Multi-objective Optimization and its Engineering Applications

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are ``efficient" in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a final solution among Pareto optimal solutions taking into account the balance among objective functions, which is called ``trade-off analysis". It is no exaggeration to say that the most important task in multi-objective optimization is trade-off analysis. Consequently, the methodology should be discussed in view of how it is easy and understandable for trade-off analysis. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively easily. Seeing Pareto frontiers, we can grasp the trade-off relation among objectives totally. Therefore, it would be the best way to depict Pareto frontiers in cases with two or three objectives. (It might be difficult to read the trade-off relation among objectives with three dimension, though). In cases with more than three objectives, however, it is impossible to depict Pareto forntier. Under this circumstance, interactive methods can help us to make local trade-off analysis showing a ``certain" Pareto optimal solution. A number of methods differing in which Pareto optimal solution is to be shown, have been developed. This paper discusses critical issues among those methods for multi-objective optimization, in particular applied to engineering design problems

Applications of the non-dominated sorting genetic algorithm (NSGA) in chemical reaction engineering

Most of the chemical reaction engineering optimization problems encounters more than one objective functions. A considerable amount of research has been reported on the multiobjective optimization of various chemical reactors using various non-dominated sorting genetic algorithms. This is reviewed in this paper. The introduction of the topic is given at the beginning, followed by the description of multi-objective optimization and Pareto set. We have then discussed various non-dominated sorting genetic algorithms and its applications in chemical reaction engineering. Some comments are also made on the future research direction in this area

Evolutionary Game Theoretic Multi-Objective Optimization Algorithms and Their Applications

Multi-objective optimization problems require more than one objective functions to be optimized simultaneously. They are widely applied in many science fields, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conicting objectives. Most of the real world multi-objective optimization problems are NP-Hard problems. It may be too computationally costly to find an exact solution but sometimes a near optimal solution is sufficient. In these cases, Multi-Objective Evolutionary Algorithms (MOEAs) provide good approximate solutions to problems that cannot be solved easily using other techniques. However Evolutionary Algorithm is not stable due to its random nature, it may produce very different results every time it runs. This dissertation proposes an Evolutionary Game Theory (EGT) framework based algorithm (EGTMOA) that provides optimality and stability at the same time. EGTMOA combines the notion of stability from EGT and optimality from MOEA to form a novel and promising algorithm to solve multi-objective optimization problems. This dissertation studies three different multi-objective optimization applications, Cloud Virtual Machine Placement, Body Sensor Networks, and Multi-Hub Molecular Communication along with their proposed EGTMOA framework based algorithms. Experiment results show that EGTMOAs outperform many well known multi-objective evolutionary algorithms in stability, performance and runtime

Global Multi-Objective Optimisation utilising Surrogate Models

While global multi-objective optimization problems continue to emerge in aerospace engineering, conventional optimization methods, in particular, evolutionary algorithms such as the Non-dominated Sorting Genetic Algorithm, have shown their capability to solve such problems. However, one distinctive disadvantage of these conventional methods is that they generally require a large number of function evaluations, which makes them incompatible with computationally intensive numerical simulations that are often employed in aerospace design problems. This thesis substantiates the idea that this limitation can be overcome by using surrogate based optimization, in particular multi-objective Bayesian global optimization that utilizes Kriging as a surrogate model and Expected Hypervolume Improvement as an infill criteria. With this approach, it is possible to obtain the Pareto front with a relatively small computational budget. This is demonstrated through test cases that are conducted by solving analytical optimization problems. The results show that Bayesian optimization is able to reduce the function evaluations by 51 times for the bi-objective problem, and by 91 times for the three-objectives problem compared to genetic algorithms. Furthermore, its applicability is tested in two aerospace design problems, where function evaluations were performed through Computational Fluid Dynamics (CFD) and Computational Aeroacoustic (CAA) simulations. The proposed optimization method returns Pareto fronts which contain various design trade-offs that result in improved performance in terms of the desired objectives, with a reasonable number of function evaluations. Firstly, in the aerodynamic shape optimization, it is able to obtain the Pareto front, which contains airfoil designs with a combination of reduced drag and reduced pitching moment. Secondly, the aerodynamic-aeroacoustic shape optimization is performed where the Pareto front is obtained for airfoil designs with three objectives: reduced drag, reduced pitching moment and reduced aeroacoustic noise. This thesis demonstrates the efficiency of the Bayesian global optimization framework by showing how the Pareto front can be obtained at a relatively smaller number of function evaluations compared to some of the conventional multi-objective optimization methods. Moreover, the results obtained from the applied problems verify its capability for practical applications in aerospace design. Hence, the outcomes of this thesis highlight the potential of multi-objective Bayesian global optimization for multidisciplinary design optimization problems in the field of aerospace engineering

Water Distribution System Computer-Aided Design by Agent Swarm Optimization

Optimal design of water distribution systems (WDS), including the sizing of components, quality control, reliability, renewal and rehabilitation strategies, etc., is a complex problem in water engineering that requires robust methods of optimization. Classical methods of optimization are not well suited for analyzing highly-dimensional, multimodal, non-linear problems, especially given inaccurate, noisy, discrete and complex data. Agent Swarm Optimization (ASO) is a novel paradigm that exploits swarm intelligence and borrows some ideas from multiagent based systems. It is aimed at supporting decisionmaking processes by solving multi-objective optimization problems. ASO offers robustness through a framework where various population-based algorithms co-exist. The ASO framework is described and used to solve the optimal design of WDS. 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MULTI-OBJECTIVE EFFICIENT PARAMETRIC OPTIMIZATION

Parametric optimization is the process of solving an optimization problem as a function of currently unknown or changing variables known as parameters. Parametric optimization methods have been shown to benefit engineering design and optimal morphing applications through its specialized problem formulation and specialized algorithms. Despite its benefits to engineering design, existing parametric optimization algorithms (similar to many optimization algorithms) can be inefficient when design analyses are expensive. Since many engineering design problems involve some level of expensive analysis, a more efficient parametric optimization algorithm is needed. Therefore, the multi-objective efficient parametric optimization (MO-EPO) algorithm is developed to allow for the efficient optimization of problems with multiple parameters and objectives. This technique relies on the new parametric hypervolume indicator (pHVI) which measures the space dominated by a given set of data involving both objectives and parameters. The pHVI benefits parametric optimization by enabling the comparison of optimization results, enabling the visualization and detection of optimization convergence, and providing information for an optimization algorithm. MO-EPO uses response surface models of expensive functions to find and evaluate a designs expected to improve the solution and/or models. With new information, response surface models are updated and the process is repeated. "Improvement" is measured by the pHVI metric allowing for the consideration of any number of objectives and parameters. The novel MO-EPO algorithm is demonstrated on a number of analytical benchmarking problems and two distinct morphing applications with various numbers of objectives and parameters. In each case, MO-EPO is shown to find solutions that are as good as or better than those found from the existing P3GA (i.e., equal or greater pHVI value) when the number of design evaluations is limited. Both the pHVI metric and the MO-EPO algorithm are significant contributions to parametric optimization methodology and engineering design