { 1, Edge e is on the selected path; x e = 0, otherwise. X {x {0, 1} m : One s d path is selected} Speed Optimization (Speed Planning) t e > 0 : Edge-e travel time { } T t : t lb e t e t ub e, e : speed limits Fuel Consumption Travel Time: t e Travel Speed: De t e Fuel Consumption Rate: f e ( De t e ) Total Fuel Consumption: t e f e ( De t e ) c e (t e ) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

25 Problem Formulation PAth selection and Speed Optimization (PASO) x e c e (t e ) min x X,t T s.t. e E x e t e T e E Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

26 Problem Formulation PAth selection and Speed Optimization (PASO) x e c e (t e ) Challenges min x X,t T s.t. e E x e t e T e E Mixed discrete-continuous optimization: x e {0, 1}, t e > 0 Non-linear non-convex: e E x et e T Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

27 Complexity-Hardness-related Theoretical Results Theorem PASO is NP-Complete. Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

28 Complexity-Hardness-related Theoretical Results Theorem PASO is NP-Complete. Definition (Fully Polynomial Time Approximation Scheme (FPTAS)) An algorithm is an FPTAS for PASO if for any given ɛ (0, 1), it can find a (1 + ɛ)-approximate solution in the sense that the solution is feasible and the corresponding fuel consumption is at most (1 + ɛ)opt, and the time complexity is polynomial in both the problem size and 1 ɛ. Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

29 Complexity-Hardness-related Theoretical Results Theorem PASO is NP-Complete. Definition (Fully Polynomial Time Approximation Scheme (FPTAS)) An algorithm is an FPTAS for PASO if for any given ɛ (0, 1), it can find a (1 + ɛ)-approximate solution in the sense that the solution is feasible and the corresponding fuel consumption is at most (1 + ɛ)opt, and the time complexity is polynomial in both the problem size and 1 ɛ. Theorem PASO has an FPTAS with network-induced time complexity O( mn2 ɛ 2 ). Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

30 FPTAS still Incurs High Complexity in Practice The network-induced complexity of the FPTAS is O( mn2 ɛ 2 ) Still large if we consider practical highway networks with m, n 10 4 Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

31 FPTAS still Incurs High Complexity in Practice The network-induced complexity of the FPTAS is O( mn2 ɛ 2 ) Still large if we consider practical highway networks with m, n N 45 N 40 N 35 N 30 N Consider the regions 17&18 n m ɛ Run Time Memory s 14.76GB 25 N 120 W 110 W 100 W W W 70 W Figure 4: USA map and 22 regions. 7.2 Fuel-Rate-Speed Function Modeling We will use Lei Deng the following (CUHK) fuel-rate-speed Energy-Efficient function model, Timely Transportation June 23, / 22

32 FPTAS still Incurs High Complexity in Practice The network-induced complexity of the FPTAS is O( mn2 ɛ 2 ) Still large if we consider practical highway networks with m, n N 45 N 40 N 35 N 30 N Consider the regions 17&18 n m ɛ Run Time Memory s 14.76GB 25 N 120 W 110 W 100 W W W Figure 4: USA map and 22 regions. 70 W We will introduce a fast dual-based heuristic algorithm with network-induced time complexity O(m + n log n) 7.2 Fuel-Rate-Speed Function Modeling We will use Lei Deng the following (CUHK) fuel-rate-speed Energy-Efficient function model, Timely Transportation June 23, / 22

33 Relax the Hard Delay for PASO PASO min x X,t T s.t. x e c e (t e ) e E x e t e T, e E [λ] Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

34 Relax the Hard Delay for PASO PASO min x X,t T s.t. x e c e (t e ) e E x e t e T, e E [λ] PASO-Relaxed(λ) λ is the delay price min x X,t T x e (c e (t e ) + λt e ) e E PASO-Relaxed(λ) can be solved efficiently by a shortest-path like algorithm Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

35 Key Observations and Result PASO-Relaxed(λ) min x X,t T x e (c e (t e ) + λt e ) e E Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

36 Key Observations and Result PASO-Relaxed(λ) min x X,t T x e (c e (t e ) + λt e ) e E For properly selected λ, solving PASO-Relaxed(λ) gives either an optimal solution or a feasible solution with a small optimality-gap to PASO Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

37 Key Observations and Result PASO-Relaxed(λ) min x X,t T x e (c e (t e ) + λt e ) e E For properly selected λ, solving PASO-Relaxed(λ) gives either an optimal solution or a feasible solution with a small optimality-gap to PASO We propose a heuristic to find the proper λ in O((m + n log n)), much faster than the FPTAS (O( mn2 ɛ 2 ) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

38 Key Observations and Result PASO-Relaxed(λ) min x X,t T x e (c e (t e ) + λt e ) e E For properly selected λ, solving PASO-Relaxed(λ) gives either an optimal solution or a feasible solution with a small optimality-gap to PASO We propose a heuristic to find the proper λ in O((m + n log n)), much faster than the FPTAS (O( mn2 ɛ 2 ) We characterize a condition under which an optimal solution to PASO is obtained, and the condition is satisfied in most instances in our case study based on real-world settings Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

39 Our Dual-Based Heuristic Runs fast The FPTAS has a network-induced complexity of O( mn2 ɛ 2 ) The dual-based heuristic has a network-induced complexity of O((m + n log n)) etwork: To construct United States ems (NHS), we use the graph dataset y Mapping (CHM) Project [17]. The ecified in [2] which consists of edges. Each node has its latinates while each edge is represented e graph data has a reasonable level of el the NHS network. aper, we only consider the grade/slope road-dependent fuel-rate-speed conn order to obtain the grade of each the Elevation Point Query Service [7] cal Survey (USGS). We write a script all nodes in the NHS graph. 30 N 25 N 40 N 35 N 50 N 45 N 120 W Consider the regions 17& W ough usually U.S. highways will specimit, it is generally meaningless to use it. Instead, it is Alg more reasonable n to m Figure ɛ 4: Run USATime map andmemory 22 regions. limit according FPTAS to historical flow3274 data s 14.76GB s. HERE map [6] has put speed dentries including U.S., and it provides Heuristic Fuel-Rate-Speed - 2s Function 0.29GB Modeling cation-based real-time speed informae, We will use the following fuel-rate-speed function model, using the corridor parameter is a r each edge (road segment), we use fe(x) = aex 3 + bex 2 + cex + de, e E (22) coordinates of its two endpoints and to specify thelei corridor. Deng (CUHK) We are keepwhich can capture most cases in [8 10,15] and also our physical interpretation Energy-Efficient in Appendix Timely Transportation A. Here x is the speed in unit June 23, / W W W 70 W

40 Simulation: Dataset Highway Network: US National Highway Systems (CHM Project) Elevation: USGS Elevation Point Query Service Speed Limits: HERE Map Heavy-duty Truck and Fuel Consumption Data: ADVISOR Simulator Kenworth T800 Drag Coefficient c d 0.7 Frontal area A f m 2 Glider Mass 2,552kg Cargo Mass 33,234kg Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

41 Simulation: Network Statistics t United States e graph dataset roject [17]. The onsists of ode has its late is represented asonable level of r the grade/slope -rate-speed cone grade of each uery Service [7] e write a script e NHS graph. hways will speceaningless to use re reasonable to torical flow data s put speed deand it provides e speed informaparameter is a gment), we use 30 N 25 N 40 N 35 N 50 N 45 N 120 W 110 W 100 W W W avg D n m e avg Re lb avg Re ub avg θ (mile) (mph) (mph) (%) Figure 4: USA map and 22 regions. 70 W 7.2 Fuel-Rate-Speed Function Modeling We will use the following fuel-rate-speed function model, f e(x) = a ex 3 + b ex 2 + c ex + d e, e E (22) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

42 Evaluate/Compare FPTAS and Heuristic 50 N Instance: (s, d, T ) 45 N 40 N 35 N 30 N 25 N 120 W 110 W 100 W W 80 W 70 W No. Network Input Reg. n m Instance ɛ S1 1& (1,2,8) 0.1 S2 17& (18,17,10) 0.1 S (4,22,40) 0.1 S4 1& (1,2,8) 0.05 Figure 4: USA map and 22 regions..2 Fuel-Rate-Speed Function Modeling We will use the following fuel-rate-speed function model, fe(x) = aex 3 + bex 2 + cex + de, e E (22) hich can capture most cases in [8 10,15] and also our physil interpretation in Appendix A. Here x is the speed in unit mph and fe(x) is the fuel rate consumption in unit of gph allons per hour). Although our model (22) can capture y road-dependent features, e.g., grade, rolling resistance, d air density, etc., in this simulation, we only consider the ad grade. This is because that grade is a major factor for uck fuel consumption Lei Deng [?]. (CUHK) Energy-Efficient Timely Transportation June 23, / 22

43 Evaluate/Compare FPTAS and Heuristic 50 N Instance: (s, d, T ) 45 N 40 N 35 N 30 N 25 N 120 W 110 W 100 W W 80 W 70 W No. Network Input Reg. n m Instance ɛ S1 1& (1,2,8) 0.1 S2 17& (18,17,10) 0.1 S (4,22,40) 0.1 S4 1& (1,2,8) 0.05 Figure 4: USA map and 22 regions..2 Fuel-Rate-Speed Function Heuri. Modeling LB/UB FPTAS Heuri. FPTAS Heuri. FPTAS We will use the following S1 fuel-rate-speed / function model, Performance (gallon) No. Time (second) Memory (GB) S / fe(x) = aex 3 + bex 2 + cex + de, e E (22) S / hich can capture most S4 cases in / [8 10,15] and also our physi-74.81l interpretation in Appendix A. Here x is the speed in unit mph and fe(x) is the fuel rate consumption in unit of gph allons per hour). Although our model (22) can capture y road-dependent features, e.g., grade, rolling resistance, d air density, etc., in this simulation, we only consider the ad grade. This is because that grade is a major factor for uck fuel consumption Lei Deng [?]. (CUHK) Energy-Efficient Timely Transportation June 23, / 22

44 Compare Performance with Baselines (One Instance) Shortest/Fastest/Optimal paths of (s, d, T ) = (9, 22, 40) Fuel consumed (gallon) F F SO S S SO OPT UB OPT LB Delay (hour) Performance of instance (s, d) = (9, 22) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

45 Compare Performance with Baselines (All Instances) Average performance of all instances (s, d, T ) Sol. Avg Time Avg Dist. Avg Fuel Avg Fuel Incre.(%) Incre.(%) Incre.(%) Econ.(mpg) Fastest path Shortest path Heuristic OPT-LB Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

46 Conclusion Propose the problem of energy efficient timely transportation Prove that the problem is NP-Complete but has an FPTAS The FPTAS has time complexity O( mn2 ɛ 2 ) Propose a fast dual-based heuristic algorithm It has time complexity O(m + n log n) It has extremely good performance in practice Extensive simulation over real-world US highway systems 17% fuel consumption reduction than the fastest path algorithm 14% fuel consumption reduction than the shortest path algorithm Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

47 Q&A Thank You! Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 22

48 Backup Slides Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 3

49 Fuel-Rate-Speed Function fuel rate speed function (gph) data ( 1%) fitted ( 1%) data (0%) fitted (0%) data (1%) fitted (1%) speed (mph) f e ( ) for a 36-ton truck for grades 0%, ±1% Polynomial fit: f e (x) = a e x 3 + b e x 2 + c e x + d e (source: ADVISOR) Grade: 0% Grade: 1% Grade: -1% Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 3

50 Preprocessing ( Define fuel-time function c e (t e ) = t e f De e t e ). Without loss of optimality, we assume that c e ( ) is strictly convex and strictly decreasing over [t lb e, t ub e ]. fuel rate speed function (gph) data ( 1%) fitted ( 1%) data (0%) fitted (0%) data (1%) fitted (1%) speed (mph) f e ( ) for a 36-ton truck (source: ADVISOR) fuel time function (gallons) data ( 1%) fitted ( 1%) data (0%) fitted (0%) data (1%) fitted (1%) time (hours) c e ( ) for the truck over a 100-mile road (source: ADVISOR) Lei Deng (CUHK) Energy-Efficient Timely Transportation June 23, / 3