IGLS/1

© P. Pongcharoen

Using Genetic Algorithms for Scheduling the

Production of Capital Goods

P. Pongcharoen, C. Hicks, P.M. Braiden,

A.V. Metcalfe, D.J. Stewardson

University of Newcastle upon Tyne

IGLS/2

© P. Pongcharoen

Scheduling

• “The allocation of resources over time to perform a collection of tasks” (Baker 1974)

• “Scheduling problems in their static and deterministic forms are extremely simple to describe and formulate, but are difficult to solve” (King and Spakis 1980)

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Scheduling Problems

• Involve complex combinatorial optimisation

• For n jobs on m machines there are potentially (n!)m sequences, e.g. n=10 m=3 => 1.7 million sequences.

• Most problems can only be solved by inefficient non-deterministic polynomial (NP) algorithms.

• Even a computer can take large amounts of time to solve only moderately large problems

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Scheduling the Production of

Capital Goods

• Deep and complex product structures

• Long routings with many types of machine and process

• Multiple constraints such as assembly, precedence operation and resource constraints.

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Conventional Optimisation Algorithms

• Integer Linear Programming• Dynamic Programming• Branch and Bound

These methods rely on enumerative search and are therefore only suitable for small problems

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More Recent Approaches

• Simulated Annealing• Taboo Search• Genetic Algorithms

Characteristics• Stochastic search.• Suitable for combinatorial optimisation

problems.• Due to combinatorial explosion, they

may not search the whole problem space. Thus, an optimal solution is not guaranteed.

IGLS/7

© P. Pongcharoen

Melting substance

Too fast cooling

Heating up

Slowly cooling

Simulated Annealing

Substance

Equilibrium statewith resulting crystal

Out of equilibrium statewith resulting defecting crystal

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Taboo Search

Current solution ( c) = initial solutionObjective function of c = F( c)

Taboo list (T) = emptyOptimal solution (x*) = c

Neighbour list (N) = Neighbour of cEvaluate solution in the list

Move to the best neighbour = x N - TCalculate offset = F( c) - F(x)New current solution ( c) = x

Termination ?

Optimal solution (x*) = xAdd the move into Taboo list (T)

Update optimaland Taboo list

offset > 0 ?No

Yes

No

Initial setting

Neighbour searchingand movement

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Evaluation criteria

• Determination coefficient (R2)

• Adjusted determination

coefficient (Ra2)

• Mean square error (MSE)

• Mallow’s statistic (Cp)

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Conclusion (1)

• BGA has been developed for the scheduling of complex products with deep product structure and multiple resource constraints.

• Within a given execution time, large population (fewer generations) produced lower penalty costs and spread than small populations (many generations).

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© P. Pongcharoen

Conclusion (2)

• BGA produced lower penalty costs than corresponding plans produced by using simulation.

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© P. Pongcharoen

Any questions

Please