The formulation of the static user equilibrium traffic assignment problem (UETAP) under some simplifying assumptions has a unique solution in terms of link flows but not in terms of path flows. Large variations are possible in the path flows obtained using different UETAP solution algorithms. Many transportation planning and management applications entail the need for path flows. This raises the issue of generating a meaningful path flow solution in practice. Past studies have sought to determine a single path flow solution using the maximum entropy concept. This study proposes an alternate approach to determine a single path flow solution that represents the entropy weighted average of the UETAP path flow solution space. It has the minimum expected Euclidean distance from all other path flow solution vectors of the UETAP. The mathematical model of the proposed entropy weighted average method is derived and its solution stability is proved. The model is easy to interpret and generalizes the proportionality condition of Bar-Gera and Boyce (1999). Results of numerical experiments using networks of different sizes suggest that the path flow solutions for the UETAP using the proposed method are about identical to those obtained using the maximum entropy approach. The entropy weighted average method requires low computational effort and is easier to implement, and can therefore serve as a potential alternative to the maximum entropy approach in practice. 相似文献
Special attention has been paid to sustainable macroalgae cultivation in Europe. The question on where suitable cultivation areas lie, without conflicting with current marine socio-economic activities and respecting the environment, remains a great challenge. Considering 13 criteria critical to seaweed farming such as depth, shipping traffic, and distance to ports, this paper aimed to identify suitable and sustainable offshore areas on the West Coast of Sweden for the cultivation of the Sugar Kelp, Saccharina latissima. An integrated approach with the tools geographic information systems (GIS) and multi-criteria analysis (MCA) was used to aggregate the criteria by means of Boolean and weighted linear combination (WLC) techniques. The Boolean method singled out 544?km2 as suitable, whereas the WLC method indicated 475?km2 as highly suitable. Both techniques complement each other in finding optimal sites. Furthermore, the integrated models excelled in providing an overview for effective spatial decision-making that fosters sustainable development of macroalgae cultivations within marine and coastal systems.
Highlights
To the authors’ knowledge no study on seaweed aquaculture site selection has been conducted using such a range of criteria with the purpose of including sustainability aspects within a comparative GIS-MCDA.
The large areas identified on the West Coast of Sweden as suitable highlight the potential of this new industry and the complexity of associated marine spatial planning.
Boolean and weighted linear combination methods were applied and compared, providing valuable insights in the selection of methods for spatial decision-making support. These insights should support a more sustainable development of macroalgae cultivation in the region, as well as a more resilient marine spatial planning process for blue growth strategies.