Smart greedy procedure for solving a multidimensional nonlinear knapsack class of reliability optimization problems

A heuristic procedure called Smart Greedy is proposed for solving a nonlinear knapsack class of reliability optimization problems with multiple constraints (multidimensional nonlinear knapsack problems). At first, by using a surrogate multiplier, the multidimensional nonlinear knapsack problem is translated into an one-dimensional nonlinear knapsack problem, which is called the surrogate problem. Second, modular approach (MA) solves the surrogate problem with the surrogate multiplier given as a centroid of the current polyhedron. Algorithm cut-off polyhedron (COP) provides a cutting plane of the polyhedron, and reduces the polyhedron recursively until the polyhedron becomes empty. Finally, a procedure called Smart Greedy generates an approximate solution of the surrogate problem with the surrogate multiplier finally obtained. The solution obtained is called Smart Greedy solution, which is feasible to the original problem. The computational experiments show hat the present algorithm provides high quality solutions.