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J OURNAL OF S PATIAL I NFORMATION S CIENCE Number 15 (2017), pp. 89120doi:10.5311/JOSIS.2017.15.379R ESEARCH A RTICLEA cuttingplane method for contiguityconstrained spatial aggregation Johannes Oehrlein.

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  4. In the section relating to contiguity constraints, specify the necessary conditions that the aggregated areas must fulfill. Make sure the entries align with the boundary conditions defined in the methodology.
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The idea of Kelley's cutting plane algorithm is to approximate the feasible region with a polytope, solve the resulting linear program (LP) and, if the LP solution is not feasible, separate it using gradient cuts to obtain a new polytope which is a better approximation of the feasible region and repeat, see Algorithm 1 ...

The cutting plane method is commonly used for solving ILP and MILP problems to find integer solutions, by solving the linear relaxation of the given integer programming model, which is a noninteger LP model.

A cutting plane algorithm is generally used to search for valid inequalities that cut-off the noninteger solutions in two cases, when the set of constraints in our integer programming model is too large, and when the inequality constraints in the original integer programming model are not sufficient to yield an integer ...

The cutting-plane algorithm modifies the solution space by adding cuts that produce an optimum integer extreme point. Figure 9.10 gives an example of two such cuts. Initially, we start with the continuous LP optimum z = 66(1/2), x1 = 4(1/2), x2 = 3(4/7).

The cutting-plane algorithm modifies the solution space by adding cuts that produce an optimum integer extreme point. Figure 9.10 gives an example of two such cuts. Initially, we start with the continuous LP optimum z = 66(1/2), x1 = 4(1/2), x2 = 3(4/7).

The idea of Kelley's cutting plane algorithm is to approximate the feasible region with a polytope, solve the resulting linear program (LP) and, if the LP solution is not feasible, separate it using gradient cuts to obtain a new polytope which is a better approximation of the feasible region and repeat, see Algorithm 1 ...

The underlying principle is to approximate the feasible region of a nonlinear (convex) program by a finite set of closed half spaces and to solve a sequence of approximating linear programs.

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