Global ETD Search

1	Various Approaches to the Stochastic K-Server and Stacker-Crane Problems Friedman, Alexander Daniel 29 June 2017 (has links) In recent years there has been a trend towards large-scale logistics for individual members of the public, such as ride-sharing services and drone package delivery. Efficient coordination of pickups and deliveries is essential in order to keep costs and wait times down. In this thesis we present these types of problems in a more general framework, expanding applicability of our discussion to an even wider domain of problems. We present fast new al- gorithms with supporting theoretical and experimental analysis, providing certain guarantees about how close our algorithms compare to a theoretically optimal approach. / Master of Science K-Server Problem Stacker-Crane Problem K-Median Zoning Algorithm Probabilistic Hyperoctree Voronoi Simplicial Decomposition
2	Efficient heuristics for large-scale vehicle routing problems Graf, Benjamin 02 September 2021 (has links) In this thesis we consider three challenging vehicle routing problems representing specific aspects of complex real-world problems: (i) the vehicle routing problem with unit demands, (ii) the preemptive stacker crane problem and (iii) a multi-period vehicle and technician routing problem. For the vehicle routing problem with units demands we continue research on the exponential multi-insertion neighborhood, investigate its properties and propose heuristic solution methods utilizing the neighborhood. For the preemptive stacker crane problem we study structural properties and provide bounds on the benefits of preemption and the benefits of so-called explicit drop nodes that are used exclusively to facilitate preemption. We propose construction heuristics that improve on the state-of-the-art in computational time and solution quality. The multi-period vehicle and technician routing problem is the subject of the VeRoLog Solver Challenge 2019. We develop a solution method that adapts to the limited computational budget and the given instance parameters. In summary, this thesis contributes to the structural analysis of the considered problems and proposes efficient heuristic solution methods that are effective even on large-scale instances and under tight restrictions of the computational budget. The methods combine global and local search approaches and take the available computational budget into account to realize an adaptive best-effort allocation of the resources. vehicle routing preemptive stacker crane problem verolog solver challenge 2019 heuristics combinatorial optimization operations research ddc:004
3	Shift gray codes Williams, Aaron Michael 11 December 2009 (has links) Combinatorial objects can be represented by strings, such as 21534 for the permutation (1 2) (3 5 4), or 110100 for the binary tree corresponding to the balanced parentheses (()()). Given a string s = s1 s2 sn, the right-shift operation shift(s, i, j) replaces the substring si si+1..sj by si+1..sj si. In other words, si is right-shifted into position j by applying the permutation (j j−1 .. i) to the indices of s. Right-shifts include prefix-shifts (i = 1) and adjacent-transpositions (j = i+1). A fixed-content language is a set of strings that contain the same multiset of symbols. Given a fixed-content language, a shift Gray code is a list of its strings where consecutive strings differ by a shift. This thesis asks if shift Gray codes exist for a variety of combinatorial objects. This abstract question leads to a number of practical answers. The first prefix-shift Gray code for multiset permutations is discovered, and it provides the first algorithm for generating multiset permutations in O(1)-time while using O(1) additional variables. Applications of these results include more efficient exhaustive solutions to stacker-crane problems, which are natural NP-complete traveling salesman variants. This thesis also produces the fastest algorithm for generating balanced parentheses in an array, and the first minimal-change order for fixed-content necklaces and Lyndon words. These results are consequences of the following theorem: Every bubble language has a right-shift Gray code. Bubble languages are fixed-content languages that are closed under certain adjacent-transpositions. These languages generalize classic combinatorial objects: k-ary trees, ordered trees with fixed branching sequences, unit interval graphs, restricted Schr oder and Motzkin paths, linear-extensions of B-posets, and their unions, intersections, and quotients. Each Gray code is circular and is obtained from a new variation of lexicographic order known as cool-lex order. Gray codes using only shift(s, 1, n) and shift(s, 1, n−1) are also found for multiset permutations. A universal cycle that omits the last (redundant) symbol from each permutation is obtained by recording the first symbol of each permutation in this Gray code. As a special case, these shorthand universal cycles provide a new fixed-density analogue to de Bruijn cycles, and the first universal cycle for the "middle levels" (binary strings of length 2k + 1 with sum k or k + 1). shorthand universal cycles combinatorial generation minimal-change order loopless algorithm efficient algorithm combinations multiset permutations balanced parentheses Dyck words Catalan paths Schroder paths Motzkin words linear-extensions posets connected unit interval graphs inversions binary trees k-ary trees Lyndon words pre-necklaces theoretical computer science discrete mathematics combinatorics brute forcs de Bruijn cycles bubble languages cool-lex order lexicographic order combinatorial enumeration stacker-crane problem traveling salesman problem middle levels fixed-density de Bruijn cycle fixed-content

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