Theory and Algorithms Commons^™

High Multiplicity Strip Packing Problem With Three Rectangle Types, Andy Yu

Electronic Thesis and Dissertation Repository

The two-dimensional strip packing problem (2D-SPP) involves packing a set R = {r₁, ..., r_n} of n rectangular items into a strip of width 1 and unbounded height, where each rectangular item r_i has width 0 < w_i ≤ 1 and height 0 < h_i ≤ 1. The objective is to find a packing for all these items, without overlaps or rotations, that minimizes the total height of the strip used. 2D-SPP is strongly NP-hard and has practical applications including stock cutting, scheduling, and reducing peak power demand in smart-grids.

This thesis considers …

Gem-Pso: Particle Swarm Optimization Guided By Enhanced Memory, Kevin Fakai Chen

Honors Projects

Particle Swarm Optimization (PSO) is a widely-used nature-inspired optimization technique in which a swarm of virtual particles work together with limited communication to find a global minimum or optimum. PSO has has been successfully applied to a wide variety of practical problems, such as optimization in engineering fields, hybridization with other nature-inspired algorithms, or even general optimization problems. However, PSO suffers from a phenomenon known as premature convergence, in which the algorithm's particles all converge on a local optimum instead of the global optimum, and cannot improve their solution any further. We seek to improve upon the standard Particle Swarm …

Two-On-One Pursuit With A Non-Zero Capture Radius, Patrick J. Wasz

Theses and Dissertations

In this paper, we revisit the "Two Cutters and Fugitive Ship" differential game that was addressed by Isaacs, but move away from point capture. We consider a two-on-one pursuit-evasion differential game with simple motion and pursuers endowed with circular capture sets of radius l > 0. The regions in the state space where only one pursuer effects the capture and the region in the state space where both pursuers cooperatively and isochronously capture the evader are characterized, thus solving the Game of Kind. Concerning the Game of Degree, the algorithm for the synthesis of the optimal state feedback strategies of the …