Abstract
Given two sets of elements, assignment problems require a mapping of the elements of one set to those of the other. Distinguishing between bijective and injective mappings we may classify two main areas, i.e., assignment and semiassignment problems. Nonlinear assignment problems (NAPs) are those (semi-) assignment problems where the objective function is nonlinear.In combinatorial optimization many NAPs are natural extensions of the linear (semi-) assignment problem and include, among others, the quadratic assignment problem (QAP) and its variants. Due to the intrinsic complexity not only of the QAP and related NAPs heuristics are a primary choice when it comes to the successful solution of these problems in time boundaries deemed practical. In this paper we survey existing heuristic approaches for various NAPs.
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