Long-Haul Vehicle Routing and Scheduling with Biomathematical Fatigue Constraints

Hours of service (HOS) regulations are among the conventional safety constraints that are compiled by long-haul truck drivers. These regulations have been considered in models and algorithms of vehicle routing problems to assign safe schedules to drivers. However, the HOS regulations neglect a few crucial fatigue risk factors and, at times, fail to generate fatigue-reducing schedules. In this study, a set of biomathematical fatigue constraints (BFCs) derived from biomathematical models are considered for a long-haul vehicle routing and scheduling problem. A BFC scheduling algorithm and a BFC-HOS scheduling algorithm have been developed and then embedded within a tabu search heuristic to solve the combined vehicle routing and scheduling problem. All the solution methods have been tested on modified Solomon instances and a real-life instance, and the computational results confirm the advantages of employing a sophisticated and fatigue-reducing scheduling procedure when planning long-haul transportation.

Computing Marginal Cost of Durability of Energy Systems Components by Structural Optimization with Fatigue Constraints

There is a relationship between product durability and the effect the product has on the environment and economy. One approach that impacts this dynamic involves a circular economy, which is gaining traction as businesses shift towards a product as a service model. One example of this is emerging in the energy sector. Given this shift, the life of the product becomes important as it impacts the bottom line of the business. This gives rise to the Marginal Cost of Durability (MCD) metric. The MCD relates the product cost to the system life. System life is particularly important for renewable energy systems that promote sustainable living. These large structures require materials and end-of-life disposal. Design requirements for material also increase as the design life increases. Additional materials safeguard against failure such as fatigue. Currently, there is no formal method for determining the MCD. This paper examines a method for measuring MCD for the commercial class of wind energy systems. A metamodel of the damage response is built instead of expensive computational models. Design optimization is used to find design parameters using fatigue damage as a constraint. This process is repeated for a set of system life values, yielding a set of designs. A mathematical relationship between life and cost is found. An example of this method is applied to the study of wind turbine tower life. The results from the proposed method provide information that is used to determine the design life of a system.

Topology optimization of the multi-fasteners jointed structure considering fatigue constraints

This paper is to present an important issue of fatigue failure in the design of multi-fasteners jointed structure. To avoid failure in the connection area, Sines criterion is utilized. Fatigue constraints are handled in the context of stress based topology optimization. To eliminate the high stresses caused by the finite element modeling, the control volume is defined to evaluate the stress states around the fasteners. The standard topology optimization is extended to minimize the structural compliance with fatigue failure constraints. To address singularity problems related to stress constraints, q-p relaxation is used. P-norm is used as the constraints aggregation scheme. Basing on the above, the design sensitivity of fatigue constraints is derived and calculated. The proposed method is verified by a numerical example of an assembled I-beam. The comparisons of the numerical results have shown the effect of the fatigue constraint.