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Combinatorial optimization is the process of finding the best, or
optimal, so lution for problems with a discrete set of feasible
solutions. Applications arise in numerous settings involving
operations management and logistics, such as routing, scheduling,
packing, inventory and production management, lo cation, logic, and
assignment of resources. The economic impact of combi natorial
optimization is profound, affecting sectors as diverse as
transporta tion (airlines, trucking, rail, and shipping), forestry,
manufacturing, logistics, aerospace, energy (electrical power,
petroleum, and natural gas), telecommu nications, biotechnology,
financial services, and agriculture. While much progress has been
made in finding exact (provably optimal) so lutions to some
combinatorial optimization problems, using techniques such as
dynamic programming, cutting planes, and branch and cut methods,
many hard combinatorial problems are still not solved exactly and
require good heuristic methods. Moreover, reaching "optimal
solutions" is in many cases meaningless, as in practice we are
often dealing with models that are rough simplifications of
reality. The aim of heuristic methods for combinatorial op
timization is to quickly produce good-quality solutions, without
necessarily providing any guarantee of solution quality.
Metaheuristics are high level procedures that coordinate simple
heuristics, such as local search, to find solu tions that are of
better quality than those found by the simple heuristics alone:
Modem metaheuristics include simulated annealing, genetic
algorithms, tabu search, GRASP, scatter search, ant colony
optimization, variable neighborhood search, and their hybrids."
Combinatorial optimization is the process of finding the best, or
optimal, so lution for problems with a discrete set of feasible
solutions. Applications arise in numerous settings involving
operations management and logistics, such as routing, scheduling,
packing, inventory and production management, lo cation, logic, and
assignment of resources. The economic impact of combi natorial
optimization is profound, affecting sectors as diverse as
transporta tion (airlines, trucking, rail, and shipping), forestry,
manufacturing, logistics, aerospace, energy (electrical power,
petroleum, and natural gas), telecommu nications, biotechnology,
financial services, and agriculture. While much progress has been
made in finding exact (provably optimal) so lutions to some
combinatorial optimization problems, using techniques such as
dynamic programming, cutting planes, and branch and cut methods,
many hard combinatorial problems are still not solved exactly and
require good heuristic methods. Moreover, reaching "optimal
solutions" is in many cases meaningless, as in practice we are
often dealing with models that are rough simplifications of
reality. The aim of heuristic methods for combinatorial op
timization is to quickly produce good-quality solutions, without
necessarily providing any guarantee of solution quality.
Metaheuristics are high level procedures that coordinate simple
heuristics, such as local search, to find solu tions that are of
better quality than those found by the simple heuristics alone:
Modem metaheuristics include simulated annealing, genetic
algorithms, tabu search, GRASP, scatter search, ant colony
optimization, variable neighborhood search, and their hybrids."
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