This research aims to improve the performance of the service of a Chemotherapy Treatment Unit by reducing the waiting time of patients within the unit. In order to fulfill the objective, initially, the chemotherapy treatment unit is deduced as an identical parallel machines scheduling problem with unequal release time and single resource. A mathematical model is developed to generate the optimum schedule. Afterwards, a Tabu search (TS) algorithm is developed. The performance of the TS algorithm is evaluated by comparing results with the mathematical model and the best results of benchmark problems reported in the literature. Later on, an additional resource is considered which converted the problem into a dual resources scheduling problem. Three approaches are proposed to solve this problem; namely, heuristics, a Tabu search algorithm with heuristic (TSHu), and Tabu search algorithm for dual resources (TSD).

This research aims to improve the performance of the service of a Chemotherapy Treatment Unit by reducing the waiting time of patients within the unit. In order to fulfill the objective, initially, the chemotherapy treatment unit is deduced as an identical parallel machines scheduling problem with unequal release time and single resource. A mathematical model is developed to generate the optimum schedule. Afterwards, a Tabu search (TS) algorithm is developed. The performance of the TS algorithm is evaluated by comparing results with the mathematical model and the best results of benchmark problems reported in the literature. Later on, an additional resource is considered which converted the problem into a dual resources scheduling problem. Three approaches are proposed to solve this problem; namely, heuristics, a Tabu search algorithm with heuristic (TSHu), and Tabu search algorithm for dual resources (TSD).

Given a graph G=(V,E), a vertex ordering of G is a total order v1,v2,...,vn of V. A graph search algorithm is a systematic method for visiting each vertex in a graph, naturally producing a vertex ordering of the graph. We explore the problem of determining whether a given vertex in a graph can be the end (last) vertex of a search ordering for various common graph search algorithms when restricted to various graph classes, as well as the related problem of determining if a vertex is an end-vertex when a start vertex is specified for the search. The former is referred to as the end-vertex problem, and the latter is the beginning-end-vertex problem. For the beginning-end-vertex problem, we show it is NP-complete on bipartite graphs as well as degree restricted bipartite graphs for Lexicographic Breadth First Search, but solvable in polynomial time on split graphs for Breadth First Search. We show that the end-vertex problem is tractable for Lexicographic Breadth First Search on proper interval bigraphs and for Lexicographic Depth First Search on chordal graphs. Further, we show that the problem is NP-complete for Lexicographic Breadth First Search and Depth First Search on bipartite graphs. / Graduate

Feature selection is an effective technique in reducing the dimensionality of features in many applications where datasets involve hundreds or thousands of features. The objective of feature selection is to find an optimal subset of relevant features such that the feature size is reduced and understandability of a learning process is improved without significantly decreasing the overall accuracy and applicability. This thesis focuses on the consistency measure where a feature subset is consistent if there exists a set of instances of length more than two with the same feature values and the same class labels. This thesis introduces a new consistency-based algorithm, Automatic Hybrid Search (AHS) and reviews several existing feature selection algorithms (ES, PS and HS) which are based on the consistency rate. After that, we conclude this work by conducting an empirical study to a comparative analysis of different search algorithms.

Quantum computation has attracted a great deal of attention from the scientific community in recent years. By using the quantum mechanical phenomena of superposition and entanglement, a quantum computer can solve certain problems much faster than classical computers. Several quantum algorithms have been developed to demonstrate this quantum speedup. Two important examples are Shor’s algorithm for the factorization problem, and Grover’s algorithm for the search problem. Significant efforts are on to build a large scale quantum computer for implementing these quantum algorithms. This thesis deals with Grover’s search algorithm, and presents its several generalizations that perform better in specific contexts. While writing the thesis, we have assumed the familiarity of readers with the basics of quantum mechanics and computer science. For a general introduction to the subject of quantum computation, see [1]. In Chapter 1, we formally define the search problem as well as present Grover’s search algorithm [2]. This algorithm, or more generally the quantum amplitude amplification algorithm [3, 4], drives a quantum system from a prepared initial state (s) to a desired target state (t). It uses O(α-1 = | (t−|s)| -1) iterations of the operator g = IsIt on |s), where { IsIt} are selective phase inversions selective phase inversions of the corresponding states. That is a quadratic speedup over the simple scheme of O(α−2) preparations of |s) and subsequent projective measurements. Several generalizations of Grover’s algorithm exist. In Chapter 2, we study further generalizations of Grover’s algorithm. We analyse the iteration of the search operator S = DsI t on |s) where Ds is a more general transformation than Is, and I t is a selective phase rotation of |t) by angle . We find sufficient conditions for S to produce a successful quantum search algorithm. In Chapter 3, we demonstrate that our general framework encapsulates several previous generalizations of Grover’s algorithm. For example, the phase-matching condition for the search operator requires the angles and and to be almost equal for a successful quantum search. In Kato’s algorithm, the search operator is where Ks consists of only single-qubit gates, which are easier to implement physically than multi-qubit gates. The spatial search algorithms consider the search operator where is a spatially local operator and provides implementation advantages over Is. The analysis of Chapter 2 provides a simpler understanding of all these special cases. In Chapter 4, we present schemes to improve our general quantum search algorithm, by controlling the operators through an ancilla qubit. For the case of two dimensional spatial search problem, these schemes yield an algorithm with time complexity . Earlier algorithms solved this problem in time steps, and it was an open question to design a faster algorithm. The schemes can also be used to find, for a given unitary operator, an eigenstate corresponding to a specified eigenvalue. In Chapter 5, we extend the analysis of Chapter 2 to general adiabatic quantum search. It starts with the ground state |s) of an initial Hamiltonian Hs and evolves adiabatically to the target state |t) that is the ground state of the final Hamiltonian The evolution uses a time dependent Hamiltonian HT that varies linearly with time . We show that the minimum excitation gap of HT is proportional to α. Also, the ground state of HT changes significantly only within a very narrow interval of width around the transition point, where the excitation gap has its minimum. This feature can be used to reach the target state (t) using adiabatic evolution for time In Chapter 6, we present a robust quantum search algorithm that iterates the operator on |s) to successfully reach |t), whereas Grover’s algorithm fails if as per the phase-matching condition. The robust algorithm also works when is generalized to multiple target states. Moreover, the algorithm provides a new search Hamiltonian that is robust against certain systematic perturbations. In Chapter 7, we look beyond the widely studied scenario of iterative quantum search algorithms, and present a recursive quantum search algorithm that succeeds with transformations {Vs,Vt} sufficiently close to {Is,It.} Grover’s algorithm generally fails if while the recursive algorithm is nearly optimal as long as , improving the error tolerance of the transformations. The algorithms of Chapters 6-7 have applications in quantum error-correction, when systematic errors affect the transformations The algorithms are robust as long as the errors are small, reproducible and reversible. This type of errors arise often from imperfections in apparatus setup, and so the algorithms increase the flexibility in physical implementation of quantum search. In Chapter 8, we present a fixed-point quantum search algorithm. Its state evolution monotonically converges towards |t), unlike Grover’s algorithm where the evolution passes through |t) under iterations of the operator . In q steps, our algorithm monotonically reduces the failure probability, i.e. the probability of not getting |t), from . That is asymptotically optimal for monotonic convergence. Though the fixed-point algorithm is of not much use for , it is useful when and each oracle query is highly expensive. In Chapter 9, we conclude the thesis and present an overall outlook.

There is a continuing demand for higher performance, particularly in the area of scientific and engineering computation. In order to achieve high performance in the context of frequent hardware upgrading, software must be adaptable for portable performance. What is required is an optimising compiler that evolves and adapts itself to environmental change without sacrificing performance. Java has emerged as a dominant programming language widely used in a variety of application areas. However, its architectural independant design means that it is frequently unable to deliver high performance especially when compared to other imperative languages such as Fortran and C/C++. This thesis presents a language- and architecture-independant approach to achieve portable high performance. It uses the mapping notation introduced in the Unified Transformation Framework to specify a large optimisation space. A heuristic random search algorithm is introduced to explore this space in a feedback-directed iterative optimisation manner. It is then extended using a machine learning approach which enables the compiler to learn from its previous optimisations and apply the knowledge when necessary. Both the heuristic random search algorithm and the learning optimisation approach are implemented in a prototype Adaptive Optimisation Framework for Java (AOF-Java). The experimental results show that the heuristic random search algorithm can find, within a relatively small number of atttempts, good points in the large optimisation space. In addition, the learning optimisation approach is capable of finding good transformations for a given program from its prior experience with other programs.

The Weapon Target Assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimum. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There do not exist any exact methods for the WTA problem which can solve even small size problems (for example, with 20 weapons and 20 targets). Though several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem. We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms which indicate that we can solve moderately large size instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few seconds

This work is aimed towards the development of an artificially intelligent search algorithm used in conjunction with an Auto Associative Neural Network (AANN) to help locate and reconstruct faulty sensor inputs in control systems. The AANN can be trained to detect when sensors go faulty but the problem of locating the faulty sensor still remains. The search algorithm aids the AANN to help locate the faulty sensors and reconstruct their actual values. The algorithm uses domain specific heuristics based on the inherent behavior of the AANN to achieve its task. Common sensor errors such as drift, shift and random errors and the algorithms response to them have been studied. The issue of noise has also been investigated. These areas cover the first part of this work. The second part focuses on the development of a web interface that implements and displays the working of the algorithm. The interface allows any client on the World Wide Web to connect to the engineering software called MATLAB. The client can then simulate a drift, shift or random error using the graphical user interface and observe the response of the algorithm.

This work is aimed towards the development of an artificially intelligent search algorithm used in conjunction with an Auto Associative Neural Network (AANN) to help locate and reconstruct faulty sensor inputs in control systems. The AANN can be trained to detect when sensors go faulty but the problem of locating the faulty sensor still remains. The search algorithm aids the AANN to help locate the faulty sensors and reconstruct their actual values. The algorithm uses domain specific heuristics based on the inherent behavior of the AANN to achieve its task. Common sensor errors such as drift, shift and random errors and the algorithms response to them have been studied. The issue of noise has also been investigated. These areas cover the first part of this work. The second part focuses on the development of a web interface that implements and displays the working of the algorithm. The interface allows any client on the World Wide Web to connect to the engineering software called MATLAB. The client can then simulate a drift, shift or random error using the graphical user interface and observe the response of the algorithm.

Solution of any search problem lies in its search space. A search is a systematic examination of candidate solutions of a search problem. In this thesis, we present a search heuristic that we can cr-smodels. cr-smodels prunes the search space to quickly reach to the solution of a problem. The idea is to pick an atom for branching , that lowers the growth rate of the linear recurrence and thuse, minimizes the remaining search space. Our goal in developing cr-smodels is to develop a search heuristic that is efficient on a wide range of problems. Then, we test cr-smodels over a wide range of randomly generated benchmarks. we observed that often randomly generated graphs with no Hamiltonian cycle were trivial to solve. Since, Hamiltonian cycle is an important benchmark problem, my other goal is to develop techniques that generate hard instances of graphs with no Hamiltonian cycle.