Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the into larger decision-making problem, for example, picking best chemical process catalyst. We study large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted penalty functions...

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse literature exists for convex problems, there have been few advances discrete despite the ubiquity applications fundamentally rely on decision making. In this paper, we present new set theoretical insights and ...

We present pure-integer Gomory cuts in a way so that they are derived with respect to a “dual form” pure-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. The input integer problem is not in standard form, and so the cuts are derived a bit differently. In this manner, we obtain a finitely-terminating version of pure-integer...

We present a new polyhedral approach to nonlinear Boolean optimization. Compared to other methods, it produces much smaller integer programming models, making it more efficient from a practical point of view. We mainly obtain this by two different ideas: first, we do not require the objective function to be in any normal form. The transformation into a normal form usually leads to the introduct...

This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand-bound IP solvers and efficient new integer...

Optimization of composite laminates requires the satisfaction constraints where design ply thicknesses and orientations can only take discrete values prescribed by manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient in cases because they provide suboptimal solutions when number variables is large. They also computationally expensive handling combinatorial natu...