An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well-established CFD package. The system's performance is illustrated through case studies - one two-dimensional, one three-dimensional - in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times - a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade- off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing power and the benefits discussed, this approach brings the adoption of such techniques in real-world engineering design practice a step closer.@en

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.@en

In real-world optimization problems, large design spaces and conflicting objectives are often combined with a large number of constraints, resulting in a highly multi-modal, challenging, fragmented landscape. The local search at the heart of Tabu Search, while being one of its strengths in highly constrained optimization problems, requires a large number of evaluations per optimization step. In this work, a modification of the pattern search algorithm is proposed: this modification, based on a Principal Components' Analysis of the approximation set, allows both a re-alignment of the search directions, thereby creating a more effective parametrization, and also an informed reduction of the size of the design space itself. These changes make the optimization process more computationally efficient and more effective - higher quality solutions are identified in fewer iterations. These advantages are demonstrated on a number of standard analytical test functions (from the ZDT and DTLZ families) and on a real-world problem (the optimization of an axial compressor preliminary design).@en

At present, optimization is an enabling technology in innovation. Multi-objective and multidisciplinary optimization tools are essential in the design process for real-world applications. In turbomaehinery design, these approaches give insight into the design space and identify the tradeoffs between the competing performance measures. This paper describes the application of a novel multi-objective variant of the tabu search algorithm to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and eventually of the whole engine. The integrated system developed for this purpose is described. It combines the optimizer with an existing geometry parameterization scheme and a well-established computational fluid dynamics package. Its performance is illustrated through a case study in which the flow characteristics most important to the overall performance of turbomachinery blades are optimized.@en

Real-world engineering optimisation problems are typically multi-objective and highly constrained, and constraints may be both costly to evaluate and binary in nature. In addition, objective functions may be computationally expensive and, in the commercial design cycle, there is a premium placed on rapid initial progress in the optimisation run. In these circumstances, evolutionary algorithms may not be the best choice; we have developed a multi-objective Tabu Search algorithm, designed to perform well under these conditions. Here we present the algorithm along with the constraint handling approach, and test it on a number of benchmark constrained test problems. In addition, we perform a parametric study on a variety of unconstrained test problems in order to determine the optimal parameter settings. Our algorithm performs well compared to a leading multi-objective Genetic Algorithm, and we find that its performance is robust to parameter settings.@en

The reliance of Tabu Search (TS) algorithms on a local search leads to a logical development of algorithms that use more than one search concurrently. In this paper we present a multi-threaded TS algorithm employing a number of threads that share information. We assess the performance of this algorithm compared to previous multi-objective TS algorithms, via the results obtained from applying the algorithms to a range of standard test functions. We also consider whether an optimal number of threads can be found, and what impact changing the number of threads used has on performance. We discover that, contrary to the popular belief that multi-threading is usually beneficial, performance only improves in a few special cases.@en

We present a novel framework for robust aerodynamic design optimization with respect to CFD modeling errors using multi-fidelity simulations, a multi-objective optimization algorithm, and a surrogate model employed to map the error landscape across the design space. We use the low- and high-fidelity CFD model divergence as a proxy for simulation risk, which is simultaneously optimized along with a measure of performance. Instead of generating high-fidelity simulations directly, we employ a Sparse Pseudo-input Gaussian Process surrogate modeling algorithm to predict the divergence. We apply this approach to a simple diffuser design problem, coupled with a multi-objective Tabu Search optimization algorithm, which shows encouraging results. We are able to generate a range of Pareto optimal design, which display a trade-off between aerodynamic performance and simulation risk. This approach is applicable to more general problems and would be of interest in an industrial design setting.@en

This paper describes the implementation of a parallel Tabu Search algorithm for multi-objective continuous optimisation problems. We compare our new algorithm with a leading multi-objective Genetic Algorithm and find it exhibits comparable performance on standard benchmark problems. In addition, for certain problem types, we expect Tabu Search to outperform other algorithms and present preliminary results from an aerodynamic shape optimisation problem. This is a real-world, highly constrained, computationally demanding design problem which requires efficient optimisation algorithms that can be run on parallel computers: with this approach optimisation algorithms are able to play a part in the design cycle.@en