Cuts for mixed 0-1 conic programming

In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 0-1 conic programs have interesting implications for comparing the semidefinite programming and the linear programming relaxations of combinatorial optimization problems, e.g. we show that all the subtour elimination inequalities for the traveling salesman problem are rank-1 Gomory cuts with respect to a single semidefinite constraint. We also include results from our preliminary computational experiments with these cuts

Constrained Optimization in Simulation: A Novel Approach

This paper presents a novel heuristic for constrained optimization of random computer simula-tion models, in which one of the simulation outputs is selected as the objective to be minimized while the other outputs need to satisfy prespecified target values. Besides the simulation out-puts, the simulation inputs must meet prespecified constraints including the constraint that the inputs be integer. The proposed heuristic combines (i) experimental design to specify the simu-lation input combinations, (ii) Kriging (also called spatial correlation modeling) to analyze the global simulation input/output data that result from this experimental design, and (iii) integer nonlinear programming to estimate the optimal solution from the Kriging metamodels. The heuristic is applied to an (s, S) inventory system and a realistic call-center simulation model, and compared with the popular commercial heuristic OptQuest embedded in the ARENA ver-sions 11 and 12. These two applications show that the novel heuristic outperforms OptQuest in terms of search speed (it moves faster towards high-quality solutions) and consistency of the solution quality