A Profile Likelihood Analysis of the Constrained MSSM with Genetic Algorithms

The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the model parameters in a way completely independent of priors, statistical measures and scanning techniques. We present a new technique for scanning supersymmetric parameter spaces, optimised for frequentist profile likelihood analyses and based on Genetic Algorithms. We apply this technique to the CMSSM, taking into account existing collider and cosmological data in our global fit. We compare our method to the MultiNest algorithm, an efficient Bayesian technique, paying particular attention to the best-fit points and implications for particle masses at the LHC and dark matter searches. Our global best-fit point lies in the focus point region. We find many high-likelihood points in both the stau co-annihilation and focus point regions, including a previously neglected section of the co-annihilation region at large m_0. We show that there are many high-likelihood points in the CMSSM parameter space commonly missed by existing scanning techniques, especially at high masses. This has a significant influence on the derived confidence regions for parameters and observables, and can dramatically change the entire statistical inference of such scans.Comment: 47 pages, 8 figures; Fig. 8, Table 7 and more discussions added to Sec. 3.4.2 in response to referee's comments; accepted for publication in JHE

Switching control systems and their design automation via genetic algorithms

The objective of this work is to provide a simple and effective nonlinear controller. Our strategy involves switching the underlying strategies in order to maintain a robust control. If a disturbance moves the system outside the region of stability or the domain of attraction, it will be guided back onto the desired course by the application of a different control strategy. In the context of switching control, the common types of controller present in the literature are based either on fuzzy logic or sliding mode. Both of them are easy to implement and provide efficient control for non-linear systems, their actions being based on the observed input/output behaviour of the system. In the field of fuzzy logic control (FLC) using error feedback variables there are two main problems. The first is the poor transient response (jerking) encountered by the conventional 2-dimensional rule-base fuzzy PI controller. Secondly, conventional 3-D rule-base fuzzy PID control design is both computationally intensive and suffers from prolonged design times caused by a large dimensional rule-base. The size of the rule base will increase exponentially with the increase of the number of fuzzy sets used for each input decision variable. Hence, a reduced rule-base is needed for the 3-term fuzzy controller. In this thesis a direct implementation method is developed that allows the size of the rule-base to be reduced exponentially without losing the features of the PID structure. This direct implementation method, when applied to the reduced rule-base fuzzy PI controller, gives a good transient response with no jerking

Joint optimization of geophysical data using multi-objective swarm intelligence

The joint inversion of multiple data sets encompasses the advantages of different geophysical methods but may yield to conflicting solutions. Global search methods have been recently developed to address the issue of local minima found by derivative-based methods, to analyse the data compatibility and to find the set of trade-off solutions, since they are not unique. In this paper, we examine two evolutionary algorithms to solve the joint inversion of electrical and electromagnetic data. These nature-inspired metaheuristics also adopt the principle of Pareto optimality in order to identify the result among the feasible solutions and then infer the data compatibility. Since the joint inversion is characterized by more than one objective, we implemented the algorithm multi-objective particle swarm optimization (MOPSO) to jointly interpret time-domain electromagnetic data and vertical electrical sounding. We first tested MOPSO on a synthetic model. The performance of MOPSO was directly compared with that of a multi-objective genetic algorithm, the non-dominated sorting genetic algorithm (NSGAIII), which has often been adopted in geophysics. The adoption of MOPSO and NSGA-III enabled avoiding both simplification into a single-objective problem and the use of a weighting factor between the objectives. We tested the two methods on real data sets collected in the northwest of Italy. The results obtained from MOPSO and NSGA-III were highly comparable to each other and largely consistent with literature findings. The MOPSO performed a rigorous selection of the best trade-off solutions and its convergence was faster than NSGA-III. The analysis of the Pareto Front reported data incompatibility, which is very common for real data due to different resolutions, sensitivities and depth of investigations. Notwithstanding this, the multi-objective optimizers provided a complementary interpretation of the data, ensuring significant advantages with respect to the separate optimizations we carried out using the single-objective particle swarm optimization algorithm

Schema theory for gene expression programming

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis studied a new variant of Evolutionary Algorithms called Gene Expression Programming. The evolution process of Gene Expression Programming was investigated from the practice to the theory. As a practice level, the original version of Gene Expression Programming was applied to a classification problem and an enhanced version of the algorithm was consequently developed. This allowed the development of a general understanding of each component of the genotype and phenotype separated representation system of the solution employed by the algorithm. Based on such an understanding, a version of the schema theory was developed for Gene Expression Programming. The genetic modifications provided by each genetic operator employed by this algorithm were analysed and a set of theorems predicting the propagation of the schema from one generation to another was developed. Also a set of experiments were performed to test the validity of the developed schema theory obtaining good agreement between the experimental results and the theoretical predictions

The synthesis of hybrid mechanisms using genetic algorithms.

This thesis presents a novel design methodology for the synthesis of hybrid mechanisms using Genetic Algorithms. GAs are a search and optimisation method which model the mechanics of population genetics to give a truly global search method. In parallel to the development of a suitable GA, the work also develops novel objective function criteria which go some way to providing an approximation to dynamic criteria whilst using only kinematic properties during calculations. This has considerable effect in reducing the time required to find a feasible solution. The thesis presents a set of results which validate the proposed methodology, both in terms of speed of convergence and quality of the final solutions obtained. The application chosen is the synthesis of a hybrid five bar path generating mechanism. A description is given of the development of a practical machine for a given test case, so as to illustrate that the solutions produced are feasible in terms of real world implementation. Results are presented which show the effectiveness of the machine. Finally, a critical analysis of both the methodology and the results is carried out. This highlights some areas in which the methodology could be improved by future work

Adaptive scaling of evolvable systems

Neo-Darwinian evolution is an established natural inspiration for computational optimisation with a diverse range of forms. A particular feature of models such as Genetic Algorithms (GA) [18, 12] is the incremental combination of partial solutions distributed within a population of solutions. This mechanism in principle allows certain problems to be solved which would not be amenable to a simple local search. Such problems require these partial solutions, generally known as building-blocks, to be handled without disruption. The traditional means for this is a combination of a suitable chromosome ordering with a sympathetic recombination operator. More advanced algorithms attempt to adapt to accommodate these dependencies during the search. The recent approach of Estimation of Distribution Algorithms (EDA) aims to directly infer a probabilistic model of a promising population distribution from a sample of fitter solutions [23]. This model is then sampled to generate a new solution set. A symbiotic view of evolution is behind the recent development of the Compositional Search Evolutionary Algorithms (CSEA) [49, 19, 8] which build up an incremental model of variable dependencies conditional on a series of tests. Building-blocks are retained as explicit genetic structures and conditionally joined to form higher-order structures. These have been shown to be effective on special classes of hierarchical problems but are unproven on less tightly-structured problems. We propose that there exists a simple yet powerful combination of the above approaches: the persistent, adapting dependency model of a compositional pool with the expressive and compact variable weighting of probabilistic models. We review and deconstruct some of the key methods above for the purpose of determining their individual drawbacks and their common principles. By this reasoned approach we aim to arrive at a unifying framework that can adaptively scale to span a range of problem structure classes. This is implemented in a novel algorithm called the Transitional Evolutionary Algorithm (TEA). This is empirically validated in an incremental manner, verifying the various facets of the TEA and comparing it with related algorithms for an increasingly structured series of benchmark problems. This prompts some refinements to result in a simple and general algorithm that is nevertheless competitive with state-of-the-art methods

Engineering Innovation (TRIZ based Computer Aided Innovation)

This thesis describes the approach and results of the research to create a TRIZ based computer aided innovation tools (AEGIS and Design for Wow). This research has mainly been based around two tools created under this research: called AEGIS (Accelerated Evolutionary Graphics Interface System), and Design for Wow. Both of these tools are discussed in this thesis in detail, along with the test data, design methodology, test cases, and research. Design for Wow (http://www.designforwow.com) is an attempt to summarize the successful inventions/ designs from all over the world on a web portal which has multiple capabilities. These designs/innovations are then linked to the TRIZ Principles in order to determine whether innovative aspects of these successful innovations are fully covered by the forty TRIZ principles. In Design for Wow, a framework is created which is implemented through a review tool. The Design for Wow website includes this tool which has been used by researcher and the users of the site and reviewers to analyse the uploaded data in terms of strength of TRIZ Principles linked to them. AEGIS (Accelerated Evolutionary Graphics Interface System) is a software tool developed under this research aimed to help the graphic designers to make innovative graphic designs. Again it uses the forty TRIZ Principles as a set of guiding rules in the software. AEGIS creates graphic design prototypes according to the user input and uses TRIZ Principles framework as a guide to generate innovative graphic design samples. The AEGIS tool created is based on TRIZ Principles discussed in Chapter 3 (a subset of them). In AEGIS, the TRIZ Principles are used to create innovative graphic design effects. The literature review on innovative graphic design (in chapter 3) has been analysed for links with TRIZ Principles and then the DNA of AEGIS has been built on the basis of this study. Results from various surveys/ questionnaires indicated were used to collect the innovative graphic design samples and then TRIZ was mapped to it (see section 3.2). The TRIZ effects were mapped to the basic graphic design elements and the anatomy of the graphic design letters was studied to analyse the TRIZ effects in the collected samples. This study was used to build the TRIZ based AEGIS tool. Hence, AEGIS tool applies the innovative effects using TRIZ to basic graphic design elements (as described in section 3.3). the working of AEGIS is designed based on Genetic Algorithms coded specifically to implement TRIZ Principles specialized for Graphic Design, chapter 4 discusses the process followed to apply TRIZ Principles to graphic design and coding them using Genetic Algorithms, hence resulting in AEGIS tool. Similarly, in Design for Wow, the content uploaded has been analysed for its link with TRIZ Principles (see section 3.1 for TRIZ Principles). The tool created in Design for Wow is based on the framework of analysing the TRIZ links in the uploaded content. The ‘Wow’ concept discussed in the section 5.1 and 5.2 is the basis of the concept of Design for Wow website, whereby the users upload the content they classify as ‘Wow’. This content then is further analysed for the ‘Wow factor’ and then mapped to TRIZ Principles as TRIZ tagging methodology is framed (section 5.5). From the results of the research, it appears that the TRIZ Principles are a comprehensive set of innovation basic building blocks. Some surveys suggest that amongst other tools, TRIZ Principles were the first choice and used most .They have thus the potential of being used in other innovation domains, to help in their analysis, understanding and potential development.Great Western Research and Systematic Innovation Ltd U