ContinuousMultimodal Global Optimization with Differential Evolution-Based Methods

Metaheuristic methods have become increasingly popular approaches in solving global optimization problems. From a practical viewpoint, it is often desirable to perform multimodal optimization which, enables the search of more than one optimal solution to the task at hand. Population-based metaheuristic methods offer a natural basis for multimodal optimization. The topic has received increasing interest especially in the evolutionary computation community. Several niching approaches have been suggested to allow multimodal optimization using evolutionary algorithms. Most global optimization approaches, including metaheuristics, contain global and local search phases. The requirement to locate several optima sets additional requirements for the design of algorithms to be effective in both respects in the context of multimodal optimization. In this thesis, several different multimodal optimization algorithms are studied in regard to how their implementation in the global and local search phases affect their performance in different problems. The study concentrates especially on variations of the Differential Evolution algorithm and their capabilities in multimodal optimization. To separate the global and local search search phases, three multimodal optimization algorithms are proposed, two of which hybridize the Differential Evolution with a local search method. As the theoretical background behind the operation of metaheuristics is not generally thoroughly understood, the research relies heavily on experimental studies in finding out the properties of different approaches. To achieve reliable experimental information, the experimental environment must be carefully chosen to contain appropriate and adequately varying problems. The available selection of multimodal test problems is, however, rather limited, and no general framework exists. As a part of this thesis, such a framework for generating tunable test functions for evaluating different methods of multimodal optimization experimentally is provided and used for testing the algorithms. The results demonstrate that an efficient local phase is essential for creating efficient multimodal optimization algorithms. Adding a suitable global phase has the potential to boost the performance significantly, but the weak local phase may invalidate the advantages gained from the global phase.

On the use of convex underestimators in global optimization

Många kvantitativa problem från vitt skilda områden kan beskrivas som optimeringsproblem. Ett mått på lösningens kvalitet bör optimeras samtidigt som vissa villkor på lösningen uppfylls. Kvalitetsmåttet kallas vanligen objektfunktion och kan beskriva kostnader (exempelvis produktion, logistik), potentialenergi (molekylmodellering, proteinveckning), risk (finans, försäkring) eller något annat relevant mått. I min doktorsavhandling diskuteras speciellt icke-linjär programmering, NLP, i ändliga dimensioner. Problem med enkel struktur, till exempel någon form av konvexitet, kan lösas effektivt. Tyvärr kan inte alla kvantitativa samband modelleras på ett konvext vis. Icke-konvexa problem kan angripas med heuristiska metoder, algoritmer som söker lösningar med hjälp av deterministiska eller stokastiska tumregler. Ibland fungerar det här väl, men heuristikerna kan sällan garantera kvaliteten på lösningen eller ens att en lösning påträffas. För vissa tillämpningar är det här oacceptabelt. Istället kan man tillämpa så kallad global optimering. Genom att successivt dela variabeldomänen i mindre delar och beräkna starkare gränser på det optimala värdet hittas en lösning inom feltoleransen. Den här metoden kallas branch-and-bound, ungefär dela-och-begränsa. För att ge undre gränser (vid minimering) approximeras problemet med enklare problem, till exempel konvexa, som kan lösas effektivt. I avhandlingen studeras tillvägagångssätt för att approximera differentierbara funktioner med konvexa underskattningar, speciellt den så kallade alphaBB-metoden. Denna metod adderar störningar av en viss form och garanterar konvexitet genom att sätta villkor på den perturberade Hessematrisen. Min forskning har lyft fram en naturlig utvidgning av de perturbationer som används i alphaBB. Nya metoder för att bestämma underskattningsparametrar har beskrivits och jämförts. I sammanfattningsdelen diskuteras global optimering ur bredare perspektiv på optimering och beräkningsalgoritmer.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

On the differential evolution algorithm and its appliation to training radial basis function networks

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin

Evoluutioalgoritmit ovat viime vuosina osoittautuneet tehokkaiksi menetelmiksi globaalien optimointitehtävien ratkaisuun. Niiden vahvuutena on etenkin yleiskäyttöisyys ja kyky löytää globaali ratkaisu juuttumatta optimoitavan tavoitefunktion paikallisiin optimikohtiin. Tässä työssä on tavoitteena kehittää uusi, normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin, joka on eräs uusimmista evoluutiopohjaisista optimointialgoritmeista. Menetelmän oletetaan vähentävän entisestään sekä populaation ennenaikaisen suppenemisen, että algoritmin tilojen juuttumisen riskiä ja se on teoreettisesti osoitettavissa suppenevaksi. Tämä ei päde alkuperäisen differentiaalievoluution tapauksessa, koska on voitu osoittaa, että sen tilanmuutokset voivat pienellä todennäköisyydellä juuttua. Työssä uuden menetelmän toimintaa tarkastellaan kokeellisesti käyttäen testiongelmina monirajoiteongelmia. Rajoitefunktioiden käsittelyyn käytetään Jouni Lampisen kehittämää, Pareto-optimaalisuuden periaatteeseen perustuvaa menetelmää. Samalla saadaan kerättyä lisää kokeellista näyttöä myös tämän menetelmän toiminnasta. Kaikki käytetyt testiongelmat kyettiin ratkaisemaan sekä alkuperäisellä differentiaalievoluutiolla, että uutta mutaatio-operaatiota käyttävällä versiolla. Uusi menetelmä osoittautui kuitenkin luotettavammaksi sellaisissa tapauksissa, joissa alkuperäisellä algoritmilla oli vaikeuksia. Lisäksi useimmat ongelmat kyettiin ratkaisemaan luotettavasti pienemmällä populaation koolla kuin alkuperäistä differentiaalievoluutiota käytettäessä. Uuden menetelmän käyttö myös mahdollistaa paremmin sellaisten kontrolliparametrien käytön, joilla hausta saadaan rotaatioinvariantti. Laskennallisesti uusi menetelmä on hieman alkuperäistä differentiaalievoluutiota raskaampi ja se tarvitsee yhden kontrolliparametrin enemmän. Uusille kontrolliparametreille määritettiin kuitenkin mahdollisimman yleiskäyttöiset arvot, joita käyttämällä on mahdollista ratkaista suuri joukko erilaisia ongelmia.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Differential evolution based classification with pool of distances and aggregation operators

The objective of this thesis is to develop and generalize further the differential evolution based data classification method. For many years, evolutionary algorithms have been successfully applied to many classification tasks. Evolution algorithms are population based, stochastic search algorithms that mimic natural selection and genetics. Differential evolution is an evolutionary algorithm that has gained popularity because of its simplicity and good observed performance. In this thesis a differential evolution classifier with pool of distances is proposed, demonstrated and initially evaluated. The differential evolution classifier is a nearest prototype vector based classifier that applies a global optimization algorithm, differential evolution, to determine the optimal values for all free parameters of the classifier model during the training phase of the classifier. The differential evolution classifier applies the individually optimized distance measure for each new data set to be classified is generalized to cover a pool of distances. Instead of optimizing a single distance measure for the given data set, the selection of the optimal distance measure from a predefined pool of alternative measures is attempted systematically and automatically. Furthermore, instead of only selecting the optimal distance measure from a set of alternatives, an attempt is made to optimize the values of the possible control parameters related with the selected distance measure. Specifically, a pool of alternative distance measures is first created and then the differential evolution algorithm is applied to select the optimal distance measure that yields the highest classification accuracy with the current data. After determining the optimal distance measures for the given data set together with their optimal parameters, all determined distance measures are aggregated to form a single total distance measure. The total distance measure is applied to the final classification decisions. The actual classification process is still based on the nearest prototype vector principle; a sample belongs to the class represented by the nearest prototype vector when measured with the optimized total distance measure. During the training process the differential evolution algorithm determines the optimal class vectors, selects optimal distance metrics, and determines the optimal values for the free parameters of each selected distance measure. The results obtained with the above method confirm that the choice of distance measure is one of the most crucial factors for obtaining higher classification accuracy. The results also demonstrate that it is possible to build a classifier that is able to select the optimal distance measure for the given data set automatically and systematically. After finding optimal distance measures together with optimal parameters from the particular distance measure results are then aggregated to form a total distance, which will be used to form the deviation between the class vectors and samples and thus classify the samples. This thesis also discusses two types of aggregation operators, namely, ordered weighted averaging (OWA) based multi-distances and generalized ordered weighted averaging (GOWA). These aggregation operators were applied in this work to the aggregation of the normalized distance values. The results demonstrate that a proper combination of aggregation operator and weight generation scheme play an important role in obtaining good classification accuracy. The main outcomes of the work are the six new generalized versions of previous method called differential evolution classifier. All these DE classifier demonstrated good results in the classification tasks.

In silico metabolic modelling of Saccharomyces cerevisiae for the overproduction of succinate using OptKnock and OptGene

Succinate is a naturally occurring metabolite in organism’s cell and is industrially important chemical with various applications in food and pharmaceutical industry. It is also widely used to produce bio-degradable plastics, surfactants, detergents etc. In last decades, emphasis has been given to bio-based chemical production using industrial biotechnology route rather than fossil-based production considering sustainability and environment friendly economy. In this thesis I am presenting a computational model for silico metabolic engineering of Saccharomyces cerevisiae for large scale production of succinate. For metabolic modelling, I have used OptKnock and OptGene optimization algorithms to identify the reactions to delete from the genome-scale metabolic model of S. cerevisiae to overproduce succinate by coupling with organism’s growth. Both OptKnock and OptGene proposed numerous straightforward and non-intuitive deletion strategies when number of constraints including growth constraint to the model were applied. The most interesting strategy identified by both algorithms was deletion combination of pyruvate decarboxylase and Ubiquinol:ferricytochrome c reductase(respiratory enzyme) reactions thereby also suggesting anaerobic fermentation of the organism in glucose medium. Such strategy was never reported earlier for growth-coupled succinate production in S.cerevisiae.

Generalized Differential Evolution for Global Multi-Objective Optimization with Constraints

The objective of this thesis work is to develop and study the Differential Evolution Algorithm for multi-objective optimization with constraints. Differential Evolution is an evolutionary algorithm that has gained in popularity because of its simplicity and good observed performance. Multi-objective evolutionary algorithms have become popular since they are able to produce a set of compromise solutions during the search process to approximate the Pareto-optimal front. The starting point for this thesis was an idea how Differential Evolution, with simple changes, could be extended for optimization with multiple constraints and objectives. This approach is implemented, experimentally studied, and further developed in the work. Development and study concentrates on the multi-objective optimization aspect. The main outcomes of the work are versions of a method called Generalized Differential Evolution. The versions aim to improve the performance of the method in multi-objective optimization. A diversity preservation technique that is effective and efficient compared to previous diversity preservation techniques is developed. The thesis also studies the influence of control parameters of Differential Evolution in multi-objective optimization. Proposals for initial control parameter value selection are given. Overall, the work contributes to the diversity preservation of solutions in multi-objective optimization.

Analyzing Carbon Trade Permits in Optimization Framework

The threats caused by global warming motivate different stake holders to deal with and control them. This Master's thesis focuses on analyzing carbon trade permits in optimization framework. The studied model determines optimal emission and uncertainty levels which minimize the total cost. Research questions are formulated and answered by using different optimization tools. The model is developed and calibrated by using available consistent data in the area of carbon emission technology and control. Data and some basic modeling assumptions were extracted from reports and existing literatures. The data collected from the countries in the Kyoto treaty are used to estimate the cost functions. Theory and methods of constrained optimization are briefly presented. A two-level optimization problem (individual and between the parties) is analyzed by using several optimization methods. The combined cost optimization between the parties leads into multivariate model and calls for advanced techniques. Lagrangian, Sequential Quadratic Programming and Differential Evolution (DE) algorithm are referred to. The role of inherent measurement uncertainty in the monitoring of emissions is discussed. We briefly investigate an approach where emission uncertainty would be described in stochastic framework. MATLAB software has been used to provide visualizations including the relationship between decision variables and objective function values. Interpretations in the context of carbon trading were briefly presented. Suggestions for future work are given in stochastic modeling, emission trading and coupled analysis of energy prices and carbon permits.

The Possibilities and Dosimetric Limitations of MLC-Based Intensity-Modulated Radiotherapy Delivery and Optimization Techniques

The use of intensity-modulated radiotherapy (IMRT) has increased extensively in the modern radiotherapy (RT) treatments over the past two decades. Radiation dose distributions can be delivered with higher conformality with IMRT when compared to the conventional 3D-conformal radiotherapy (3D-CRT). Higher conformality and target coverage increases the probability of tumour control and decreases the normal tissue complications. The primary goal of this work is to improve and evaluate the accuracy, efficiency and delivery techniques of RT treatments by using IMRT. This study evaluated the dosimetric limitations and possibilities of IMRT in small (treatments of head-and-neck, prostate and lung cancer) and large volumes (primitive neuroectodermal tumours). The dose coverage of target volumes and the sparing of critical organs were increased with IMRT when compared to 3D-CRT. The developed split field IMRT technique was found to be safe and accurate method in craniospinal irradiations. By using IMRT in simultaneous integrated boosting of biologically defined target volumes of localized prostate cancer high doses were achievable with only small increase in the treatment complexity. Biological plan optimization increased the probability of uncomplicated control on average by 28% when compared to standard IMRT delivery. Unfortunately IMRT carries also some drawbacks. In IMRT the beam modulation is realized by splitting a large radiation field to small apertures. The smaller the beam apertures are the larger the rebuild-up and rebuild-down effects are at the tissue interfaces. The limitations to use IMRT with small apertures in the treatments of small lung tumours were investigated with dosimetric film measurements. The results confirmed that the peripheral doses of the small lung tumours were decreased as the effective field size was decreased. The studied calculation algorithms were not able to model the dose deficiency of the tumours accurately. The use of small sliding window apertures of 2 mm and 4 mm decreased the tumour peripheral dose by 6% when compared to 3D-CRT treatment plan. A direct aperture based optimization (DABO) technique was examined as a solution to decrease the treatment complexity. The DABO IMRT technique was able to achieve treatment plans equivalent with the conventional IMRT fluence based optimization techniques in the concave head-and-neck target volumes. With DABO the effective field sizes were increased and the number of MUs was reduced with a factor of two. The optimality of a treatment plan and the therapeutic ratio can be further enhanced by using dose painting based on regional radiosensitivities imaged with functional imaging methods.

Simulation and optimization tools in paper machine concept design

The last decade has shown that the global paper industry needs new processes and products in order to reassert its position in the industry. As the paper markets in Western Europe and North America have stabilized, the competition has tightened. Along with the development of more cost-effective processes and products, new process design methods are also required to break the old molds and create new ideas. This thesis discusses the development of a process design methodology based on simulation and optimization methods. A bi-level optimization problem and a solution procedure for it are formulated and illustrated. Computational models and simulation are used to illustrate the phenomena inside a real process and mathematical optimization is exploited to find out the best process structures and control principles for the process. Dynamic process models are used inside the bi-level optimization problem, which is assumed to be dynamic and multiobjective due to the nature of papermaking processes. The numerical experiments show that the bi-level optimization approach is useful for different kinds of problems related to process design and optimization. Here, the design methodology is applied to a constrained process area of a papermaking line. However, the same methodology is applicable to all types of industrial processes, e.g., the design of biorefiners, because the methodology is totally generalized and can be easily modified.