Multi-objective hyper-heuristics: a survey

Abstract In recent years, research on the integration of evolutionary multi-objective optimization and (hyper-) heuristics (MOHHs) has significantly grown. This paper presents a comprehensive survey of MOHH research, categorizing existing approaches into four main classes: selection, generation, portfolio, and configuration MOHHs. Each category is analyzed in terms of methodology, key contributions, and open challenges. The analysis reveals an imbalance in research focus, with selection and portfolio MOHHs receiving the most attention, followed by configuration MOHHs, while generation MOHHs remain largely unaddressed. Selection MOHHs are further divided by the hierarchy of components they control: low-level approaches (which typically manage evolutionary operators) require further study on move acceptance methods, whereas mid-level approaches (which typically manage multi-objective evolutionary algorithms) need deeper exploration of selection strategies. Generation MOHHs, primarily based on genetic programming and grammatical evolution, lack investigation into alternative methodologies. Portfolio MOHHs, which produce a set of non-dominated constructive (hyper-) heuristics based on performance trade-offs, have been predominantly applied to combinatorial problems and exhibit limited diversity in the use of MOEAs as underlying optimizers. Configuration MOHHs, which focus on configuring algorithmic components for multi-objective optimizers, have largely relied on a single performance indicator, leaving room for multi-criteria performance approaches. Beyond this, the paper also reviews the test problems and practical applications that have been addressed by MOHHs, and outlines potential avenues for future research in the field.