The Convex Hull Heuristic (CHH) is a heuristic for mixed-integer programming problems with a nonlinear objective function and linear constraints. It is a matheuristic in two ways: it is based on the mathematical programming algorithm called simplicial decomposition, or SD, and at each iteration, one solves a mixed-integer programming problem with a linear objective function and the original constraints, and a continuous problem with a nonlinear objective function and a single linear constraint. Its purpose is to produce quickly feasible and often near optimal or optimal solutions for convex and nonconvex problems. It is usually multi-start. We have tested it on a number of hard quadratic 0-1 optimization problems and present numerical results for generalized quadratic assignment problems (GQAP), cross-dock door assignment problems (CDAP), quadratic assignment problems (QAP) and quadratic knapsack problems (QKP). We compare solution quality and solution times with results from the literature, when possible.

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View The Convex Hull Heuristic for Nonlinear 0-1 Programming Problems with Linear Constraints