Hybridization of SBX based NSGA-II and sequential quadratic programming for solving multi-objective optimization problems

Most real-world search and optimization problems involve multiple conflicting objectives and results in a Pareto-optimal set. Various multi-objective optimization algorithms have been proposed for solving such problems with the goals of finding as many trade-off solutions as possible and maintaining diversity among them. Since last decade, evolutionary multi-objective optimization (EMO) algorithms have been applied successfully to various test and real-world optimization problems. These population based algorithms provide a diverse set of non-dominated solutions. The obtained non-dominated set is close to the true Pareto-optimal front but it's convergence to the true Pareto-optimal front is not guaranteed. Hence to ensure the same, a local search method using classical algorithm can be applied. In the present work, SBX based NSGA-II is used as a population based approach and the sequential quadratic programming (SQP) method is used as a local search procedure. This hybridization of evolutionary and classical algorithms approach provides a confidence of converging near to the true Pareto-optimal set with a good diversity. The proposed procedure is successfully applied to 13 test problems consisting two, three and five objectives. The obtained results validate our motivation of hybridizing evolutionary and classical methods

A hybrid multi-objective optimization procedure using PCX based NSGA-II and sequential quadratic programming

Despite the existence of a number of procedures for multi-objective optimization using evolutionary algorithms, there is still the need for a systematic and unbiased comparison of different approaches on a carefully chosen set of test problems. In this paper, a hybrid approach using PCX based NSGA- II and sequential quadratic programming (SQP) is applied on 19 benchmark test problems consisting of two, three and five objectives. PCX-NSGA-II is used as a population based algorithm where SQP is used as a local search procedure. A population based approach helps in finding the non-dominated set of solutions with a good spread, whereas SQP improves the obtained set of non-dominated solutions locally. The results obtained by the present approach shows mixed performance on the chosen test problems

Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems

Evolutionary multi-objective optimization algorithms are commonly used to obtain a set of non-dominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficient and convergent procedure. In this paper, we test an augmented local search based EMO procedure rigorously on a test suite of constrained and unconstrained multi-objective optimization problems. The success of our approach on most of the test problems not only provides confidence but also stresses the importance of hybrid evolutionary algorithms in solving multi-objective optimization problems

MULTI-OBJECTIVE POWER SYSTEM SCHEDULING USING EVOLUTIONARY ALGORITHMS

Ph.DDOCTOR OF PHILOSOPH

A new memetic strategy for the numerical treatment of multi-objective optimization problems

In this paper we propose a novel iterative search procedure for multi-objective optimization problems. The iteration process – though derivative free – utilizes the geometry of the directional cones of such optimization problems, and is capable both of moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. Next, we give one possible way of integrating this local search procedure into a given EMO algorithm result-ing in a novel memetic strategy. Finally, we present some numerical results on some well-known benchmark problems indicating the strength of both the local search strategy as well as the new hybrid approach

Many-Objective Hybrid Optimization Under Uncertainty With Applications

A novel method for solving many-objective optimization problems under uncertainty was developed. It is well known that no single optimization algorithm performs best for all problems. Therefore, the developed method, a many-objective hybrid optimizer (MOHO), uses five constitutive algorithms and actively switches between them throughout the optimization process allowing for robust optimization. MOHO monitors the progress made by each of the five algorithms and allows the best performing algorithm more attempts at finding the optimum. This removes the need for user input for selecting algorithm as the best performing algorithm is automatically selected thereby increasing the probability of converging to the optimum. An uncertainty quantification framework, based on sparse polynomial chaos expansion, to propagate the uncertainties in the input parameter to the objective functions was also developed and validated. Where the samples and analysis runs needed for standard polynomial chaos expansion increases exponentially with the dimensionality, the presented sparse polynomial chaos approach efficiently propagates the uncertainty with only a few samples, thereby greatly reducing the computational cost. The performance of MOHO was investigated on a total of 65 analytical test problems from the DTLZ and WFG test suite, for which the analytical solution is known. MOHO is also applied to two additional real-life cases of aerodynamic shape design of subsonic and hypersonic bodies. Aerodynamic shape optimization is often computationally expensive and is, therefore, a good test case to investigate MOHO`s ability to reduce the computational time through robust optimization and accelerated convergence. The subsonic design optimization had three objectives: maximize lift and minimize drag and moment. The hypersonic design optimization had two objectives: maximize volume and minimize drag. Two accelerated solvers based on fast multipole method and Newton impact theory are developed for simulating subsonic and hypersonic flows. The results show that MOHO performed, on average, better than all five remaining algorithms in 52% of the DTLZ+WFG problems. The results of robust optimization of a subsonic body and hypersonic bodies were in good agreement with theory. The MOHO developed is capable of solving many-objective, multi-objective and single objective, constrained and unconstrained optimization problems with and without uncertainty with little user input

Development and Integration of Geometric and Optimization Algorithms for Packing and Layout Design

The research work presented in this dissertation focuses on the development and application of optimization and geometric algorithms to packing and layout optimization problems. As part of this research work, a compact packing algorithm, a physically-based shape morphing algorithm, and a general purpose constrained multi-objective optimization algorithm are proposed. The compact packing algorithm is designed to pack three-dimensional free-form objects with full rotational freedom inside an arbitrary enclosure such that the packing efficiency is maximized. The proposed compact packing algorithm can handle objects with holes or cavities and its performance does not degrade significantly with the increase in the complexity of the enclosure or the objects. It outputs the location and orientation of all the objects, the packing sequence, and the packed configuration at the end of the packing operation. An improved layout algorithm that works with arbitrary enclosure geometry is also proposed. Different layout algorithms for the SAE and ISO luggage are proposed that exploit the unique characteristics of the problem under consideration. Several heuristics to improve the performance of the packing algorithm are also proposed. The proposed compact packing algorithm is benchmarked on a wide variety of synthetic and hypothetical problems and is shown to outperform other similar approaches. The physically-based shape morphing algorithm proposed in this dissertation is specifically designed for packing and layout applications, and thus it augments the compact packing algorithm. The proposed shape morphing algorithm is based on a modified mass-spring system which is used to model the morphable object. The shape morphing algorithm mimics a quasi-physical process similar to the inflation/deflation of a balloon filled with air. The morphing algorithm starts with an initial manifold geometry and morphs it to obtain a desired volume such that the obtained geometry does not interfere with the objects surrounding it. Several modifications to the original mass-spring system and to the underlying physics that governs it are proposed to significantly speed-up the shape morphing process. Since the geometry of a morphable object continuously changes during the morphing process, most collision detection algorithms that assume the colliding objects to be rigid cannot be used efficiently. And therefore, a general-purpose surface collision detection algorithm is also proposed that works with deformable objects and does not require any preprocessing. Many industrial design problems such as packing and layout optimization are computationally expensive, and a faster optimization algorithm can reduce the number of iterations (function evaluations) required to find the satisfycing solutions. A new multi-objective optimization algorithm namely Archive-based Micro Genetic Algorithm (AMGA2) is presented in this dissertation. Improved formulation for various operators used by the AMGA2 such as diversity preservation techniques, genetic variation operators, and the selection mechanism are also proposed. The AMGA2 also borrows several concepts from mathematical sciences to improve its performance and benefits from the existing literature in evolutionary optimization. A comprehensive benchmarking and comparison of AMGA2 with other state-of-the-art optimization algorithms on a wide variety of mathematical problems gleaned from literature demonstrates the superior performance of AMGA2. Thus, the research work presented in this dissertation makes contributions to the development and application of optimization and geometric algorithms

Design methodologies and architectures of hardware-based evolutionary algorithms for aerospace optimisation applications on FPGAS

This thesis is a study of new design methods for allowing evolutionary algorithms to be more effectively utilised in aerospace optimisation applications where computation needs are high and computation platform space may be restrictive. It examines the applicability of special hardware computational platforms known as field programmable gate arrays and shows that with the right implementation methods they can offer significant benefits. This research is a step forward towards the advancement of efficient and highly automated aircraft systems for meeting compact physical constraints in aerospace platforms and providing effective performance speedups over traditional methods

Evolutionary multiobjective optimization : review, algorithms, and applications

Programa Doutoral em Engenharia Industrial e SistemasMany mathematical problems arising from diverse elds of human activity can be formulated as optimization problems. The majority of real-world optimization problems involve several and con icting objectives. Such problems are called multiobjective optimization problems (MOPs). The presence of multiple con icting objectives that have to be simultaneously optimized gives rise to a set of trade-o solutions, known as the Pareto optimal set. Since this set of solutions is crucial for e ective decision-making, which generally aims to improve the human condition, the availability of e cient optimization methods becomes indispensable. Recently, evolutionary algorithms (EAs) have become popular and successful in approximating the Pareto set. The population-based nature is the main feature that makes them especially attractive for dealing with MOPs. Due to the presence of two search spaces, operators able to e ciently perform the search in both the decision and objective spaces are required. Despite the wide variety of existing methods, a lot of open research issues in the design of multiobjective evolutionary algorithms (MOEAs) remains. This thesis investigates the use of evolutionary algorithms for solving multiobjective optimization problems. Innovative algorithms are developed studying new techniques for performing the search either in the decision or the objective space. Concerning the search in the decision space, the focus is on the combinations of traditional and evolutionary optimization methods. An issue related to the search in the objective space is studied in the context of many-objective optimization. Application of evolutionary algorithms is addressed solving two di erent real-world problems, which are modeled using multiobjective approaches. The problems arise from the mathematical modelling of the dengue disease transmission and a wastewater treatment plant design. The obtained results clearly show that multiobjective modelling is an e ective approach. The success in solving these challenging optimization problems highlights the practical relevance and robustness of the developed algorithms.Muitos problemas matemáticos que surgem nas diversas áreas da atividade humana podem ser formulados como problemas de otimização. A maioria dos problemas do mundo real envolve vários objetivos conflituosos. Tais problemas chamam-se problemas de otimização multiobjetivo. A presença de vários objetivos conflituosos, que têm de ser otimizados em simultâneo, dá origem a um conjunto de soluções de compromisso, conhecido como conjunto de soluções ótimas de Pareto. Uma vez que este conjunto de soluções é fundamental para uma tomada de decisão eficaz, cujo objetivo em geral é melhorar a condição humana, o desenvolvimento de métodos de otimização eficientes torna-se indispensável. Recentemente, os algoritmos evolucionários tornaram-se populares e bem-sucedidos na aproximação do conjunto de Pareto. A natureza populacional é a principal característica que os torna especialmente atraentes para lidar com problemas de otimização multiobjetivo. Devido à presença de dois espaços de procura, operadores capazes de realizar a procura de forma eficiente, tanto no espaço de decisão como no espaço dos objetivos, são necessários. Apesar da grande variedade de métodos existentes, várias questões de investigação permanecem em aberto na área do desenvolvimento de algoritmos evolucionários multiobjetivo. Esta tese investiga o uso de algoritmos evolucionários para a resolução de problemas de otimização multiobjetivo. São desenvolvidos algoritmos inovadores que estudam novas técnicas de procura, quer no espaço de decisão, quer no espaço dos objetivos. No que diz respeito à procura no espaço de decisão, o foco está na combinação de métodos de otimização tradicionais com algoritmos evolucionários. A questão relacionada com a procura no espaço dos objetivos é desenvolvida no contexto da otimização com muitos objetivos. A aplicação dos algoritmos evolucionários é abordada resolvendo dois problemas reais, que são modelados utilizando abordagens multiobjectivo. Os problemas resultam da modelação matemática da transmissão da doença do dengue e do desenho ótimo de estações de tratamento de águas residuais. O sucesso na resolução destes problemas de otimização constitui um desafio e destaca a relevância prática e robustez dos algoritmos desenvolvidos