A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM

Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq); (ii) Coordination for the Improvement of Higher Education (CAPES) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese)

A learning automata based multiobjective hyper-heuristic

Metaheuristics, being tailored to each particular domain by experts, have been successfully applied to many computationally hard optimisation problems. However, once implemented, their application to a new problem domain or a slight change in the problem description would often require additional expert intervention. There is a growing number of studies on reusable cross-domain search methodologies, such as, selection hyper-heuristics, which are applicable to problem instances from various domains, requiring minimal expert intervention or even none. This study introduces a new learning automata based selection hyper-heuristic controlling a set of multiobjective metaheuristics. The approach operates above three well-known multiobjective evolutionary algorithms and mixes them, exploiting the strengths of each algorithm. The performance and behaviour of two variants of the proposed selection hyper-heuristic, each utilising a different initialisation scheme are investigated across a range of unconstrained multiobjective mathematical benchmark functions from two different sets and the realworld problem of vehicle crashworthiness. The empirical results illustrate the effectiveness of our approach for cross-domain search, regardless of the initialisation scheme, on those problems when compared to each individual multiobjective algorithm. Moreover, both variants perform signicantly better than some previously proposed selection hyper-heuristics for multiobjective optimisation, thus signicantly enhancing the opportunities for improved multiobjective optimisation

Multi‐Objective Hyper‐Heuristics

Multi‐objective hyper‐heuristics is a search method or learning mechanism that operates over a fixed set of low‐level heuristics to solve multi‐objective optimization problems by controlling and combining the strengths of those heuristics. Although numerous papers on hyper‐heuristics have been published and several studies are still underway, most research has focused on single‐objective optimization. Work on hyper‐heuristics for multi‐objective optimization remains limited. This chapter draws attention to this area of research to help researchers and PhD students understand and reuse these methods. It also provides the basic concepts of multi‐objective optimization and hyper‐heuristics to facilitate a better understanding of the related research areas, in addition to exploring hyper‐heuristic methodologies that address multi‐objective optimization. Some design issues related to the development of hyper‐heuristic framework for multi‐objective optimization are discussed. The chapter concludes with a case study of multi‐objective selection hyper‐heuristics and its application on a real‐world problem

Migration in Multi-Population Differential Evolution for Many Objective Optimization

The paper proposes a novel extension of many objective optimization using differential evolution (MaODE). MaODE solves a many objective optimization (MaOO) problem by parallel optimization of individual objectives. MaODE involves N populations, each created for an objective to be optimized using MaODE. The only mode of knowledge transfer among populations in MaODE is the modified version of mutation policy of DE, where every member of the population during mutation is influenced by the best members of all the populations under consideration. The present work aims at further increasing the communication between the members of the population by communicating between a superior and an inferior population, using a novel migration strategy. The proposed migration policy enables poor members of an inferior population to evolve with a superior population. Simultaneously, members from the superior population are also transferred to the inferior one to help it improving its performance. Experiments undertaken reveal that the proposed extended version of MaODE significantly outperforms its counterpart and the state-of-the-art techniques

New Insights to Approximate the Pareto Optimal Front in Evolutionary Multiobjective Optimization. An Application to Students’ Satisfaction

Los resultados de la segunda parte demuestran el buen comportamiento de la combinación de técnicas econométricas y multiobjetivo, especialmente cuando utilizamos algoritmos evolutivos, para la resolución de problemas socio-económicos con la finalidad de encontrar la compensación (trade-offs) entre los objetivos estudiados y así poder sugerir mejoras, en este caso, en economía de la educación.La tesis presentada se basa en el desarrollo de nuevos algoritmos evolutivos para resolver problemas de optimización multiobjetivo, especialmente problemas con más de tres funciones objetivos, y en la modelización y resolución de un problema de economía de la educación. Dicha tesis está realizada en la modalidad de compendio de artículos y se compone de tres de los mismos. Los dos primeros relacionados con el desarrollo de un nuevo algoritmo evolutivo. En ellos, partiendo del algoritmo Global Weighting Achievement Scalarizing Fucntion Genetic Algorithm (GWASF-GA) (Saborido, Ruiz, and Luque, 2017), se plantea y desarrolla un nuevo algoritmo centrado en la adaptación de los vectores de pesos durante el proceso de ejecución, que ofrece muy buenos resultados en comparación con algoritmos muy conocidos y muy contrastados dentro del campo de los algoritmos evolutivos. El tercer artículo se centra en la modelización y resolución de un problema multiobjetivo obtenido a partir del análisis econométrico de datos referidos al rendimiento académico y satisfacción de los estudiantes andaluces con diferentes aspectos del proceso enseñanza-aprendizaje en los colegios de secundaria. Con los resultados obtenidos y teniendo en cuenta los algoritmos considerados, aunque los frentes óptimos de Pareto aproximados por A-GWASF-GA no sean los mejores en todos los casos (especialmente para los problemas con tres funciones objetivo), podemos asegurar que el nuevo algoritmo algoritmo evolutivo aquí propuesto (A-GWASF-GA) muestra resultados muy prometedores en problemas con más de tres funciones objetivo. De esta forma, A-GWASF-GA se autodefine como un algoritmo para trabajar con problemas manyobjective (con más de tres objetivos)