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Adaptive Large Neighborhood Search for Scheduling of Mobile Robots Quang-Vinh Dang 1 , 2 Hana Rudov 1 Cong Thang Nguyen 3 1 Masaryk University, Czech Republic 2 Eindhoven University of Technology, The Netherlands 3 Ho Chi Minh City University of

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Adaptive Large Neighborhood Search for Scheduling of Mobile Robots

Quang-Vinh Dang1,2 Hana Rudová1 Cong Thang Nguyen3

1 Masaryk University, Czech Republic 2 Eindhoven University of Technology, The Netherlands 3 Ho Chi Minh City University of Technology, Vietnam

This presentation: http://www.fi.muni.cz/~hanka/publ/gecco19-slides.pdf

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Adaptive large neighborhood search for scheduling of mobile robots: outline

Problem = scheduling with mobile robots Algorithm = extension of adaptive large neighborbood search [1] New: exploration & exploitation heuristics Experiments Impact of proposed heuristics Comparison with MIP and hybrid GA Real-time results: important for smart factories

1. Ropke and Pisinger, An adaptive large neighborhood search heuristic for the pickup and delivery problem with time
windows. Transportation science 40(4):455–472, 2006.

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Scheduling with mobile robots

Job shop problem with robot processing and transportation

Machines Distance matrix One machine can process at most one job any time Jobs Several non-overlapping operations Given order of operations Different machine for each operation Robots Identical Transport jobs between machines Process some operations with machines

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Scheduling with mobile robots: example

Machine L/U M1 M2 M3 M4 L/U 6 8 10 12 M1 12 6 8 10 M2 10 6 6 8 M3 8 8 6 6 M4 6 10 8 6 Job 1 M1(8) M2(16) M4(12) Job 2 M1(20) M3(10) M2(18) Job 3 M3(12) M4(8) M1(15) Job 4 M4(14) M2(18) – Job 5 M3(10) M1(15) – Goal Assign time and robot for processing and transportation Minimize makespan

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Our adaptive large neighborhood search (ALNS)

s ← so; sbest ← so; i → 1; exploit ← 0; while i ≤ maxIterations do i ← i + 1; if exploit ≤ maxExploit then select exploitation heuristic h; else select exploration heuristic h; generate and evaluate new solution snew from s using heuristic h; if f (snew) < f (sbest) then sbest ← snew; s ← snew; exploit ← 0; elseif f (snew) < f (s) or f (snew)−f (sbest)

f (snew)

≤ T then s ← snew; decrease threshold T; each u-th iteration: increase adaptive weights of heuristics;

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Adaptive heuristics

Learning process Selection of heuristics successful in past Increase of the weight of heuristics when Best solution was found Improving solution was found We have accepted solution

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Exploration heuristics

Diversify the search Destroy and repair a large number of elements of a solution or Random destroy and repair Examples Random change transporting robots for several random operations Move several operations with close starting times 9 heuristics in total

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Exploitation heuristics

Intensify the search Destroy and repair one or a couple of elements of a solution or Deterministic destroy and repair Examples Change all transporting robots arriving too late Swap two random operations and their robots 9 heuristics in total

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Impact of heuristics

Explore % Chosen % Best Exploit % Chosen % Best found found h1 10.9 4.4 h10 0.1 10.4 h2 18.4 1.1 h11 0.1 12.7 h3 3.5 0.3 h12 0.3 1.1 h4 20.3 7.2 h13 0.3 0.8 h5 20.3 6.9 h14 0.5 9.0 h6 15.8 3.5 h15 0.6 12.5 h7 1.1 0.1 h16 0.4 6.6 h8 1.6 0.3 h17 0.7 16.6 h9 4.8 0.3 h18 0.4 6.2 High weight of heuristics ⇒ Chosen many times ⇒ Explore search space

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Summary of experiments

Benchmark problems from [2,3]

40 problems: transportation times ∼ processing times 42 problems: transportation times « processing times

Impact of heuristics Parameter tuning

ANOVA for parameters adaptive weights, initial threshold, iterations for exploitations

ALNS vs. hybrid genetic algorithm [3]

Computation with default setting / within 1 second Pair T-test

ALNS vs. MIP [3]

2. Bilge and Ulusoy, A time window approach to simultaneous scheduling of machines and material handling system in

an FMS. Operations Research 43(6):1058–1070, 1995.

3. Dang, Nguyen, Rudová, Scheduling of mobile robots for transportation and manufacturing tasks. Journal of

Heuristics, 25(2):175–213, 2019.

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Our ALNS vs. MIP

Runtimes ALNS: 0.49 seconds MIP: mins to hours

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Our ALNS vs. hybrid GA: 40 problems

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Our ALNS vs. hybrid GA: 42 problems

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Conclusion

ALNS extended by exploration and exploitation heuristics Exploration heuristics

Chosen many times & explore the search space

Exploitation heuristics

Find the best solutions

Proposed heuristics of scheduling of mobile robots Near-optimal quality solutions in real time

Important for smart factories In order of magnitude faster than hybrid GA

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Future & ongoing work

Further experiments on larger problems ALNS combined with integer linear programming Scheduling of automated guided vehicles (AGVs) under battery constraints Project Advanced Manufacturing Logistics Brainport Industries Campus Eindhoven, the Netherlands Real demonstrations with online algorithms 5–6 workstations/machines, 20 transportation requests 2 AGVs: different type

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Additional slides

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Solution representation

Element e e1 e2 e3 e4 e5 e6 Sequence of operations 21 11 31 12 22 32 Transporting robot 1 2 1 2 1 1 Processing robot – 2 – – 2 1 Machine 1 3 2 1 2 3

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Our ALNS vs. hybrid GA: pair T-tests

40 problems 42 problems default 1s default 1s ALNS with better mean & statist. diff. 3 39 8 29 ALNS with better mean 2 – 2 1 Same results 3 1 26 12 ALNS with worse mean 6 – 2 – ALNS with worse mean & statist. diff. 26 – 4 –

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Further experiments: our ALNS with even stronger results

Current/additional benchmark problems from [3] 5–8 / 8–9 jobs 13–21 / 40–50 operations 4 / 8–10 machines 2 / 3–4 robots Computation with default setting: ALNS vs. hybrid GA 16.1 vs. 1.70 seconds Gap in mean: from -0.7 % to 3.0% Gap in best: from 0.0 % to 4.9% Pair T-test: there is no difference between means based on P-value Computation within 1 second: ALNS vs. hybrid GA Gap in mean: from -29.4 % to -9.9% Gap in best: from -30.1 % to -5.4%

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Our ALNS vs. hybrid GA: default setting → 5.2 seconds

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Our ALNS vs. hybrid GA: 1 second

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