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7/31/2019 What is a Metaheuristic
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What is a Metaheuristic?
Spring 2009
Instructor: Dr. Masoud Yaghini
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Optimization Problems
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What is a Metaheuristic?
Optimization problems
The many decision-making problems can beoften expressed as an constrainedoptimization problem with some decisionvariables that are restricted by a set of
.
Types of constrained optimization problems:
Combinatorial problems: When the decisionvariables are discrete
Continuous problems: When the decisionvariables are continuous
Mixed problems
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What is a Metaheuristic?
Combinatorial Problems Examples of real-world combinatorial
optimization problems include:
Assembly-line balancing problems
Vehicle routing and scheduling problems
Facility layout design problems
Job sequencing and machine scheduling problems
Manpower planning problems
Production planning and distribution
Etc.
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What is a Metaheuristic?
Combinatorial Optimization Combinatorial optimization problems are often
easy to state but very difficult to solve.
Many of the problems arising in applicationsare NP-hard, that is, it is strongly believed that
polynomially bounded computation time.
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What is a Metaheuristic?
Combinatorial Optimization Two classes of algorithms are available for the
solution of combinatorial optimizationproblems:
Exact algorithms
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What is a Metaheuristic?
Combinatorial Optimization Exact algorithms are guaranteed to find the
optimal solution and to prove its optimality forevery finite size instance of a combinatorialoptimization problem within an instance-
.
In the case of NP-hard problems, in the worstcase, exponential time to find the optimum.
For most NP-hard problems the performanceof exact algorithms is not satisfactory.
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What is a Metaheuristic?
Combinatorial Optimization If optimal solutions cannot be efficiently
obtained in practice, the only possibility is totrade optimality for efficiency.
Approximate algorithms, often also called,
to obtain good, that is, near-optimal solutionsat relatively low computational cost withoutbeing able to guarantee the optimality of
solutions.
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Metaheuristics
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What is a Metaheuristic?
Metaheuristics A disadvantage of heuristic methods is that
they:
either generate only a very limited number ofdifferent solutions, or
h r li l l im whi h i h
case for iterative improvement methods.
Metaheuristics have been proposed which tryto bypass these problems.
Metaheuristics apply to solve the problemsknown as of difficult optimization
Available from the 1980s
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What is a Metaheuristic?
Metaheuristics Definition:
A metaheuristic is a set of algorithmic conceptsthat can be used to define heuristic methodsapplicable to a wide set of different problems.
A metaheuristic can be seen as a eneral-
purpose heuristic method toward promisingregions of the search space containing high-qualitysolutions.
A metaheuristic is a general algorithmic frameworkwhich can be applied to different optimizationproblems with relatively few modifications to makethem adapted to a specific problem.
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What is a Metaheuristic?
Capability of Metaheuristics
Metaheuristics have capability to beextracted from a local minimum
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What is a Metaheuristic?
Metaheuristics The metaheuristics are from now on regularly
employed in all the sectors of engineering,
Examples of metaheuristics algorithms: The evolutionary algorithms
The tabu search method
The ant colony optimization The simulated annealing method
Etc.
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What is a Metaheuristic?
Metaheuristics
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References
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What is a Metaheuristic?
References J. Dreo A. Petrowski, P. Siarry E. Taillard,
Metaheuristics for Hard Optimization, Springer-
Verlag, 2006. R.J. Moraga, G.W. DePuy, G.E. Whitehouse,
Metaheuristics: A Solution Methodology forp m za on ro ems, an oo o n us r a an
Systems Engineering, A.B. Badiru (Ed.), 2006.
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The End