A Simple and Fast Bi-Objective Search Algorithm andez 1 , William - - PowerPoint PPT Presentation

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Jul 04, 2023 458 likes •739 views

A Simple and Fast Bi-Objective Search Algorithm andez 1 , William Yeoh 2 , Jorge A. Baier 3 , Han Zhang 4 , Carlos Hern Luis Suazo 1 and Sven Koenig 4 1 Universidad Andr es Bello, Chile 2 Washington University in St. Louis 3 Pontificia

SLIDE 1

A Simple and Fast Bi-Objective Search Algorithm Carlos Hern´ andez1, William Yeoh2, Jorge A. Baier3, Han Zhang4, Luis Suazo1 and Sven Koenig4

1Universidad Andr´

es Bello, Chile

2Washington University in St. Louis 3Pontificia Universidad Cat´

lica de Chile

4University of Southern California

ICAPS-2020

SLIDE 2

Bi-objective search has many applications

Path-planning in robotics: distance and battery consumption HAZMAT transport in cities: travel time and risk of exposure for residents Cycling (path-finding): distance and driver safety Vehicle routing: monetary cost and travel time To our knowledge, bi-objective search not supported in PDDL

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 2 / 27

SLIDE 3

Bi-objective search

Two objective cost functions g1, g2 Dominance relation: (a, b) ≺ (a′, b′) iff a ≤ a′ and b ≤ b′ but (a, b) = (a′, b′) Pareto-optimal set: contains all non-dominated solutions (10, 5) ≺ (10, 8), (10, 5) ⊀ (8, 6)

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 3 / 27

SLIDE 4

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 4 / 27

SLIDE 5

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 5 / 27

SLIDE 6

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 6 / 27

SLIDE 7

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 7 / 27

SLIDE 8

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 8 / 27

SLIDE 9

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm 9 / 27

SLIDE 10

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. The process takes linear time.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm10 / 27

SLIDE 11

Contribution: a New Bi-Objective Search Algorithm

Highlights of Bi-Objective A* (BOA*)

1 Dominance checking in constant time (instead of linear time). 2 Simple. Resembling standard A*. 3 Empirical evaluation: find a Pareto set orders of magnitude

faster.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm11 / 27

SLIDE 12

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm12 / 27

SLIDE 13

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm13 / 27

SLIDE 14

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm14 / 27

SLIDE 15

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm15 / 27

SLIDE 16

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm16 / 27

SLIDE 17

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm17 / 27

SLIDE 18

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm18 / 27

SLIDE 19

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm19 / 27

SLIDE 20

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm20 / 27

SLIDE 21

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). In BOA*, dominance check takes constant time.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm21 / 27

SLIDE 22

Bi-Objective A*

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm22 / 27

SLIDE 23

Bi-Objective A*

Theorem

BOA* computes a cost-unique Pareto-optimal solution set.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm23 / 27

SLIDE 24

Experimental Evaluation: Setup

We compare to:

NAMOAdr (Pulido et al., 2015) BOA with standard linear-time dominance checking (sBOA*), Bi-Objective Dijkstra (BDijkstra), and Bidirectional Bi-Objective Dijkstra (BBDijkstra) (Sede˜ no et al., 2019).

We use 5 road maps from the “9th DIMACS Implementation Challenge: Shortest Path”.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm24 / 27

SLIDE 25

Experimental Evaluation

Runtime (sec) on 50 instances. After 3,600 seconds, we use 3,600 seconds in the calculation of the average.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm25 / 27

SLIDE 26

Experimental Evaluation

BOA* versus the best algorithms of the state-of-the-art in the Great Lakes (LKS) map with 2,758,119 states and 6,885,658 edges.

5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 10 20 30 40 50 60 70 80 Cumulative Runtime (seconds) # Instance

BDijkstra BOA* NAMOA*dr

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm26 / 27

SLIDE 27

Conclusions and Future Work

We present BOA* a simple and fast Bi-Objective A* search algorithm. BOA* resembling standard A. BOA is orders of magnitude faster than state-of-the-art. Research directions: Bounded-optimal Bi-Objective search and Multi-Objective search.

Hernandez et al. (UNAB,PUC,WUSTL,USC): A Simple and Fast Bi-Objective Search Algorithm27 / 27

A Simple and Fast Bi-Objective Search Algorithm Carlos Hern´ andez1, William Yeoh2, Jorge A. Baier3, Han Zhang4, Luis Suazo1 and Sven Koenig4

es Bello, Chile

ICAPS-2020

Bi-objective search has many applications

Path-planning in robotics: distance and battery consumption HAZMAT transport in cities: travel time and risk of exposure for residents Cycling (path-finding): distance and driver safety Vehicle routing: monetary cost and travel time To our knowledge, bi-objective search not supported in PDDL

Bi-objective search

Two objective cost functions g1, g2 Dominance relation: (a, b) ≺ (a′, b′) iff a ≤ a′ and b ≤ b′ but (a, b) = (a′, b′) Pareto-optimal set: contains all non-dominated solutions (10, 5) ≺ (10, 8), (10, 5) ⊀ (8, 6)

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. Example

Bi-Objective Search Algorithms

State-of-the-art NAMOA*dr (Pulido et al., 2015). Dominance check: Does the newly found path to a state s is dominate (or is dominated by) a previously found path to s. Dominance checking has a big impact in performance. The process takes linear time.

Contribution: a New Bi-Objective Search Algorithm

Highlights of Bi-Objective A* (BOA*)

1 Dominance checking in constant time (instead of linear time). 2 Simple. Resembling standard A*. 3 Empirical evaluation: find a Pareto set orders of magnitude

faster.

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). Example

Bi-Objective A* (Dominance checking)

The heuristic values h1 and h2 are consistent. The Open list is sorted lexicographically by (f1,f2). For each state s, BOA* maintains a gmin

2

(s). In BOA*, dominance check takes constant time.

Bi-Objective A*

Bi-Objective A*

Theorem

BOA* computes a cost-unique Pareto-optimal solution set.

Experimental Evaluation: Setup

We compare to:

NAMOA*dr (Pulido et al., 2015) BOA* with standard linear-time dominance checking (sBOA*), Bi-Objective Dijkstra (BDijkstra), and Bidirectional Bi-Objective Dijkstra (BBDijkstra) (Sede˜ no et al., 2019).

We use 5 road maps from the “9th DIMACS Implementation Challenge: Shortest Path”.

Experimental Evaluation

Runtime (sec) on 50 instances. After 3,600 seconds, we use 3,600 seconds in the calculation of the average.

Experimental Evaluation

BOA* versus the best algorithms of the state-of-the-art in the Great Lakes (LKS) map with 2,758,119 states and 6,885,658 edges.

Conclusions and Future Work

We present BOA* a simple and fast Bi-Objective A* search algorithm. BOA* resembling standard A*. BOA* is orders of magnitude faster than state-of-the-art. Research directions: Bounded-optimal Bi-Objective search and Multi-Objective search.

NAMOAdr (Pulido et al., 2015) BOA with standard linear-time dominance checking (sBOA*), Bi-Objective Dijkstra (BDijkstra), and Bidirectional Bi-Objective Dijkstra (BBDijkstra) (Sede˜ no et al., 2019).

We present BOA* a simple and fast Bi-Objective A* search algorithm. BOA* resembling standard A. BOA is orders of magnitude faster than state-of-the-art. Research directions: Bounded-optimal Bi-Objective search and Multi-Objective search.