A memetic algorithm based on Artificial Bee Colony for optimal synthesis of mechanisms

En este documento se presenta una propuesta novedosa de un algoritmo híbrido modular, como herramienta para resolver problemas de ingeniería del mundo real. Se implementa y aplica un algoritmo memético, MemMABC, para la solución de dos casos de diseño de mecanismos, con el fin de evaluar su eficiencia y rendimiento. El algoritmo propuesto es simple y flexible debido a su modularidad; estas características lo vuelven altamente reutilizable para ser aplicado en una amplia gama de problemas de optimización. Las soluciones de los casos de estudio también son modulares, siguiendo un esquema de programación estructurada que incluye el uso de variables globales para la configuración, y de subrutinas para la función objetivo y el manejo de las restricciones. Los algoritmos meméticos son una buena opción para resolver problemas duros de optimización, debido a la sinergia derivada de la combinación de sus componentes: una metaheurística poblacional para búsqueda global y un método de refinamiento local. La calidad en los resultados de las simulaciones sugiere que el MemMABC puede aplicarse con éxito para la solución de problemas duros de diseño en ingeniería.In this paper a novel proposal of a modular hybrid algorithm as a tool for solving real-world engineering problems is presented. A memetic algorithm, MemMABC, is implemented with this approach and applied to solve two case studies of mechanism design, in order to evaluate its efficiency and performance. Because of its modularity, the proposed algorithm is simple and flexible; these features make it quite reusable to be applied on different optimization problems, with a wide scope. The solutions of the optimization problems are also modular, following a scheme of structured programming that includes the use of global variables for configuration, and subroutines for the objective function and the restrictions. Memetic algorithms are a good option to solve hard optimization problems, because of the synergy derived from the combination of their components: a global search population-based metaheuristic and a local refinement method. The quality of simulation results suggests that MemMABC can be successfully applied to solve hard problems in engineering design.Peer Reviewe

A Framework for Hyper-Heuristic Optimisation of Conceptual Aircraft Structural Designs

Conceptual aircraft structural design concerns the generation of an airframe that will provide sufficient strength under the loads encountered during the operation of the aircraft. In providing such strength, the airframe greatly contributes to the mass of the vehicle, where an excessively heavy design can penalise the performance and cost of the aircraft. Structural mass optimisation aims to minimise the airframe weight whilst maintaining adequate resistance to load. The traditional approach to such optimisation applies a single optimisation technique within a static process, which prevents adaptation of the optimisation process to react to changes in the problem. Hyper-heuristic optimisation is an evolving field of research wherein the optimisation process is evaluated and modified in an attempt to improve its performance, and thus the quality of solutions generated. Due to its relative infancy, hyper-heuristics have not been applied to the problem of aircraft structural design optimisation. It is the thesis of this research that hyper-heuristics can be employed within a framework to improve the quality of airframe designs generated without incurring additional computational cost. A framework has been developed to perform hyper-heuristic structural optimisation of a conceptual aircraft design. Four aspects of hyper-heuristics are included within the framework to promote improved process performance and subsequent solution quality. These aspects select multiple optimisation techniques to apply to the problem, analyse the solution space neighbouring good designs and adapt the process based on its performance. The framework has been evaluated through its implementation as a purpose-built computational tool called AStrO. The results of this evaluation have shown that significantly lighter airframe designs can be generated using hyper-heuristics than are obtainable by traditional optimisation approaches. Moreover, this is possible without penalising airframe strength or necessarily increasing computational costs. Furthermore, improvements are possible over the existing aircraft designs currently in production and operation

Co-evolutionary Hybrid Bi-level Optimization

Multi-level optimization stems from the need to tackle complex problems involving multiple decision makers. Two-level optimization, referred as ``Bi-level optimization'', occurs when two decision makers only control part of the decision variables but impact each other (e.g., objective value, feasibility). Bi-level problems are sequential by nature and can be represented as nested optimization problems in which one problem (the ``upper-level'') is constrained by another one (the ``lower-level''). The nested structure is a real obstacle that can be highly time consuming when the lower-level is $\mathcal{NP}-hard$. Consequently, classical nested optimization should be avoided. Some surrogate-based approaches have been proposed to approximate the lower-level objective value function (or variables) to reduce the number of times the lower-level is globally optimized. Unfortunately, such a methodology is not applicable for large-scale and combinatorial bi-level problems. After a deep study of theoretical properties and a survey of the existing applications being bi-level by nature, problems which can benefit from a bi-level reformulation are investigated. A first contribution of this work has been to propose a novel bi-level clustering approach. Extending the well-know ``uncapacitated k-median problem'', it has been shown that clustering can be easily modeled as a two-level optimization problem using decomposition techniques. The resulting two-level problem is then turned into a bi-level problem offering the possibility to combine distance metrics in a hierarchical manner. The novel bi-level clustering problem has a very interesting property that enable us to tackle it with classical nested approaches. Indeed, its lower-level problem can be solved in polynomial time. In cooperation with the Luxembourg Centre for Systems Biomedicine (LCSB), this new clustering model has been applied on real datasets such as disease maps (e.g. Parkinson, Alzheimer). Using a novel hybrid and parallel genetic algorithm as optimization approach, the results obtained after a campaign of experiments have the ability to produce new knowledge compared to classical clustering techniques combining distance metrics in a classical manner. The previous bi-level clustering model has the advantage that the lower-level can be solved in polynomial time although the global problem is by definition $\mathcal{NP}$-hard. Therefore, next investigations have been undertaken to tackle more general bi-level problems in which the lower-level problem does not present any specific advantageous properties. Since the lower-level problem can be very expensive to solve, the focus has been turned to surrogate-based approaches and hyper-parameter optimization techniques with the aim of approximating the lower-level problem and reduce the number of global lower-level optimizations. Adapting the well-know bayesian optimization algorithm to solve general bi-level problems, the expensive lower-level optimizations have been dramatically reduced while obtaining very accurate solutions. The resulting solutions and the number of spared lower-level optimizations have been compared to the bi-level evolutionary algorithm based on quadratic approximations (BLEAQ) results after a campaign of experiments on official bi-level benchmarks. Although both approaches are very accurate, the bi-level bayesian version required less lower-level objective function calls. Surrogate-based approaches are restricted to small-scale and continuous bi-level problems although many real applications are combinatorial by nature. As for continuous problems, a study has been performed to apply some machine learning strategies. Instead of approximating the lower-level solution value, new approximation algorithms for the discrete/combinatorial case have been designed. Using the principle employed in GP hyper-heuristics, heuristics are trained in order to tackle efficiently the $\mathcal{NP}-hard$ lower-level of bi-level problems. This automatic generation of heuristics permits to break the nested structure into two separated phases: \emph{training lower-level heuristics} and \emph{solving the upper-level problem with the new heuristics}. At this occasion, a second modeling contribution has been introduced through a novel large-scale and mixed-integer bi-level problem dealing with pricing in the cloud, i.e., the Bi-level Cloud Pricing Optimization Problem (BCPOP). After a series of experiments that consisted in training heuristics on various lower-level instances of the BCPOP and using them to tackle the bi-level problem itself, the obtained results are compared to the ``cooperative coevolutionary algorithm for bi-level optimization'' (COBRA). Although training heuristics enables to \emph{break the nested structure}, a two phase optimization is still required. Therefore, the emphasis has been put on training heuristics while optimizing the upper-level problem using competitive co-evolution. Instead of adopting the classical decomposition scheme as done by COBRA which suffers from the strong epistatic links between lower-level and upper-level variables, co-evolving the solution and the mean to get to it can cope with these epistatic link issues. The ``CARBON'' algorithm developed in this thesis is a competitive and hybrid co-evolutionary algorithm designed for this purpose. In order to validate the potential of CARBON, numerical experiments have been designed and results have been compared to state-of-the-art algorithms. These results demonstrate that ``CARBON'' makes possible to address nested optimization efficiently