Recursive subdivision algorithms for curve and surface design

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis, the author studies recursIve subdivision algorithms for curves and surfaces. Several subdivision algorithms are constructed and investigated. Some graphic examples are also presented. Inspired by the Chaikin's algorithm and the Catmull-Clark's algorithm, some non-uniform schemes, the non-uniform corner cutting scheme and the recursive subdivision algorithm for non-uniform B-spline curves, are constructed and analysed. The adapted parametrization is introduced to analyse these non-uniform algorithms. In order to solve the surface interpolation problem, the Dyn-Gregory-Levin's 4-point interpolatory scheme is generalized to surfaces and the 10-point interpolatory subdivision scheme for surfaces is formulated. The so-called Butterfly Scheme, which was firstly introduced by Dyn, Gregory Levin in 1988, is just a special case of the scheme. By studying the Cross-Differences of Directional Divided Differences, a matrix approach for analysing uniform subdivision algorithms for surfaces is established and the convergence of the 10-point scheme over both uniform and non-uniform triangular networks is studied. Another algorithm, the subdivision algorithm for uniform bi-quartic B-spline surfaces over arbitrary topology is introduced and investigated. This algorithm is a generalization of Doo-Sabin's and Catmull-Clark's algorithms. It produces uniform Bi-quartic B-spline patches over uniform data. By studying the local subdivision matrix, which is a circulant, the tangent plane and curvature properties of the limit surfaces at the so-called Extraordinary Points are studied in detail.The Chinese Educational Commission and The British Council (SBFSS/1987

A variable neighborhood search algorithm with reinforcement learning for a real-life periodic vehicle routing problem with time windows and open routes

Based on a real-life container transport problem, a model of Open Periodic Vehicle Routing Problem with Time Windows (OPVRPTW) is proposed in this paper. In a wide planning horizon, which is divided into a number of shifts, a fixed number of trucks are scheduled to complete container transportation tasks between terminals subject to time constraints. In this problem, the routes traveled by trucks are open, as returning to the starting depot is not required in every single shift but every two shifts.Our study shows that it is unrealistic to address this large scale and nonlinearly constrained problem with exact search methods. A Reinforcement Learning Based Variable Neighbourhood Search algorithm (VNSRLS) is developed for OPVRPTW. The initial solution is constructed with an urgency level-based insertion heuristic, while different insertion selection strategies are compared. In the local search phase of VNS-RLS, reinforcement learning is used to guide the search, adjusting the probabilities of operators being invoked adaptively according to the change of generated solutions’ feasibility and quality. In addition, the impact of sampling neighbourhood space in single solution-based algorithms is also investigated. Three indicators are designed in the proposed Sampling module to set the starting configuration of local search.Experiment results on different sizes of real and artificial benchmark instances show that, the proposed Sampling scheme and feasibility indicator decrease the infeasible rate during the search. However, Sampling’s contribution to solution quality improvement is not significant in this single solution-based algorithm. Comparing to the exact search and two state-of-the-art algorithms, VNS-RLS produces promising result

A dynamic truck dispatching problem in marine container terminal

In this paper, a dynamic truck dispatching problem of a marine container terminal is described and discussed. In this problem, a few containers, encoded as work instructions, need to be transferred between yard blocks and vessels by a fleet of trucks. Both the yard blocks and the quay are equipped with cranes to support loading/unloading operations. In order to service more vessels, any unnecessary idle time between quay crane (QC) operations need to be minimised to speed up the container transfer process. Due to the unpredictable port situations that can affect routing plans and the short calculation time allowed to generate one, static solution methods are not suitable for this problem. In this paper, we introduce a new mathematical model that minimises both the QC makespan and the truck travelling time. Three dynamic heuristics are proposed and a genetic algorithm hyperheuristic (GAHH) under development is also described. Experiment results show promising capabilities the GAHH may offer

Cooperative Double-Layer Genetic Programming Hyper-Heuristic for Online Container Terminal Truck Dispatching

In a marine container terminal, truck dispatching is a crucial problem that impacts on the operation efficiency of the whole port. Traditionally, this problem is formulated as an offline optimisation problem, whose solutions are, however, impractical for most real-world scenarios primarily because of the uncertainties of dynamic events in both yard operations and seaside loading–unloading operations. These solutions are either unattractive or infeasible to execute. Herein, for more intelligent handling of these uncertainties and dynamics, a novel cooperative double-layer genetic programming hyper-heuristic (CD-GPHH) is proposed to tackle this challenging online optimisation problem. In this new CD-GPHH, a novel scenario genetic programming (GP) approach is added on top of a traditional GP method that chooses among different GP heuristics for different scenarios to facilitate optimised truck dispatching. In contrast to traditional arithmetic GP (AGP) and GP with logic operators (LGP) which only evolve on one population, our CD-GPHH method separates the scenario and the calculation into two populations, which improved the quality of solutions in multi-scenario problems while reducing the search space. Experimental results show that our CD-GPHH dominates AGP and LGP in solving a multi-scenario function fitting problem as well as a truck dispatching problem in container terminal

A hybrid pricing and cutting approach for the multi-shift full truckload vehicle routing problem

Full truckload transportation (FTL) in the form of freight containers represents one of the most important transportation modes in international trade. Due to large volume and scale, in FTL, delivery time is often less critical but cost and service quality are crucial. Therefore, efficiently solving large scale multiple shift FTL problems is becoming more and more important and requires further research. In one of our earlier studies, a set covering model and a three-stage solution method were developed for a multi-shift FTL problem. This paper extends the previous work and presents a significantly more efficient approach by hybridising pricing and cutting strategies with metaheuristics (a variable neighbourhood search and a genetic algorithm). The metaheuristics were adopted to find promising columns (vehicle routes) guided by pricing and cuts are dynamically generated to eliminate infeasible flow assignments caused by incompatible commodities. Computational experiments on real-life and artificial benchmark FTL problems showed superior performance both in terms of computational time and solution quality, when compared with previous MIP based three-stage methods and two existing metaheuristics. The proposed cutting and heuristic pricing approach can efficiently solve large scale real-life FTL problems

A path-oriented encoding evolutionary algorithm for network coding resource minimization

Network coding is an emerging telecommunication technique, where any intermediate node is allowed to recombine incoming data if necessary. This technique helps to increase the throughput, however, very likely at the cost of huge amount of computational overhead, due to the packet recombination performed (ie coding operations). Hence, it is of practical importance to reduce coding operations while retaining the benefits that network coding brings to us. In this paper, we propose a novel evolutionary algorithm (EA) to minimize the amount of coding operations involved. Different from the state-of-the-art EAs which all use binary encodings for the problem, our EA is based on path-oriented encoding. In this new encoding scheme, each chromosome is represented by a union of paths originating from the source and terminating at one of the receivers. Employing path-oriented encoding leads to a search space where all solutions are feasible, which fundamentally facilitates more efficient search of EAs. Based on the new encoding, we develop three basic operators, that is, initialization, crossover and mutation. In addition, we design a local search operator to improve the solution quality and hence the performance of our EA. The simulation results demonstrate that our EA significantly outperforms the state-of-the-art algorithms in terms of global exploration and computational time

Search with evolutionary ruin and stochastic rebuild: a theoretic framework and a case study on exam timetabling

This paper presents a state transition based formal framework for a new search method, called Evolutionary Ruin and Stochastic Recreate, which tries to learn and adapt to the changing environments during the search process. It improves the performance of the original Ruin and Recreate principle by embedding an additional phase of Evolutionary Ruin to mimic the survival-of-the-fittest mechanism within single solutions. This method executes a cycle of Solution Decomposition, Evolutionary Ruin, Stochastic Recreate and Solution Acceptance until a certain stopping condition is met. The Solution Decomposition phase first uses some problem-specific knowledge to decompose a complete solution into its components and assigns a score to each component. The Evolutionary Ruin phase then employs two evolutionary operators (namely Selection and Mutation) to destroy a certain fraction of the solution, and the next Stochastic Recreate phase repairs the “broken” solution. Last, the Solution Acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution. Hence, optimisation is achieved by an iterative process of component evaluation, solution disruption and stochastic constructive repair. From the state transitions point of view, this paper presents a probabilistic model and implements a Markov chain analysis on some theoretical properties of the approach. Unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments, our model is based on state transitions within the space of partial assignments. The exam timetabling problems are used to test the performance in solving real-world hard problems

Hybridising heuristics within an estimation distribution algorithm for examination timetabling

This paper presents a hybrid hyper-heuristic approach based on estimation distribution algorithms. The main motivation is to raise the level of generality for search methodologies. The objective of the hyper-heuristic is to produce solutions of acceptable quality for a number of optimisation problems. In this work, we demonstrate the generality through experimental results for different variants of exam timetabling problems. The hyper-heuristic represents an automated constructive method that searches for heuristic choices from a given set of low-level heuristics based only on non-domain-specific knowledge. The high-level search methodology is based on a simple estimation distribution algorithm. It is capable of guiding the search to select appropriate heuristics in different problem solving situations. The probability distribution of low-level heuristics at different stages of solution construction can be used to measure their effectiveness and possibly help to facilitate more intelligent hyper-heuristic search methods

Systematic Identification of Synergistic Drug Pairs Targeting HIV

The systematic identification of effective drug combinations has been hindered by the unavailability of methods that can explore the large combinatorial search space of drug interactions. Here we present a multiplex screening method named MuSIC (Multiplex Screening for Interacting Compounds), which expedites the comprehensive assessment of pair-wise compound interactions. We examined ~500,000 drug pairs from 1000 FDA-approved or clinically tested drugs and identified drugs that synergize to inhibit HIV replication. Our analysis reveals an enrichment of anti-inflammatory drugs in drug combinations that synergize against HIV, indicating HIV benefits from inflammation that accompanies its infection. Multiple drug pairs identified in this study, including glucocorticoid and nitazoxanide, synergize by targeting different steps of the HIV life cycle. As inflammation accompanies HIV infection, our findings indicate that inhibiting inflammation could curb HIV propagation. MuSIC can be applied to a wide variety of disease-relevant screens to facilitate efficient identification of compound combinations

Search with evolutionary ruin and stochastic rebuild: a theoretic framework and a case study on exam timetabling

This paper presents a state transition based formal framework for a new search method, called Evolutionary Ruin and Stochastic Recreate, which tries to learn and adapt to the changing environments during the search process. It improves the performance of the original Ruin and Recreate principle by embedding an additional phase of Evolutionary Ruin to mimic the survival-of-the-fittest mechanism within single solutions. This method executes a cycle of Solution Decomposition, Evolutionary Ruin, Stochastic Recreate and Solution Acceptance until a certain stopping condition is met. The Solution Decomposition phase first uses some problem-specific knowledge to decompose a complete solution into its components and assigns a score to each component. The Evolutionary Ruin phase then employs two evolutionary operators (namely Selection and Mutation) to destroy a certain fraction of the solution, and the next Stochastic Recreate phase repairs the “broken” solution. Last, the Solution Acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution. Hence, optimisation is achieved by an iterative process of component evaluation, solution disruption and stochastic constructive repair. From the state transitions point of view, this paper presents a probabilistic model and implements a Markov chain analysis on some theoretical properties of the approach. Unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments, our model is based on state transitions within the space of partial assignments. The exam timetabling problems are used to test the performance in solving real-world hard problems