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Automated generation of high-performance heuristics from flexible algorithm frameworks: Challenges and Perspectives Thomas St utzle IRIDIA, CoDE, Universit e Libre de Bruxelles (ULB) Brussels, Belgium stuetzle@ulb.ac.be

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Automated generation of high-performance heuristics from flexible algorithm frameworks: Challenges and Perspectives

Thomas St¨ utzle

IRIDIA, CoDE, Universit´ e Libre de Bruxelles (ULB) Brussels, Belgium stuetzle@ulb.ac.be iridia.ulb.ac.be/~stuetzle

IRIDIA

Institut de Recherches

Interdisciplinaires et de Développements en Intelligence Artificielle

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Outline

1. What we have been done / are doing
2. Next steps?, challenges and perspectives

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Automatic offline configuration / algorithm design

Typical performance measures

◮ maximize solution quality (within given computation time) ◮ minimize computation time (to reach optimal solution)

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Configurators

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The irace package

Manuel L´

pez-Ib´

a˜ nez, J´ er´ emie Dubois-Lacoste, Thomas St¨ utzle, and Mauro

Birattari. The irace package, Iterated Race for Automatic Algorithm
Configuration. Technical Report TR/IRIDIA/2011-004, IRIDIA, Universit´

e Libre de Bruxelles, Belgium, 2011. The irace Package: User Guide, 2016, Technical Report TR/IRIDIA/2016-004 http://iridia.ulb.ac.be/irace

◮ implementation of Iterated Racing in R

Goal 1: flexible Goal 2: easy to use

◮ but no knowledge of R necessary ◮ parallel evaluation (MPI, multi-cores, grid engine .. ) ◮ currently various extensions done (soon publicly available)

irace has shown to be effective for configuration tasks with several hundred of variables

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Automatic design of algorithms from algorithm frameworks

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General approach

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Main approaches

Top-down approaches

◮ develop flexible framework following a fixed algorithm

template with alternatives

◮ apply high-performing configurators ◮ Examples: Satenstein, MOACO, MOEA, MIP Solvers?(!)

Bottom-up approaches

◮ flexible framework implementing algorithm components ◮ define rules for composing algorithms from components e.g.

through grammars

◮ frequently usage of genetic programming, grammatical

evolution etc.

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Top-down configuration

Multi-objective evolutionary algorithms (MOEA)

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Multi-objective evolutionary algorithms

Pareto based Indicator based Weight based

(NSGA-II, SPEA2) (IBEA, SMS-EMOA) (MOGLS, MOEA/D)

We initially focused on building an automatically configurable component-wise framework for Pareto- and indicator-based MOEAs

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MOEA Framework — outline

[Bezerra, L´

pes-Ib´

a˜ nez, St¨ utzle, 2016]

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Preference relations in mating / replacement

Component Parameters Preference Set-partitioning, Quality, Diversity BuildMatingPool PreferenceMat, Selection Replacement PreferenceRep, Removal ReplacementExt PreferenceExt, RemovalExt

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Representing known MOEAs

BuildMatingPool Replacement Alg. SetPart Quality Diversity Selection SetPart Quality Diversity Removal MOGA rank — niche-sh. DT — — — generational NSGA-II depth — crowding DT depth — crowding

ne-shot

SPEA2 strength — kNN DT strength — kNN sequential IBEA — binary — DT — binary —

ne-shot

HypE — I h

— DT depth I h

— sequential SMS — — — random depth-rank I 1

— —

(All MOEAs above use fixed size population and no external archive; in addition, SMS-EMOA uses λ = 1)

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MO configuration

irace + performance indicator (e.g. hypervolume) = automatic configuration of multi-objective solvers!

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Experimental results

DTLZ WFG 2-obj 3-obj 5-obj 2-obj 3-obj 5-obj ∆R = 126 ∆R = 127 ∆R = 107 ∆R = 169 ∆R = 130 ∆R = 97

AutoD2 AutoD3 AutoD5 AutoW2 AutoW3 AutoW5

(1339) (1500) (1002) (1692) (1375) (1170) SPEA2D2 IBEAD3 SMSD5 SPEA2W2 SMSW3 SMSW5 (1562) (1719) (1550) (2097) (1796) (1567) IBEAD2 SMSD3 IBEAD5 NSGA-IIW2 IBEAW3 IBEAW5 (1940) (1918) (1867) (2542) (1843) (1746) NSGA-IID2 HypED3 SPEA2D5 SMSW2 SPEA2W3 SPEA2W5 (2143) (2019) (2345) (2621) (2600) (2747) HypED2 SPEA2D3 NSGA-IID5 IBEAW2 NSGA-IIW3 NSGA-IIW5 (2338) (2164) (2346) (2777) (3315) (3029) SMSD2 NSGA-IID3 HypED5 HypEW2 HypEW3 MOGAW5 (2406) (2528) (2674) (2851) (3431) (4268) MOGAD2 MOGAD3 MOGAD5 MOGAW2 MOGAW3 HypEW5 (2970) (2851) (2915) (4320) (4540) (4373)

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Additional remarks

◮ additional results

◮ time-constrained scenarios ◮ cross-benchmark comparison ◮ applications to multi-objective flow-shop scheduling

◮ extended version of AutoMOEA

◮ extensions of template (weights, local search, etc.) ◮ more comprehensive benchmarks sets ◮ in-depth comparison of MOEAs ◮ design space analysis (e.g. ablation)

◮ Other examples

◮ Single-objective frameworks for MIP: CPLEX, SCIP ◮ Single-objective framework for SAT, SATenstein ◮ Continuous optimization: UACOR, ABC-X ◮ Multi-objective algorithm frameworks (TP+PLS, MOACO) Automated Algorithm Selection and Configuration, Dagstuhl, Germany 16

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Bottom up configuration of hybrid SLS algorithms

Automatic design of hybrid SLS algorithms

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Automatic design of hybrid SLS algorithms

[Marmion, Mascia, L´

pes-Ib´

a˜ nez, St¨ utzle, 2013]

Approach

◮ decompose single-point SLS methods into components ◮ derive generalized metaheuristic structure ◮ component-wise implementation of metaheuristic part

Implementation

◮ present possible algorithm compositions by a grammar ◮ instantiate grammer using a parametric representation

◮ allows use of standard automatic configuration tools ◮ shows good performance when compared to, e.g., grammatical

evolution [Mascia, L´

pes-Ib´

a˜ nez, Dubois-Lacoste, St¨ utzle, 2014]

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General Local Search Structure: ILS

s0 :=initSolution s∗ := ls(s0) repeat s′ :=perturb(s∗,history) s∗′ :=ls(s′) s∗ :=accept(s∗,s∗′,history) until termination criterion met

◮ many SLS methods instantiable from this structure ◮ abilities

◮ hybridization (through recursion) ◮ problem specific implementation at low-level ◮ separation of generic and problem-specific components Automated Algorithm Selection and Configuration, Dagstuhl, Germany 19

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Grammar

<algorithm> ::= <initialization> <ils> <initialization> ::= random | <pbs_initialization> <ils> ::= ILS(<perturb>, <ls>, <accept>, <stop>)

<perturb> ::= none | <initialization> | <pbs_perturb> <ls> ::= <ils> | <descent> | <sa> | <rii> | <pii> | <vns> | <ig> | <pbs_ls> <accept> ::= alwaysAccept | improvingAccept <comparator> | prob(<value_prob_accept>) | probRandom | <metropolis> | threshold(<value_threshold_accept>) | <pbs_accept> <descent> ::= bestDescent(<comparator>, <stop>) | firstImprDescent(<comparator>, <stop>) <sa> ::= ILS(<pbs_move>, no_ls, <metropolis>, <stop>) <rii> ::= ILS(<pbs_move>, no_ls, probRandom, <stop>) <pii> ::= ILS(<pbs_move>, no_ls, prob(<value_prob_accept>), <stop>) <vns> ::= ILS(<pbs_variable_move>, firstImprDescent(improvingStrictly), improvingAccept(improvingStrictly), <stop>) <ig> ::= ILS(<deconst-construct_perturb>, <ls>, <accept>, <stop>) <comparator> ::= improvingStrictly | improving <value_prob_accept> ::= [0, 1] <value_threshold_accept> ::= [0, 1] <metropolis> ::= metropolisAccept(<init_temperature>, <final_temperature>, <decreasing_temperature_ratio>, <span>) <init_temperature> ::= {1, 2,..., 10000} <final_temperature> ::= {1, 2,..., 100} <decreasing_temperature_ratio> ::= [0, 1] <span> ::= {1, 2,..., 10000} Automated Algorithm Selection and Configuration, Dagstuhl, Germany 20

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System overview

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Flow-shop problem with makespan objective

[Pagnozzi, St¨ utzle, 2016]

◮ Automatic configuration:

◮ max. three levels of recursion ◮ biased / unbiased grammar resulting in 262 and 502

parameters, respectively

◮ budget: 200 000 trials of n · m · 0.03 seconds

95% confidence limits

Algorithms ARPD 0.22 0.24 0.26 0.28 0.30 IGrs IGtb irace1 irace2 irace3 irace4

Results are clearly superior to state-of-the-art

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Flow-shop problem with total completion time objective

◮ Automatic configuration:

◮ max. three levels of recursion ◮ biased / unbiased grammar resulting in 262 and 502

parameters, respectively

◮ budget: 100 000 trials of n · m · 0.03 seconds

Relative Percentage Deviation

0.50 0.55 0.60 0.65 0.70 0.75 ALGirtct IGA IGAb

Results are clearly superior to state-of-the-art

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Flow-shop problem with total tardiness objective

◮ Automatic configuration:

◮ max. three levels of recursion ◮ biased / unbiased grammar resulting in 262 and 502

parameters, respectively

◮ budget: 100 000 trials of n · m · 0.03 seconds

Relative Deviation Index

TSM63 TSMe63 irace4 1 2 3 4 5 6

Results are clearly superior to state-of-the-art

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Comparison

Comparison of SLS algorithms

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Example: Comparison of MOEAs

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Exploration and Extension

Exploration of SLS algorithm variants

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SA in components

Input: a neighbourhood S for the solutions, an initial solution s0, control parameters s∗ = ˆ s = s0 t0 = initialize temperature while stopping criterion is not met choose si+1 ∈ S(ˆ s) using search space exploration criterion if si+1 meets acceptance criterion: ˆ s = si+1 if ˆ s improves over s∗: s∗ = ˆ s if temperature length is reached update temperature according to cooling scheme if temperature has to be reset reset temperature following temperature restart scheme return locally optimal solution s∗

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SA components

List of the SA components (# of options implemented):

◮ initial temperature t0 (7 options) ◮ neighbourhood exploration (2 options) ◮ acceptance criterion (9 options) ◮ cooling scheme (10 options) ◮ temperature length (12 options) ◮ temperature restart (21 options) ◮ termination condition (11 options)

to be combined with 2 problem-specific components:

◮ neighbourhood S (problem-specific # options) ◮ initial solution s0 (problem-specific # options)

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Summary

Contributions

◮ approach to automate design and analysis of (hybrid)

metaheuristics

◮ not a silver bullet, but needs right components, especially

low-level problem-specific ones

◮ directly extendible for unbiased comparisons of metaheuristics

and to capture current knowledge

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Can we boost frameworks and automated design to new solver paradigm (for SLS algorithms)?

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Configurable SLS framework XXL

◮ paradigm shift in SLS algorithm development ◮ configurable frameworks XXL ◮ solve = model + configure + search

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Unfiltered list of ingredients / extensions

Problem side

◮ define appropriate problems classes ◮ hierarchy of problem classes / representations ◮ problem specification language / representation ◮ advantages: combinatorial structure exploitable as explicitly

defined

Algorithmic side

◮ low-level heuristics (constructive, neighborhoods etc.) ◮ high-level guidance strategies ◮ integration of other techniques (e.g. matheuristics)

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Unfiltered list of ingredients / extensions

Low-level SLS components

◮ automatic generation of constructive heuristics from problem

specification

◮ automatic generation of perturbative local searches, incl.

VLNS

◮ search restrictions and speed-up

Higher-level SLS side

◮ decomposition and re-composition of SLS methods ◮ components XXL ◮ generation of templates and evaluation functions

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Unfiltered list of ingredients / extensions

Automatic configuration techniques

◮ extension to very-large scale configuration tasks ◮ informers, feature generation ◮ learning relationship problem-space to algorithm design space ◮ methodological improvements

Extensions

◮ stochastic / dynamic / multi-objective problems ◮ other techniques (MIP, CP etc.)

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Design questions

◮ how many frameworks? how to integrate various? ◮ what type of problems? ◮ what specific types of techniques?

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Design questions

◮ how many frameworks? how to integrate various? ◮ what type of problems? ◮ what specific types of techniques?

Automatic configuration of solver integration?

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