•Landscape analysis is extended to constrained multiobjective optimization.•New landscape features are derived to facilitate problem characterization.•Test suites of constrained multiobjective ...optimization problems are thoroughly analyzed.•Artificial test problems fail to fully represent real-world problem characteristics.•The main source of complexity in artificial test problems is violation multimodality.
Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still insufficiently understood and characterized. For this reason, the selection of appropriate CMOPs for benchmarking is difficult and lacks a formal background. We address this issue by extending landscape analysis to constrained multiobjective optimization. By employing four exploratory landscape analysis techniques, we propose 29 landscape features (of which 19 are novel) to characterize CMOPs. These landscape features are then used to compare eight frequently used artificial test suites against a recently proposed suite consisting of real-world problems based on physical models. The experimental results reveal that the artificial test problems fail to adequately represent some realistic characteristics, such as strong negative correlation between the objectives and the overall constraint violation. Moreover, our findings show that all the studied artificial test suites have advantages and limitations, and that no “perfect” suite exists. Additionally, the effectiveness of the proposed features at predicting algorithm performance is demonstrated for two multiobjective optimization algorithms. Benchmark designers can use the obtained results to select or generate appropriate CMOP instances based on the characteristics they want to explore.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ
Human development has made remarkable social and economic progress possible for most of us but has also entailed a range of serious impacts on natural resources, local communities and the economy at ...multiple scales. Thus, achieving sustainable territorial management that combines healthy and prosperous societies with the long-term maintenance of biodiversity and productive ecosystem services remains the biggest challenge of our modern world. This Special Issue seeks to collect a coherent set of studies on techniques and experiences (case studies) aimed at increasing the environmental, social, economic &/or institutional sustainability of landscapes and seascapes from a range of geographic and socioeconomic contexts. Ten case studies representing urban areas, rural areas (chiefly protected areas) and coastal areas from four countries in Europe and Asia by internationally renowned authors are shown.
