Adaptive modelling strategy for continuous multi-objective optimization

The Pareto optimal set of a continuous multi-objective optimization problem is a piecewise continuous manifold under some mild conditions. We have recently developed several multi-objective evolutionary algorithms based on this property. However, the modelling methods used in these algorithms are rather costly. In this paper, a cheap and effective modelling strategy is proposed for building the probabilistic models of promising solutions. A new criterion is proposed for measuring the convergence of the algorithm. The locality degree of each local model is adjusted according to the proposed convergence criterion. Experimental results show that the algorithm with the proposed strategy is very promising. © 2007 IEEE

Multi-objective reinforcement learning for AUV thruster failure recovery

This paper investigates learning approaches for discovering fault-tolerant control policies to overcome thruster failures in Autonomous Underwater Vehicles (AUV). The proposed approach is a model-based direct policy search that learns on an on-board simulated model of the vehicle. When a fault is detected and isolated the model of the AUV is reconfigured according to the new condition. To discover a set of optimal solutions a multi-objective reinforcement learning approach is employed which can deal with multiple conflicting objectives. Each optimal solution can be used to generate a trajectory that is able to navigate the AUV towards a specified target while satisfying multiple objectives. The discovered policies are executed on the robot in a closed-loop using AUVs state feedback. Unlike most existing methods which disregard the faulty thruster, our approach can also deal with partially broken thrusters to increase the persistent autonomy of the AUV. In addition, the proposed approach is applicable when the AUV either becomes under-actuated or remains redundant in the presence of a fault. We validate the proposed approach on the model of the Girona500 AUV

Solving Many-Objective Car Sequencing Problems on Two-Sided Assembly Lines Using an Adaptive Differential Evolutionary Algorithm

The car sequencing problem (CSP) is addressed in this paper. The original environment of the CSP is modified to reflect real practices in the automotive industry by replacing the use of single-sided straight assembly lines with two-sided assembly lines. As a result, the problem becomes more complex caused by many additional constraints to be considered. Six objectives (i.e. many objectives) are optimised simultaneously including minimising the number of colour changes, minimising utility work, minimising total idle time, minimising the total number of ratio constraint violations and minimising total production rate variation. The algorithm namely adaptive multi-objective evolutionary algorithm based on decomposition hybridised with differential evolution algorithm (AMOEA/D-DE) is developed to tackle this problem. The performances in Pareto sense of AMOEA/D-DE are compared with COIN-E, MODE, MODE/D and MOEA/D. The results indicate that AMOEA/D-DE outperforms the others in terms of convergence-related metrics

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

Wind turbine blade geometry design based on multi-objective optimization using metaheuristics

Abstract: The application of Evolutionary Algorithms (EAs) to wind turbine blade design can be interesting, by reducing the number of aerodynamic-to-structural design loops in the conventional design process, hence reducing the design time and cost. Recent developments showed satisfactory results with this approach, mostly combining Genetic Algorithms (GAs) with the Blade Element Momentum (BEM) theory. The general objective of the present work is to define and evaluate a design methodology for the rotor blade geometry in order to maximize the energy production of wind turbines and minimize the mass of the blade itself, using for that purpose stochastic multi-objective optimization methods. Therefore, the multi-objective optimization problem and its constraints were formulated, and the vector representation of the optimization parameters was defined. An optimization benchmark problem was proposed, which represents the wind conditions and present wind turbine concepts found in Brazil. This problem was used as a test-bed for the performance comparison of several metaheuristics, and also for the validation of the defined design methodology. A variable speed pitch-controlled 2.5 MW Direct-Drive Synchronous Generator (DDSG) turbine with a rotor diameter of 120 m was chosen as concept. Five different Multi-objective Evolutionary Algorithms (MOEAs) were selected for evaluation in solving this benchmark problem: Non-dominated Sorting Genetic Algorithm version II (NSGA-II), Quantum-inspired Multi-objective Evolutionary Algorithm (QMEA), two approaches of the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multi-objective Optimization Differential Evolution Algorithm (MODE). The results have shown that the two best performing techniques in this type of problem are NSGA-II and MOEA/D, one having more spread and evenly spaced solutions, and the other having a better convergence in the region of interest. QMEA was the worst MOEA in convergence and MODE the worst one in solutions distribution. But the differences in overall performance were slight, because the algorithms have alternated their positions in the evaluation rank of each metric. This was also evident by the fact that the known Pareto Front (PF) consisted of solutions from several techniques, with each dominating a different region of the objective space. Detailed analysis of the best blade design showed that the output of the design methodology is feasible in practice, given that flow conditions and operational features of the rotor were as desired, and also that the blade geometry is very smooth and easy to manufacture. Moreover, this geometry is easily exported to a Computer-Aided Design (CAD) or Computer-Aided Engineering (CAE) software. In this way, the design methodology defined by the present work was validated

Population-based algorithms for improved history matching and uncertainty quantification of Petroleum reservoirs

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality

Rotationally invariant techniques for handling parameter interactions in evolutionary multi-objective optimization

In traditional optimization approaches the interaction of parameters associated with a problem is not a significant issue, but in the domain of Evolutionary Multi-Objective Optimization (EMOO) traditional genetic algorithm approaches have difficulties in optimizing problems with parameter interactions. Parameter interactions can be introduced when the search space is rotated. Genetic algorithms are referred to as being not rotationally invariant because their behavior changes depending on the orientation of the search space. Many empirical studies in single and multi-objective evolutionary optimization are done with respect to test problems which do not have parameter interactions. Such studies provide a favorably biased indication of genetic algorithm performance. This motivates the first aspect of our work; the improvement of the testing of EMOO algorithms with respect to the aforementioned difficulties that genetic algorithms experience in the presence of parameter interactions. To this end, we examine how EMOO algorithms can be assessed when problems are subject to an arbitrarily uniform degree of parameter interactions. We establish a theoretical basis for parameter interactions and how they can be measured. Furthermore, we ask the question of what difficulties a multi-objective genetic algorithm experiences on optimization problems exhibiting parameter interactions. We also ask how these difficulties can be overcome in order to efficiently find the Pareto-optimal front on such problems. Existing multi-objective test problems in the literature typically introduce parameter interactions by altering the fitness landscape, which is undesirable. We propose a new suite of test problems that exhibit parameter interactions through a rotation of the decision space, without altering the fitness landscape. In addition, we compare the performance of a number of recombination operators on these test problems. The second aspect of this work is concerned with developing an efficient multi-objective optimization algorithm which works well on problems with parameter interactions. We investigate how an evolutionary algorithm can be made more efficient on multi-objective problems with parameter interactions by developing four novel rotationally invariant differential evolution approaches. We also ask whether the proposed approaches are competitive in comparison with a state-of-the-art EMOO algorithm. We propose several differential evolution approaches incorporating directional information from the multi-objective search space in order to accelerate and direct the search. Experimental results indicate that dramatic improvements in efficiency can be achieved by directing the search towards points which are more dominant and more diverse. We also address the important issue of diversity loss in rotationally invariant vector-wise differential evolution. Being able to generate diverse solutions is critically important in order to avoid stagnation. In order to address this issue, one of the directed approaches that we examine incorporates a novel sampling scheme around better individuals in the search space. This variant is able to perform exceptionally well on the test problems with much less computational cost and scales to very high decision space dimensions even in the presence of parameter interactions