Learning Solutions of Similar Linear Programming Problems using Boosting Trees

In many optimization problems, similar linear programming (LP) problems occur in the nodes of the branch and bound trees that are used to solve integer (mixed or pure, deterministic or stochastic) programming problems. Similar LP problems are also found in problem domains where the objective function and constraint coefficients vary due to uncertainties in the operating conditions. In this report, we present a regression technique for learning a set of functions that map the objective function and the constraints to the decision variables of such an LP system by modifying boosting trees, an algorithm we term the Boost-LP algorithm. Matrix transformations and geometric properties of boosting trees are utilized to provide theoretical performance guarantees on the predicted values. The standard form of the loss function is altered to reduce the possibility of generating infeasible LP solutions. Experimental results on three different problems, one each on scheduling, routing, and planning respectively, demonstrate the effectiveness of the Boost-LP algorithm in providing significant computational benefits over regular optimization solvers without generating solutions that deviate appreciably from the optimum values

Efficiently Solving Repeated Integer Linear Programming Problems by Learning Solutions of Similar Linear Programming Problems using Boosting Trees

It is challenging to obtain online solutions of large-scale integer linear programming (ILP) problems that occur frequently in slightly different forms during planning for autonomous systems. We refer to such ILP problems as repeated ILP problems. The branch-and-bound (BAB) algorithm is commonly used to solve ILP problems, and a significant amount of computation time is expended in solving numerous relaxed linear programming (LP) problems at the nodes of the BAB trees. We observe that the relaxed LP problems, both within a particular BAB tree and across multiple trees for repeated ILP problems, are similar to each other in the sense that they contain almost the same number of constraints, similar objective function and constraint coefficients, and an identical number of decision variables. We present a boosting tree-based regression technique for learning a set of functions that map the objective function and the constraints to the decision variables of such a system of similar LP problems; this enables us to efficiently infer approximately optimal solutions of the repeated ILP problems. We provide theoretical performance guarantees on the predicted values and demonstrate the effectiveness of the algorithm in four representative domains involving a library of benchmark ILP problems, aircraft carrier deck scheduling, vehicle routing, and vehicle control

Real-Time Path Planning for Automating Optical Tweezers based Particle Transport Operations

Optical tweezers (OT) have been developed to successfully trap, orient, and transport micro and nano scale components of many different sizes and shapes in a fluid medium. They can be viewed as robots made out of light. Components can be simply released from optical traps by switching off laser beams. By utilizing the principle of time sharing or holograms, multiple optical traps can perform several operations in parallel. These characteristics make optical tweezers a very promising technology for creating directed micro and nano scale assemblies. In the infra-red regime, they are useful in a large number of biological applications as well. This dissertation explores the problem of real-time path planning for autonomous OT based transport operations. Such operations pose interesting challenges as the environment is uncertain and dynamic due to the random Brownian motion of the particles and noise in the imaging based measurements. Silica microspheres having diameters between (1-20) µm are selected as model components. Offline simulations are performed to gather trapping probability data that serves as a measure of trap strength and reliability as a function of relative position of the particle under consideration with respect to the trap focus, and trap velocity. Simplified models are generated using Gaussian Radial Basis Functions to represent the data in a compact form. These metamodels can be queried at run-time to obtain estimated probability values accurately and efficiently. Simple trapping probability models are then utilized in a stochastic dynamic programming framework to compute optimum trap locations and velocities that minimizes the total, expected transport time by incorporating collision avoidance and recovery steps. A discrete version of an approximate partially observable Markov decision process algorithm, called the QMDP_NLTDV algorithm, is developed. Real-time performance is ensured by pruning the search space and enhancing convergence rates by introducing a non-linear value function. The algorithm is validated both using a simulator as well as a physical holographic tweezer set-up. Successful runs show that the automated planner is flexible, works well in reasonably crowded scenes, and is capable of transporting a specific particle to a given goal location by avoiding collisions either by circumventing or by trapping other freely diffusing particles. This technique for transporting individual particles is utilized within a decoupled and prioritized approach to move multiple particles simultaneously. An iterative version of a bipartite graph matching algorithm is also used to assign goal locations to target objects optimally. As in the case of single particle transport, simulation and some physical experiments are performed to validate the multi-particle planning approach

Computer Aided Design of Side Actions for Injection Molding of Complex Parts

Often complex molded parts include undercuts, patches on the part boundaries that are not accessible along the main mold opening directions. Undercuts are molded by incorporating side actions in the molds. Side actions are mold pieces that are removed from the part using translation directions different than the main mold opening direction. However, side actions contribute to mold cost by resulting in an additional manufacturing and assembly cost as well as by increasing the molding cycle time. Therefore, generating shapes of side actions requires solving a complex geometric optimization problem. Different objective functions may be needed depending upon different molding scenarios (e.g., prototyping versus large production runs). Manually designing side actions is a challenging task and requires considerable expertise. Automated design of side actions will significantly reduce mold design lead times. This thesis describes algorithms for generating shapes of side actions to minimize a customizable molding cost function. Given a set of undercut facets on a polyhedral part and the main parting direction, the approach works in the following manner. First, candidate retraction space is computed for every undercut facet. This space represents the candidate set of translation vectors that can be used by the side action to completely disengage from the undercut facet. As the next step, a discrete set of feasible, non-dominated retractions is generated. Then the undercut facets are grouped into undercut regions by performing state space search over such retractions. This search step is performed by minimizing the customizable molding cost function. After identifying the undercut regions that can share a side action, the shapes of individual side actions are computed. The approach presented in this work leads to practically an optimal solution if every connected undercut region on the part requires three or fewer side actions. Results of computational experiments that have been conducted to assess the performance of the algorithms described in the thesis have also been presented. Computational results indicate that the algorithms have acceptable computational performance, are robust enough to handle complex part geometries, and are easy to implement. It is anticipated that the results shown here will provide the foundations for developing fully automated software for designing side actions in injection molding

Towards Understanding Hierarchical Natural Language Commands for Robotic Navigation and Manipulation

We describe a new model for understanding hierarchical natural language commands for robot navigation and manipulation. The model has three components: a semantic structure that captures the hierarchical structure of language; a cost function that maps the command's semantic structure to the robot's sensorimotor capabilities; and an efficient search method for finding the lowest-cost plan. We present a proof-of-concept system that carries out navigation commands in a simulated setting

Geometric Algorithms for Automated Design of Side Actions in Injection Molding of Complex Parts

This document contains the draft version of the following paper: A.G. Banerjee and S.K. Gupta. Geometric algorithms for automated design of side actions in injection molding of complex parts. Computer Aided Design