Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming

Computing efficient exact designs of experiments using integer quadratic programming

We propose a method of computing exact experimental designs by integer quadratic programming. The key idea is a suitable quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix, which we call the criterion of Q-optimality. We demonstrate on several examples that the D-efficiency of the exact Q-optimal designs is usually very ...

Optimal Factorial Designs for Cdna Microarray Experiments

We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the more common orthogonal parametrization. First, analytical results are given for the 2× 2 factorial. Since practical applications often involve a more complex...

Exact Mixed Integer Programming for Integrated Scheduling and Process Planning in Flexible Environment

This paper presented a mixed integer programming for integrated scheduling and process planning. The presented process plan included some orders with precedence relations similar to Multiple Traveling Salesman Problem (MTSP), which was categorized as an NP-hard problem. These types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...

Semidefinite relaxations for non-convex quadratic mixed-integer programming

We present semidefinite relaxations for unconstrained nonconvex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for mediumsized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We us...

Valid Linear Programming Bounds for Exact Mixed-Integer Programming