Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

The study focuses on a multiple constrained reliable path problem in which travel time reliability and resource constraints are collectively considered. Nonlinear optimization model is developed to model constrained robust shortest path problem. The dual nature of the proposed problem is deduced based on the Lagrangian duality theory. An efficient algorithm based on Lagrangian dual relaxation is designed to solve constrained robust shortest path problem. An extension problem that considers multiple constraints is discussed. Numerical studies indicate that the proposed algorithm is efficient in terms of obtaining the close-to-optimal solutions within reasonable computational times.

Phthalocyanine supported dinuclear LnIIIcomplexes: the solvent-induced change of magnetic properties in dysprosium(iii) analogues

Three phthalocyanine-supported dinuclear LnIIIcomplexes were obtained and characterized. The DyIIIanalogue exhibits reversible solvent dependent single-molecule magnetic properties between a single relaxation and a dual relaxation process.

Dual relaxation and structural changes under uniaxial strain in main-chain smectic-C liquid crystal elastomer

Relaxation rate of the chevron angle, α becomes about ten times faster at strains exceeding 0.7 than at low strains.