Coordinated Platoon Routing in a Metropolitan Network Jeffrey - PowerPoint PPT Presentation

Coordinated Platoon Routing in a Metropolitan Network Jeffrey Larson Todd Munson Vadim Sokolov Argonne National Laboratory October 10, 2016

Computationally Enhanced Mobility ◮ Developing high-fidelity simulation tools to estimate the energy impact of Connected and Automated Vehicles. ◮ Developing algorithms for optimally routing vehicles with platooning capabilities. 2 of 15 .

Computationally Enhanced Mobility ◮ Developing high-fidelity simulation tools to estimate the energy impact of Connected and Automated Vehicles. ◮ Developing algorithms for optimally routing vehicles with platooning capabilities. POLARIS 2 of 15 .

Workflow Vehicles Network Optimization Model POLARIS Autonomie 3 of 15 .

Workflow Vehicles Network Optimization Model POLARIS Autonomie 3 of 15 .

Workflow Vehicles Network Optimization Model POLARIS Autonomie 3 of 15 .

Workflow Vehicles Network Optimization Model POLARIS Autonomie 3 of 15 .

Networks 4 of 15 .

Networks 4 of 15 .

Animation Grid Chicago 5 of 15 .

Optimization Model - Model Parameters Set Meaning Vehicles to route V I Network nodes Network edges E ⊆ I × I 6 of 15 .

Optimization Model - Model Parameters Set Meaning Vehicles to route V I Network nodes Network edges E ⊆ I × I Parameter Meaning v ∈ V origin node O v D v v ∈ V destination node T O v ∈ V origin time v T D v ∈ V destination time v C W waiting cost for v ∈ V v C i , j cost for taking ( i , j ) ∈ E 6 of 15 .

Optimization Model - Model Variables Variable Meaning f v , i , j 1 if v travels on ( i , j ) q v , w , i , j 1 if v follows w on ( i , j ) Time v enters ( i , j ) e v , i , j w v , i Time v waits at i 7 of 15 .

Optimization Model - Model Constraints Node outflows must equal inflows. When platooning, enter times are equal. Platooning requires at least two vehicles. Only one vehicle can follow. T O plus waiting time is the origin enter time. v T D v is the final enter time plus the time required to travel the final edge plus waiting at the end. Intermediate enter times are equal plus the travel and waiting times. Can’t have nonzero enter time if there is no flow. Can’t have nonzero wait time if there is no flow. Platoon requires flow for the leader. Platoon requires flow for the followers. 8 of 15 .

Optimization Model - Example Constraints Can’t have nonzero enter time if there is no flow. e v , i , j ≤ Mf v , i , j ; ∀ v ∈ V , ( i , j ) ∈ E 9 of 15 .

Optimization Model - Example Constraints Can’t have nonzero enter time if there is no flow. e v , i , j ≤ Mf v , i , j ; ∀ v ∈ V , ( i , j ) ∈ E Enter times are equal when platooning. − M ( 1 − q v , w , i , j ) ≤ e v , i , j − e w , i , j ≤ M ( 1 − q v , w , i , j ) 9 of 15 .

Optimization Model - Example Constraints Can’t have nonzero enter time if there is no flow. e v , i , j ≤ Mf v , i , j ; ∀ v ∈ V , ( i , j ) ∈ E Enter times are equal when platooning. − M ( 1 − q v , w , i , j ) ≤ e v , i , j − e w , i , j ≤ M ( 1 − q v , w , i , j ) Objective: � � � � � C W minimize C i , j f v , i , j − η q v , w , i , j + v w v , i w v , i , j v , i 9 of 15 .

Helping the MIP solver 10 of 15 .

Helping the MIP solver Consider v and w platooning on edge ( i , j ) only if T O v + M O v , i , T O T D v − M D v , j , T D � � � � w + M O w , i + T i , j ≤ min w − M D w , j max where M a , b is the minimum time required to reach b from a . 10 of 15 .

Helping the MIP solver Consider v and w platooning on edge ( i , j ) only if T O v + M O v , i , T O T D v − M D v , j , T D � � � � w + M O w , i + T i , j ≤ min w − M D w , j max where M a , b is the minimum time required to reach b from a . Lemma If vehicles use a fraction η less fuel when trailing in a platooning and t s is the shortest time for a vehicle to travel from its origin to destination, 1 1 − η t s . it will never travel a path longer than 10 of 15 .

Helping the MIP solver Consider v and w platooning on edge ( i , j ) only if T O v + M O v , i , T O T D v − M D v , j , T D � � � � w + M O w , i + T i , j ≤ min w − M D w , j max where M a , b is the minimum time required to reach b from a . Lemma If vehicles use a fraction η less fuel when trailing in a platooning and t s is the shortest time for a vehicle to travel from its origin to destination, 1 1 − η t s . it will never travel a path longer than Lemma There exists an optimal platoon routing in which no two vehicles split and then merge together. 10 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes ◮ Start times drawn uniformly from [0,100] 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes ◮ Start times drawn uniformly from [0,100] ◮ Destination times T v D = T v O + M O v , D v + p , for some time p ≥ 0 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes ◮ Start times drawn uniformly from [0,100] ◮ Destination times T v D = T v O + M O v , D v + p , for some time p ≥ 0 ◮ No cost for waiting 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes ◮ Start times drawn uniformly from [0,100] ◮ Destination times T v D = T v O + M O v , D v + p , for some time p ≥ 0 ◮ No cost for waiting ◮ 10 replications 11 of 15 .

Problem Setup ◮ Vehicles all travel at free-flow speeds ◮ 10% savings for platooning ◮ 25 vehicles ◮ Grid: random origin/destination pairs ◮ Chicago: origin/destination pairs drawn from the most common morning commutes ◮ Start times drawn uniformly from [0,100] ◮ Destination times T v D = T v O + M O v , D v + p , for some time p ≥ 0 ◮ No cost for waiting ◮ 10 replications ◮ Running Gurobi until its optimality gap is less than 1e-8 11 of 15 .

Example solution times 12 of 15 .

Example solution times Objective value After 1 minute 145 1600 1400 144 1200 143 Seconds to solution 1000 142 Fuel use 800 141 600 140 400 139 200 0 138 0 20 40 60 80 100 120 Pauses Grid, waiting allowed at intermediate nodes 12 of 15 .

Example solution times Objective value After 1 minute 145 1600 1400 144 1200 143 Seconds to solution 1000 142 Fuel use 800 141 600 140 400 139 200 0 138 0 20 40 60 80 100 120 Pauses Grid, no waiting allowed at intermediate nodes 12 of 15 .

Example solution times 12 of 15 .

Example solution times Objective value Lower bound After 1 minute 4000 1700 3500 1680 3000 1660 Seconds to solution 2500 1640 Fuel use 2000 1620 1500 1600 1000 1580 500 1560 0 1540 0 20 40 60 80 100 120 Pauses Chicago, waiting allowed at intermediate nodes 12 of 15 .

Example solution times Objective value Lower bound After 1 minute 4000 1700 3500 1680 3000 1660 Seconds to solution 2500 1640 Fuel use 2000 1620 1500 1600 1000 1580 500 1560 0 1540 0 20 40 60 80 100 120 Pauses Chicago, no waiting allowed at intermediate nodes 12 of 15 .

Example solution times Objective value Lower bound After 1 minute 8100 600 8000 500 7900 Seconds to solution 7800 400 Fuel use 7700 300 7600 7500 200 7400 100 7300 0 7200 0 20 40 60 80 100 120 Pauses Chicago, 100 vehicles, (20 from each of the 5 most common origin/destination pairs), stopping at 1% optimality gap 12 of 15 .

Example solution times Objective value Lower bound After 1 minute 8100 600 8000 500 7900 Seconds to solution 7800 400 Fuel use 7700 300 7600 7500 200 7400 100 7300 0 7200 0 20 40 60 80 100 120 Pauses Chicago, 100 vehicles, (20 from each of the 5 most common origin/destination pairs), stopping at 1% optimality gap, using lemmas 12 of 15 .