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Basic concepts MOLS/D Experimental Study Final Considerations IEEE CEC 2018 A Decomposition-based Local Search Algorithm for Multi-objective Sequence Dependent Setup Times Permutation Flowshop Scheduling Murilo Zangari, Ademir Constantino,

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Basic concepts MOLS/D Experimental Study Final Considerations

IEEE CEC 2018

A Decomposition-based Local Search Algorithm for Multi-objective Sequence Dependent Setup Times Permutation Flowshop Scheduling

Murilo Zangari, Ademir Constantino, and Josu Ceberio

State University of Maringa, Brazil University of the Basque Country, Spain

July 11, 2018

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Schedule

1 Basic concepts 2 MOLS/D 3 Experimental Study 4 Final Considerations

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Flowshop Scheduling Problem (FSP)

  • FSP serves as a model for several real-world problems from

manufacturing, engineering, and other fields of application

  • Different objectives have been considered as optimization goals, e.g.,

i) Makespan, ii) Total Flowtime, and iii) Total Tardiness

Figure: An example of flow-shop scheduling problem with 4 jobs and 4 machines

  • Problem restriction: When the sequence of jobs is the same for all

machines, the problem is denoted Permutation Flowshop Scheduling (PFSP)

  • Goal: To find a permutation of jobs such that a criteria is minimized

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Flowshop Scheduling Problem (FSP)

  • Setup Times: In FSP, setups can reflect some non-productive operations

that have to be processed on machines that are not part of the processing times of the jobs

  • Sequence-dependent: When the setups dependents on the job being

processed and on the next job in the sequence

  • Multi-objective optimization: Multiple PFSP objectives to be optimized

simultaneously.

Figure: An example of maximization of two objectives

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PFSP solvers

  • Heuristics Algorithms
  • Meta-heuristics Algorithms
  • Evolutionary Strategies (e.g., genetic search)
  • Simulated Annealing
  • Iterated Local Search (ILS)
  • Hybrid Approaches
  • Example: Heuristic + Evolutionary Strategies + local search
  • Goal: An effective balance between Convergence × Diversity

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Concept Definition: Iterated Local Search

  • A solution x′ is a neighbor solution of x if x′ can be achieved by a single

move from x, and its depends on a basic underlying operator and a given distance between any two solutions

  • Iterated Local Search (ILS): consists of repeatedly applying local search
  • procedures. When the search is trapped in a local optimal solution, ILS

can perturb the solution to allow the search to escape from the trap without losing many of the good properties of the current solution

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Concept Definition: Multi-objective EA based on Decomposition

  • MOEA/D framework: The idea is to decompose a multi-objective

problem into a number of scalar single-objective subproblems (by using a set of weight vectors and an aggregation function). Each subproblem is

  • ptimized using an EA and the information mainly from its several

neighboring subproblems

  • Well effective for solving combinatorial optimization problems with 2 and

3 objectives.

Figure: An example of the decomposition strategy used in MOEA/D

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Multi-objective ILS based on Decomposition

  • Ingredients:
  • Decomposition strategy: Weighted Sum Approach
  • Heuristic initialization of the population using variants of the

NEH heuristic

  • Local search operators in a space of permutations: 1-insert

and 1-interchange (exploitation)

  • Shaking procedure: to move the current solution of a

subproblem to another region of the search (exploration)

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Multi-objective ILS based on Decomposition

  • Input:
  • N: population size
  • W 1, ..., W N: distributed weight vectors
  • T: neighborhood size for update
  • nr: maximum replacements allowed by a new solution
  • nsh: number of random insert moves
  • Output:
  • Pop: The final set of N solutions
  • External Pareto (all non-dominated solutions found)
  • Initialization: Pop := {σ1, ..., σN}
  • While a stopping criterion is not met:
  • Search Process: For each k ∈ 1, ..., N:
  • Generate σ′ using a LS move on σk and compute F(σ′)
  • Update Pop with σ′ according to the scalar aggregation

function and the T closest neighbor subproblems

  • Check if the subproblem has not been improved after n

generations

  • Update External Pareto

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Experimental setup

  • Benchmark: 220 instances extended from the Taillard benchmark that

vary according to the number of jobs n = {20, 50, 100}, number of machines m = {10, 20}, and setup times.

  • Bi-objective case: makespan and total weighted tardiness
  • Comparison:
  • The best-known results from the literature (in the form of

approximated Pareto fronts) obtained by the best performer algorithms (RIPG and MOSA VM)

  • MOEA/D (which employs genetic operators, specially toileted for

permutation problems)

  • Performance assessment: 1) Hypervolume, 2) Coverage, and 3)

Empirical Attained function (EAF)

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Experimental setup

  • Parameters settings: N = 100, T = 20, nr = 2, nsh = 14 random insert

moves

  • Maximum Generations: 1000n
  • 20 independent runs for each algorithm and problem instance
  • Statistical tests: Friedman’s ranked based at 95% of confidence level and

post-hoc Nemenyi

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Results: MOLS/D components

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-insert 1-interchange average Hypervolume local search operators

Figure: Boxplot of the average HV values

  • btained by MOLS/D using the 1-insert move and the

1-interchange move.

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 LS LS+NEH LS+SH LS+NEH+SH average Hypervolume

Figure: Boxplot of the average HV values obtained

by four algorithm configurations: (i) without both heuristic initialization and shaking procedure (LS), (ii)

  • nly with the heuristic initialization (LS+NEH), (iii)
  • nly with the shaking procedure (LS+SH), and (iv)

with all the components together (LS+NEH+SH). 12 / 17

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Results: Comparison to the best-known results from literature

0.785 0.79 0.795 0.8 0.805 0.81 0.815 0.82 0.825 0.83 1 2 3 4 5 6 7 8 9 Hypervolume Generations (%)

(a) 20x05

0.855 0.86 0.865 0.87 0.875 0.88 0.885 1 2 3 4 5 6 7 8 9 Hypervolume Generations (%)

(b) 20x05

0.85 0.855 0.86 0.865 0.87 0.875 0.88 0.885 1 2 3 4 5 6 7 8 9 Hypervolume Generations (%)

(c) 20x05

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(d) 20x05

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(e) 20x10

0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(f) 20x20

0.6 0.65 0.7 0.75 0.8 0.85 0.9 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(g) 50x05

0.6 0.65 0.7 0.75 0.8 0.85 0.9 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(h) 50x10

0.6 0.65 0.7 0.75 0.8 0.85 0.9 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(i) 50x20

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%)

(j) 100x05

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 10 20 30 40 50 60 70 80 90 100 Hypervolume Generations (%) MOLS/D MOSA_VM RIPG

(k) 100x10 Figure: Average HV values obtained by MOLS/D throughout 10 different stages of the search compared to the

HV obtained by the reference sets of MOSA and RIPG (constant lines) for the different problem scales (11 in total) 13 / 17

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Results: Comparison results

Table: Average HV values obtained by MOLS/D, MOEA/D, MOSA VM, and RIPG

problem n × m SSD50 SSD125 MOLS/D MOEA/D MOSA VM RIPG MOLS/D MOEA/D MOSA VM RIPG 20 × 05 0.847 0.649 0.832 0.852 0.822 0.542 0.799 0.835 20 × 10 0.893 0.774 0.874 0.890 0.867 0.684 0.852 0.871 20 × 20 0.874 0.712 0.856 0.881 0.863 0.668 0.834 0.870 50 × 05 0.877 0.413 0.704 0.788 0.869 0.357 0.656 0.812 50 × 10 0.869 0.440 0.706 0.801 0.856 0.412 0.659 0.816 50 × 20 0.867 0.487 0.717 0.817 0.872 0.445 0.678 0.831 100 × 05 0.897 0.348 0.612 0.735 0.874 0.251 0.509 0.764 100 × 10 0.875 0.382 0.632 0.752 0.862 0.309 0.517 0.767 100 × 20 0.873 0.377 0.633 0.763 0.885 0.347 0.554 0.787 200 × 10 0.914 0.320 0.549 0.538 0.906 0.285 0.420 0.549 200 × 20 0.896 0.375 0.565 0.574 0.906 0.369 0.479 0.627 14 / 17

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Results: Diff-EAF tool

5000 5150 5300 5450 5600 1.5e+05 2e+05 2.5e+05 3e+05 TWT [0.8, 1.0] [0.6, 0.8) [0.4, 0.6) [0.2, 0.4) [0.0, 0.2) 5000 5150 5300 5450 5600 makespan 1.5e+05 2e+05 2.5e+05 3e+05 TWT 8500 8700 8900 9100 9300 8e+05 1e+06 1.2e+06 1.4e+06 TWT [0.8, 1.0] [0.6, 0.8) [0.4, 0.6) [0.2, 0.4) [0.0, 0.2) 8500 8700 8900 9100 9300 8e+05 1e+06 1.2e+06 1.4e+06 TWT 1.55e+04 1.6e+04 1.65e+04 makespan 5e+06 6e+06 7e+06 TWT

MOLS/D

[0.8, 1.0] [0.6, 0.8) [0.4, 0.6) [0.2, 0.4) [0.0, 0.2) 1.55e+04 1.6e+04 1.65e+04 5e+06 6e+06 7e+06 TWT

RIPG

Figure: Diff-EAF between MOLS/D (left) and RIPG (right) for SSD50 051 (50 × 20) (top), SSD50 071

(100 × 20) (middle), and SSD50 101 (200 × 20) (bottom). 15 / 17

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Final Considerations

  • A simple yet efficient population-based algorithm: Multi-objective

Iterated Local Search Algorithm based on Decomposition

  • Hybrid approach: heuristic + ILS strategy + diversity mechanism
  • Experimental study using 220 benchmark instances with different problem

scales

  • Contributions:
  • MOLS/D outperforms a tailored MOEA/D
  • MOLS/D is able to achieve better results than the state-of-the-art

approaches for the benchmark considered

  • We made our results (in the form of approximated Pareto fronts)

available for further investigations by other researches. Available at https://github.com/murilozangari/sdst results.

  • Future work:
  • The application of MOLS/D to solve i) SDST flowshop with three
  • bjectives, ii) flexible job-shop scheduling, and iii) other kind of

permutation problems.

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Basic concepts MOLS/D Experimental Study Final Considerations

Acknowledgment

This work has been supported by:

  • PNPD/CAPES (Brazilian Program of Post-Doctoral)
  • CNPq (Productivity Grant Nos. 306754/2015-0)
  • Research Groups 2013-2018 (IT-609-13) programs (Basque Government)
  • TIN2016-78365-R (Spanish Ministry of Economy, Industry, and

Competitiveness) Thank you!

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