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The generalized assignment problem is a classical combinatorialoptimization problem known to be NP-hard. Itcan model a variety of real world applications in location,allocation, machine assignment, and so forth. In this paper,we review recent metaheuristic algorithms we developedfor this problem. The algorithms use the ejection chainapproach, which is embedded in a neighborhood constructionto create more complex and powerful moves. We alsoincorporate an automatic mechanism for adjusting searchparameters, to maintain a balance between visits to the feasibleand infeasible regions. Computational comparisons onbenchmark instances show that the methods are very effectivecompared to other existing metaheuristic algorithms.