On the design of (meta)heuristics · A Metaheuristic is a high-level problem independent...

On the design of

(meta)heuristics

Tony Wauters

CODeS Research group, KU Leuven, Belgium

Tony Wauters, Department of Computer Science, CODeS research group2

• Those who use heuristics • And those who don’t ☺

There are two types of people

Heuristics

3Tony Wauters, Department of Computer Science, CODeS research group

Origin: Ancient Greek: εὑρίσκω, "find" or "discover"

Oxford Dictionary: Proceeding to a solution by trial and error or

by rules that are only loosely defined.

+ Fast*

+ Scalable*

+ High quality solutions*

+ Solve any type of problem (complex constraints, non-linear, …)

- Problem specific (but usually transferable to other problems)

- Cannot guarantee optimallity


Properties of heuristics

* if well designed

• Constructive heuristics

• Metaheuristics

• Hybrid heuristics

• Matheuristics: hybrid of Metaheuristics and Mathematical Programming

• Other hybrids: Machine Learning, Constraint Programming,…

• Hyperheuristics


Heuristic types

• Incrementally construct a solution from scratch.

• Easy to understand and implement

• Usually very fast

• Reasonably good solutions


Constructive heuristics


A Metaheuristic is a high-level problem independent algorithmic framework

that provides a set of guidelines or strategies to develop heuristic

optimization algorithms.

Instead of reinventing the wheel when developing a heuristic for each

different problem, metaheuristics offer several tools that can be used as the

skeleton for the development of a heuristic.

Metaheuristics

• Key property: iteratively improve one or more solutions

• Can be combined with constructive heuristics (initial solution)

• Local search based

• Steepest descent / Hill climbing

• Tabu search, Variable Neighbourhood Search (VNS)

• Simulated Annealing, Late Acceptance

• GRASP, Guided Local Search

• Population based

• Genetic algorithms / memetic algorithms

• Ant Colony Optimization

• PSO (Particle swarm optimization)


Metaheuristics


• Variants

• Stochastic Hill-climbing

• First-improving

Hill climbing

Late acceptance Hill-climbing [Burke and

Bykov 2017]

Tony Wauters, Department of Computer Science, CODeS research group 10

Metaheuristicsthe metaphor

exposedSlides based on: Sörensen, K. Metaheuristics – the metaphor exposed. International

Transactions in Operational Research, 22: 3-18, 2015.

Thanks to Everton for sharing these slides!


• Early research on heuristics focused on human intuition, insight and

learning as a way of solving problems.

• Metaheuristics followed the same strategy.

• Example: Tabu search

• Memorizes part of the trajectory the search had taken in the recent and

not-so-recent past.

• Similar to a person looking for water in the desert trying to avoid running

in circles.

History


• Eventually new methods were based on processes that had little to do with

human intuition.

• Simulated annealing

• Natural evolution

• Ant-colony optimization

History


• Simulated annealing

• One of the earliest metaphor-based heuristics.

• Analogy to the thermodynamic process of annealing.

• Attempt to settle atoms into the lowest possible energy state.

• Total energy state of the atoms quality of the solution.

• Change of atom positions changes in the solution (moves).

History


• Natural evolution

• Probably the most successful metaphor used until now.

• Individuals in a population competing for survival.

• Individuals or chromosomes solutions.

• Fitness objective function value.

• Crossover / Mutation changes in the solution.

History

History

• Ant-colony optimization

• Models the optimization process upon the behavior of a colony of ants searching for food.

• Agents (ants) construct solutions in parallel.

• Each element of each solution has its own measure

• pheromone

• Elements with stronger pheromones have higher probability of being selected for future solutions.

17Tony Wauters, Department of Computer Science, CODeS research group


• With the increase in number of metaheuristics being created comes the

question:

Until what point creating metaphors would result in really effective

approaches?

History

Not so good metaphors



“Models of nature that are relied upon for inspiration [in creating new

metaheuristics] are ubiquitous, and it is easy to conjure up examples whose

metaphorical possibilities have not yet been tapped.[…]

It is perhaps surprising in retrospect that the behavior of bees has not

been selected as a basis for one of the ‘new’ problem solving methods.”

– Glover & Laguna (1998)

Metaphors


• People took seriously what he meant as sarcasm:

• Bees optimization algorithm (2004).

• Bee colony algorithm (2005).

• Bee mating optimization algorithm (2006).

• Difference between all insect algorithms proved marginal at best.

Metaphors


• Harmony search metaheuristic (2001)

• Changes the terminology of optimization into a musical one.

• Harmony solution.

• Note decision variable.

• Sounds better has a better objective function.

• Harmony memory set of solutions.

• Concept: A musician playing or composing music has to “draw notes from a

uniform random distribution”.

“Novel” metaphor-based method


• General idea:

• generates a set of random initial solutions;

• tries to find better solutions by combining existing ones;

• changes the values of decision variables in some of the solutions in the

set.

• In the end it is just another evolutionary algorithm…

Harmony search


• “Most importantly, when I searched Wikipedia, I could not find the structure which equals Harmony Search”.

• HS was originally “created” to solve the design of water distribution networks.

• 3 or 4 instances are tested.

• A simple constructive heuristic outperformed the method.

• Google scholar search for “harmony search”:

• 2010 – around 500 results.

• 2012 – around 3000 results

• 2 hours ago – around 23000 results

Harmony search


• Fetish with novelty.

• Race to make new scientific discoveries.

• Most common is for the method to be marketed by a single researcher:

• Co-authors a sizeable fraction of all papers on this method.

• Social media website profiles for these methods:

• Intelligent water drops algorithm officially “likes” the galaxy-based search

algorithm.

How are these heuristics accepted?


• Up-the-wall game (Burke et al., 2009)

• Game with no rules, just a goal:

• To obtain better results than your opponents

• Papers on metaheuristics are not accepted if they contain only an

interesting insight

• The methods presented need to be successful players in the up-the-wall

game.

• Methods have to be “tuned” for an instance-specific basis.

How are these heuristics accepted?


• Which components it consists of?

• Which other metaheuristics these components appear?

• How to adapt this components to a specific problem that is being solved?

• Please, use the general terminology

• Call a solution as solution.

Metaheuristic deconstruction

Design of (meta)heuristics


• Solution representation

• Direct vs indirect representation

• Often a permutation

• Datastructures

• N-dimensional array

• Tree, graph

• Linked List, Queue, Stack


Design of heuristic techniques I

• How can we modify our solutions (and make them better)?

• Solution modifications (aka the moves)

• For example: insert, remove, swap, shift, rotate, ..

• Depends on solution representation.

• Important points to consider:

• Maximum coverage of the solution space

• Connectivity

• Some basic Landscape analysis might help


Design of heuristic techniques II

• Intensification vs diversification [Glover and Laguna 1997]

• In intensification, the promising regions are explored more thoroughly in

the hope to find better solutions.

• In diversification, non-explored must be visited to be sure that all regions

of the search space are evenly explored and that the search is not confined

to only a reduced number of regions.


Intensification vs diversification

• Greediness

• Randomness

• Memory (e.g. Tabu Search)

• Adaptiveness

• Other things to consider:

• Decomposition (e.g. solving a subproblem with a specialized technique)


Key Ingredients

Heuristics in cutting &

packing


• Constructive heuristics:

• Bottom-Left , Best-fit

• Metaheuristics:

• Greedy randomized adaptive search procedure (GRASP)• Alvarez-Valdés, R., Parreño, F., & Tamarit, J. M. (2008). Reactive GRASP for the strip-packing

problem. Computers & Operations Research, 35(4), 1065-1083.

• Gomes, A. M., & Oliveira, J. F. (2001, July). A GRASP approach to the nesting problem. In 4th

Metaheuristics International Conference MIC’2001.

• Biased random-key genetic algorithm (BRKGA)• Gonçalves, J. F., & Resende, M. G. (2013). A biased random key genetic algorithm for 2D and

3D bin packing problems. International Journal of Production Economics, 145(2), 500-510.


Popular heuristic choices in cutting & packing


• If stochastic → Multiple runs

• Stopping condition?

• Iterations or time

• Convergence

• Gap to a known bound

• What to measure in a single run?

• Quality of best solution?

• Time/iterations to best solution?

• Runtime characteristics

• Time-cost plots

• Time-to-target plots [Ribeiro, C. C., Rosseti, I. (2015). ]

• Statistical analysis

How to evaluate heuristics?

Framework

Name

Languages Usage/license Metaheuristics Features

OptaPlanner Java, Kotlin,

Scala

Open source Hill Climbing, Tabu search,

Simulated Annealing, Late

Acceptance, Construction

heuristics

Good documentation, many

examples (Vehicle routing,

Scheduling, Nurse

Rostering,…). Full algorithm

configuration.

LocalSolver APIs for Python,

Java, C#, C++

Commercial

(1 Month free

academic)

?heuristic search? Powerful modeling language,

Limited algorithm

configuration.

EasyLocal++ C++ Open source Hillclimbing , simulated

annealing, and tabu search

Limited documentation


Localsearch Frameworks

• A well designed heuristic can:

• Produce high quality solutions

• In a reasonable amount of time

• Solve large-scale real-world problems

• Many design choices:

• Solution representation and data structures?

• Initial solution?

• How to modify solutions?

• Which metaheuristic?


Wrap-up

Extra: Bestiary of metaheuristics



Bestiary


• Catalogs the many different types of metaphors

• Animals

• Plants

• Microbes

• Natural Phenomena

• Supernatural Activities

• No distinction about their quality

• The island of Doctor Moreau

• https://github.com/fcampelo/EC-Bestiary

Bestiary

https://github.com/fcampelo/EC-Bestiary


• Frogs leaping.

• Blind naked mole rats.

• Flowing of water to the sea.

• 8 different metaheuristics that use water properties.

• Community of scientists.

• The life of a killer whale.

• 3 different metaheuristics based on whales.

• Reincarnation.

ExamplesSperm: Raouf OA and Hezam IM (2017). “Sperm motility

algorithm: a novel metaheuristic approach for global

optimisation.” International Journal of Operational

Research, 28(2), pp. 143. doi: 10.1504/ijor.2017.10002079

https://doi.org/10.1504/ijor.2017.10002079

Thank you

Tony Wauters, Department of Computer Science, CODeS research group 42

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