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Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks…
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…
Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control…
We propose an efficient motion planning method designed to efficiently find collision-free trajectories for multiple manipulators. While multi-manipulator systems offer significant advantages, coordinating their motions is computationally…
At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al.…
The problem of kinodynamic multi-goal motion planning is to find a trajectory over multiple target locations with an apriori unknown sequence of visits. The objective is to minimize the cost of the trajectory planned in a cluttered…
Autonomous exploration is a new technology in the field of robotics that has found widespread application due to its objective to help robots independently localize, scan maps, and navigate any terrain without human control. Up to present,…
This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…
Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
Planning long duration robotic manipulation sequences is challenging because of the complexity of exploring feasible trajectories through nonlinear contact dynamics and many contact modes. Moreover, this complexity grows with the problem's…
This paper presents GRT, a domain-independent heuristic planning system for STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase, it estimates the distance between each fact and the goals of the problem, in a…
A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective…
Verification planning is a sequential decision-making problem that specifies a set of verification activities (VA) and correction activities (CA) at different phases of system development. While VAs are used to identify errors and defects,…
Many robotics applications, from object manipulation to locomotion, require planning methods that are capable of handling the dynamics of contact. Trajectory optimization has been shown to be a viable approach that can be made to support…
In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by,…
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied.…
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…