This paper introduces a fully general, exact algorithm for nesting irregular shapes. Both the shapes and material resource can be arbitrary nonconvex polygons. Moreover, the shapes can have holes and the material can have defective areas. Finally, the shapes can be arranged using both...

This paper provides a canonical dual approach for minimizing a general quadratic function over a set of linear constraints. We first perturb the feasible domain by a quadratic constraint, and then solve a “restricted” canonical dual program of the perturbed problem at each iteration to...

The Standard Quadratic Problem (StQP) is an NP-hard problem with many local minimizers (stationary points). In the literature, heuristics based on unconstrained continuous non-convex formulations have been proposed (Bomze & Palagi, 2005; Bomze, Grippo, & Palagi, 2012) but none dominates the other in...

Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new...