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An Overview of Evolutionary Algorithms
and Hyper-HeuristicsNelishia PillaySchool of Mathematics, Statistics and Computer ScienceUniversity of [email protected]
Introduction An overview of hyper-heuristics
◦ Low-level heuristics◦ Classification hyper-heuristics◦ Hyper-heuristic frameworks
Evolutionary algorithm hyper-heuristics◦ Overview◦ Selection hyper-heuristics◦ Generation hyper-heuristics◦ Theoretical aspects◦ Challenges
Recent and emerging directions◦ Cross domain challenges◦ Hybridization of solution and heuristic search space◦ Hyper-Heuristics and Design◦ Hyper-Hyper Heuristics
Discussion
Outline
Tutorial site
http://titancs.ukzn.ac.za/CEC2015Tutorial.aspx
Tutorial material http://titancs.ukzn.ac.za/Files/TutorialCEC2015.pdf
Online Sites
Hyper-heuristics aim to provide a more generalized solution.
Explore a heuristic space rather than a solution space.
Heuristic space – low-level heuristics◦ Constructive◦ Perturbative
Selection vs. Generation Role played by evolutionary algorithms
Introduction
An Overview Hyper-Heuristics
Low-Level Heuristics
Heuristics vs. low-level heuristics Construction heuristics – used to create a
candidate solution Perturbative heuristics – used to improve a
solution created randomly or using a construction heuristic
Low-Level Heuristics
This problem involves the allocation of examinations to a set of specified timetable periods.
Constraints◦ Hard constraints◦ Soft constraints
Objective function◦ Hard constraint cost must be zero◦ Minimize soft constraint cost
Case Study: Examination Timetabling (ETP)
Largest degree (l) - The examination with the most clashes is scheduled first.
Largest enrollment (e) - The examination with the largest number of students is scheduled first.
Largest weighted degree (w) - The examination with the largest number of students involved in clashes is scheduled first.
Saturation degree (s) - The examination with the least number of feasible periods on the timetable is scheduled first.
Low-Level Construction Heuristics for the ETP
Example of a Static Heuristic
0 10 50 20
20 0 0 0
50 0 0 30
20 0 30 0
E1 E2 E3 E4 E5
E1
E2
E3E4
Clash matrix:
Examination
Largest Degree
E1
E2
E3
E4
Static heuristics:
Period
Examinations
P1
P2
P3
P4
3
3
1
1
2
2
2
2
E1
E3E4
E2
Timetable:
Example of a DynamicHeuristic
0 10 50 20
20 0 0 0
50 0 0 30
20 0 30 0
E1 E2 E3 E4 E5
E1
E2
E3E4
Clash matrix:
Examination
Saturation Degree
E1 4
E2 4
E3 4
E4 4
Static heuristics:
Period
Examinations
P1
P2
P3
P4
Timetable:
E1
3 E2 E33
3 2
E4
Swapping two randomly selected exams Swapping subsets of exams De-allocating exams Rescheduling exams Swapping timeslots of two randomly selected
examinations
Low-Level Perturbative Heuristics for the ETP
Define low-level construction heuristics for this problem.
Define low-level perturbative heuristics for this problem.
Can any of the heuristics used for the examination timetabling problem above be used for this problem?
One-Dimensional Bin-Packing
An Overview Hyper-Heuristics
Classification of Hyper-Heuristics
Hyper-heuristics select or create low-level heuristics.
Low-level heuristics are constructive or perturbative.
Classification:◦ Selection constructive◦ Selection perturbative◦ Generation constructive◦ Generation perturbative
Learning – offline vs. online
Hyper-Heuristic Classification
Selects the constructive heuristic to use at each stage in constructing a solution.
A problem specific objective function and low-level construction heuristics provide input to the hyper-heuristic.
Applications: educational timetabling, production scheduling, bin packing and cutting stock problems.
Methods used by the hyper-heuristic: case-based reasoning, tabu search, evolutionary algorithms, simulated annealing, variable neighbourhood search.
Selection Constructive
Selection perturbative hyper-heuristics choose a low-level perturbative heuristic at each stage in the improvement.
Multi-point vs. single-point search Single-point
◦ Heuristic selection – random, choice function, roulette wheel, reinforcement learning
◦ Move acceptance – deterministic vs. non-deterministic Multi-point search uses population based methods, e.g.
genetic algorithms, ant colonization. Applications: educational timetabling, sports
scheduling, personnel scheduling and vehicle routing
Selection Perturbative
Create low-level heuristics. Genetic programming has primarily been used for
this. More recently variations of genetic programming:
grammatical evolution and gene expression programming.
Have produced good results for the domains of educational timetabling and packing problems.
Disposable vs. reusable low-level heuristics.
Generation Hyper-Heuristics
An Overview Hyper-Heuristics
Hyper-Heuristic Frameworks
Hyflex – created for the cross domain challenge (CheSC)◦ Development of selection perturbative hyper-heuristics◦ Low-level heuristics, method to create initial solution and
objective function provided.◦ Implementation in Java
HYPERION2 - For analyzing the trace performance of metaheuristics and hyper-heuristics◦ Implementation in Java
Frameworks
Evolutionary Algorithms Hyper-Heuristics
Evolutionary algorithms have been used for both the selection and generation of low-level construction and perturbative hyper-heuristics.
Genetic algorithms have essentially been used for selection and genetic programming for generation.
More recently, variations of genetic programming have proven to be effective for generation.
Overview
Evolutionary Algorithms Hyper-Heuristics
Selection hyper-heuristics
Genetic algorithms explore the heuristic spaces. Selection construction – find a combination of
heuristics that will produce a solution minimizing the objective function.
Selection perturbative – find a combination of heuristics that will minimize the objective function further.
Each chromosome is composed of genes representing the low-level heuristics.
EA Selection Hyper-Heuristics
Low-level construction heuristics◦ Largest degree (l)◦ Largest enrollment (e)◦ Largest weighted degree (w)◦ Saturation degree (s)
Chromosome representation and initial population generation◦ Example: lwwse◦ Chromosome length – longer than the number of
examinations vs. shorter than number of examinations.
Case Study: Selection Constructive Hyper-Heuristic for the ETP
Fitness calculation◦ Each chromosome is used to create a timetable◦ The fitness is a function of the hard and soft constraint
cost.◦ Product of the hard constraints plus one and the soft
constraints Example: lwwse to allocate the four examinations
in the previous example:l → E1 w → E2 w → E3 s → E4
Case Study: Selection Constructive Hyper-Heuristic for the ETP
Selection methods◦ Tournament selection◦ Fitness proportionate selection
Genetic operators◦ Mutation – Parent: ssde
Mutation point: 2 Offspring: swde
◦ Crossover – Parents: ssde lwws Crossover point: 2 Offspring: ssws lwde
Case Study: Selection Constructive Hyper-Heuristic for the ETP
For a selection perturbative hyper-heuristic the low-level heuristics will change.
An initial solution will be created by using a low-level construction heuristic.
Example low-level heuristics:◦ Swapping two randomly selected exams (e)◦ Swapping subsets of exams (s)◦ Deallocating exams (d)◦ Rescheduling exams (a)◦ Swapping timeslots of two randomly selected examinations (t)
Example chromosome: tdsse
Selection Perturbative Hyper-Heuristic for the ETP
ExamplesApproach Application Hyper-
HeuristicStudy
Genetic algorithm Trainer Scheduling Selection perturbative
Cowling et al. [3]
Messy GA One and two dimensional bin-packing
Selection constructive
Lopez-Camacho et al. [17]
Genetic algorithm Distributed staff trainer scheduling
Selection perturbative
Han and Kendall
Genetic algorithm One dimensional bin-packing
Selection constructive Pillay[13]
Genetic algorithm Educational timetabling
Selection constructive
Pillay [10], Pillay[11], Pillay [14], Pillay [15]
Genetic programming and variations of genetic programming, e.g. grammar-based genetic programming and grammatical evolution have been used.
Generative construction heuristics combine:◦ variables representing the characteristics of the problem◦ existing low-level construction heuristics to create new
heuristics. Generative perturbative hyper-heuristics combine
different heuristic selection and move acceptance components to create new perturbative heuristics.
Applications: educational timetabling, packing problems and vehicle routing problems
Generation Hyper-Heuristics
Function set:◦ Standard addition (+), subtraction (-) and multiplication (*).◦ % - protected division which will return a 1 if the
denominator is zero.◦ < - will return a value of 1 if its first argument is less than
or equal to its second and -1 otherwise. Terminal set
◦ F - the fullness of a bin, i.e. the sum of the sizes of the elements in the bin.
◦ C - the bin capacity◦ S - the size of the item to place next.
Case Study: One-Dimensional Bin-Packing
Fitness ◦ Each heuristic in the population is evaluated by using it to solve
the problem instance. ◦ The fitness is calculated to be the difference of the number of bins
used and the ratio of the sum of the items to the sum of the capacity of all bins used.
Example heuristic
Case Study: One-Dimensional Bin-Packing
<
F -
C S
ExamplesApproach Application Hyper-
HeuristicStudy
Genetic programming
Packing problem Generation constructive
Burke et al. [1], Burke et al. [2], Hyde [6]
Genetic programming
Multidimensional knapsack problem
Generativeconstructive
Drake et al. [4]
Grammatical evolution
One dimensional knapsack problem
Generativeconstructive
Sotelo-Figueroa [25]
Genetic programming
Educational timetabling
Generativeconstructive
Pillay [9], Pillay[12], Pillay and Banzhaf [17], Pillay and Banzhaf [18]
Grammatical evolution
Educational timetabling
Generativeperturbative
Sabar et al. [22]
Grammatical evolution
Vehicle routing Generativeperturbative
Sabar et al. [22]
Some studies show that hyper-heuristics produce results than searching the search some directly.
Why is this the case? Some initial work on this:
◦ Allows for quicker movement through the solution space indirectly. Small movements in the heuristic space results in larger movement in the solution space.
◦ Fitness landscape has a big valley structure in which a global optimum is not isolated but surrounded by local optima.
Further theoretic investigations
Theoretic aspects
High runtimes◦ Distributed architectures◦ Distributed frameworks
Parameter tuning◦ Tuning tools, e.g iRace, ParamILS◦ Hyper-heuristics for design – using evolutionary
algorithms with co-evolution
Challenges
Recent and Emerging Directions
Cross domain hyper-heuristics Hybridizing solution and heuristic space search Evolutionary algorithm hyper-heuristics for design Hyper-heuristics for evolutionary algorithm design Evolutionary algorithm hyper-hyper-heuristics
Overview
CHeSC 2011 and CHeSC 2014 HyFlex (Java implementation)
◦ Provides method to create the initial solution◦ Provides low-level perturbative heuristics◦ Provides objective function◦ Researcher to create selection perturbative hyper-
heuristic Problem domains
◦ Boolean satisfiability, one dimensional bin packing, flowshop scheduling, personnel scheduling.
◦ Hidden domains: TSP and vehicle routing
Cross Domain Challenges
CHeSC 2014◦ Introduces “batching”.◦ Allows multithreading strategies
Adaptive evolutionary algorithm to select perturbative heuristics which produces good results for the vehicle routing problem.
Further investigations into using evolutionary algorithm hyper-heuristics.
Cross Domain Challenges
Searching the heuristic space and solution space – initial work in this area illustrates potential (Qu et al. 2009).
How should these be combined? Evolutionary algorithms and co-evolution?
Hybridization of Solution and Heuristic Space Search
Recent and Emerging Directions
Evolutionary Algorithm Hyper-Heuristics for Design
Selection and generation evolutionary algorithms have been used for design.
Evolutionary algorithms used: genetic algorithms, genetic programming, grammatical evolution.
Design aspects◦ Selecting parameter values◦ Selecting operators/methods and deciding control flow◦ Hybridization of methods
Low-level heuristics are the parameter values, operators and methods.
Overview
ExamplesApproach Design Aspect Study
Grammar based GP Decision tree generation and design
Barros et al. [1]
Evolutionary algorithms
Decision tree generation Barros et al. [2], Barros et al. [3]
NSGA-II Combine neural networks into a stacked neural network.
Furtuna et al. [5]
Grammatical evolution Selects operators and parameter values to solve a vehicle routing problem
Marshall et al. [11]
Genetic programming Generates black box search algorithms to solve the deceptive trap problem.
Martin and Tauritz [12]
Examples
Approach Design Aspect Study
Grammatical evolution Selects operators and parameter values for ant colonization to solve the travelling salesman problem.
Tavares and Pereira [20]
Genetic programming Generates mutation operators for evolutionary programming
Hong et al. [6]
Grammatical evolution Selects operators and parameter values for an evolutionary algorithm to solve the knapsack problem.
Lourenco et al. [9]
Recent and Emerging Directions
Hyper-Heuristics for Evolutionary Algorithm Design
Hyper-heuristics have also proven to be effective for the design of evolutionary algorithms.
Has been used to: ◦ decide on the control flow in an evolutionary algorithm by
choosing when during the evolution process to use which operators
◦ select of parameter values◦ hybridize evolutionary algorithms
Overview
ExamplesDesign Aspect Study
Selection of recombination operator and selection method in differential evolution.
Tinoco and Coelllo [21]
Selects one of three multi-objective evolutionary algorithms to solve at each point of solving the problem
Maashi et al. [10]
Parameter tuning and determining the stopping condition in and implementation of MOEA.
Segredo et al. [19]
Selection of crossover operator, mutation operator and selection method in an evolutionary algorithm.
Kumari and Srinivas [7], Kumaria and Srinivas [8]
Generation of mutation operators in a genetic algorithm Woodward and Swan [21]
Hyper-hyper-heuristics is the extension of the idea of hyper-heuristics to select or combine hyper-heuristics and generate new hyper-heuristics.
Evolutionary algorithms can be used for the design of hyper-heuristics as well.
Example: using gene expression programming to evolve a selection perturbative hyper-heuristic which is used in the HyFlex framework to generalize over 6 problem domains (Sabar et al. 2014)
Hyper-Hyper Heuristics
Discussion Session: Future Research Directions