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For many important practical or theoretical problems, the objective is to choose a “best” solution out of a large number of possible solutions. Such problems are typically known as combinatorial optimization problems [Lawl76, PaSt82], In many combinatorial optimization problems, a solution is an arrangement of a set of discrete objects according to a given set of constraints. A solution is also called a configuration. The set of all solutions is referred to as the solution space. A cost function f is defined on all solutions. That is, for a solution x, f(x) is the cost of the solution. Our goal is to develop efficient algorithms for determining a configuration that minimizes the value of the cost function. An example of combinatorial optimization problems is the well-known Traveling Salesman Problem [PaSt82] which is the problem of determining a traveling salesman route (a route which passes through each of a given set of cities once and returns finally to the starting city) with minimum cost. In this case, the cities are the discrete objects to be rearranged. That each city must be visited once and only once is the constraint which must be satisfied.
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