Mixed Integer Neural Inverse Design

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired target performance? Here, we show that the piecewise linear property, very common in everyday neural networks, allows for an inverse design formulation based on mixed-integer linear programming. Our mixed-integer inverse design uncovers globally optimal or near optimal solutions in a principled manner. Furthermore, our method significantly facilitates emerging, but challenging, combinatorial inverse design tasks, such as material selection. For problems where finding the optimal solution is not desirable or tractable, we develop an efficient yet near-optimal hybrid optimization. Eventually, our method is able to find solutions provably robust to possible fabrication perturbations among multiple designs with similar performances

Mixed Integer Neural Inverse Design

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired target performance? Here, we show that the piecewise linear property, very common in everyday neural networks, allows for an inverse design formulation based on mixed-integer linear programming. Our mixed-integer inverse design uncovers globally optimal or near optimal solutions in a principled manner. Furthermore, our method significantly facilitates emerging, but challenging, combinatorial inverse design tasks, such as material selection. For problems where finding the optimal solution is not desirable or tractable, we develop an efficient yet near-optimal hybrid optimization. Eventually, our method is able to find solutions provably robust to possible fabrication perturbations among multiple designs with similar performances

Inferring Update Sequences in Boolean Gene Regulatory Networks

International audienceThis paper employs mathematical programming and mixed integer linear programming techniques for solving a problem arising in the study of geneticregulatory networks. More precisely, we solve the inverse problem consisting in the determination of the sequence of updates in the digraph representingthe gene regulatory network (GRN) of Arabidopsis thaliana in such a way that the generated gene activity is as close as possible to the observed data

Automated Vehicle Highway Merging: Motion Planning via Adaptive Interactive Mixed-Integer MPC

A new motion planning framework for automated highway merging is presented in this paper. To plan the merge and predict the motion of the neighboring vehicle, the ego automated vehicle solves a joint optimization of both vehicle costs over a receding horizon. The non-convex nature of feasible regions and lane discipline is handled by introducing integer decision variables resulting in a mixed integer quadratic programming (MIQP) formulation of the model predictive control (MPC) problem. Furthermore, the ego uses an inverse optimal control approach to impute the weights of neighboring vehicle cost by observing the neighbor's recent motion and adapts its solution accordingly. We call this adaptive interactive mixed integer MPC (aiMPC). Simulation results show the effectiveness of the proposed framework.Comment: Submitted to American Control Conferenc

Using slacks-based model to solve inverse DEA with integer intervals for input estimation

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of DMUo increases from Y-o to /beta(o), such the new DMU is given by (alpha(o)& lowast;, /3) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables

Mechanism Design via Dantzig-Wolfe Decomposition

In random allocation rules, typically first an optimal fractional point is calculated via solving a linear program. The calculated point represents a fractional assignment of objects or more generally packages of objects to agents. In order to implement an expected assignment, the mechanism designer must decompose the fractional point into integer solutions, each satisfying underlying constraints. The resulting convex combination can then be viewed as a probability distribution over feasible assignments out of which a random assignment can be sampled. This approach has been successfully employed in combinatorial optimization as well as mechanism design with or without money. In this paper, we show that both finding the optimal fractional point as well as its decomposition into integer solutions can be done at once. We propose an appropriate linear program which provides the desired solution. We show that the linear program can be solved via Dantzig-Wolfe decomposition. Dantzig-Wolfe decomposition is a direct implementation of the revised simplex method which is well known to be highly efficient in practice. We also show how to use the Benders decomposition as an alternative method to solve the problem. The proposed method can also find a decomposition into integer solutions when the fractional point is readily present perhaps as an outcome of other algorithms rather than linear programming. The resulting convex decomposition in this case is tight in terms of the number of integer points according to the Carath{\'e}odory's theorem