There are increasing interests in improving public transportation systems. One of the proposed strategies for this improvement is the use of Battery Electric Vehicles (BEVs). This approach leads to a new challenge as the BEVs' routing is exposed to the traditional routing problems of conventional vehicles, as well as the particular requirements of the electrical technologies of BEVs. Examples of BEVs' routing problems include the autonomy, battery degradation, and charge process. This work presents a differential evolution algorithm for solving an electric vehicle routing problem (EVRP). The formulation of the EVRP to be solved is based on a scheme to coordinate the BEVs' routing and recharge scheduling, considering operation and battery degradation costs. A model based on the longitudinal dynamics equation of motion estimates the energy consumption of each BEV. A case study, consisting of an airport shuttle service scenario, is used to illustrate the proposed methodology. For this transport service, the BEV energy consumption is estimated based on experimentally measured driving patterns.
A novel formulation aiming to achieve optimal design of reinforced concrete (RC) structures is presented here. Optimal sizing and reinforcing for beam and column members in multi-bay and multistory RC structures incorporates optimal stiffness correlation among all structural members and results in cost savings over typical-practice design solutions. A Nonlinear Programming algorithm searches for a minimum cost solution that satisfies ACI 2005 code requirements for axial and flexural loads. Material and labor costs for forming and placing concrete and steel are incorporated as a function of member size using RS Means 2005 cost data. Successful implementation demonstrates the abilities and performance of MATLAB's (The Mathworks, Inc.) Sequential Quadratic Programming algorithm for the design optimization of RC structures. A number of examples are presented that demonstrate the ability of this formulation to achieve optimal designs.
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative sizes of cross-section dimensions of elements within the structure. Other restrictions define a stiffness and displacement correlation among all structural elements via finite element analysis.The design of minimum cost RC structures introduces a new class of optimization problems, namely, mixed-integer nonlinear programs with complementarity constraints. The complementarity constraints are used to model RC element strength and ACI code-required safety factors. We reformulate the complementarity constraints as nonlinear equations and show that the resulting ill-conditioned MINLPs can be solved by using an off-the-shelf MINLP solver. Our work provides discrete-valued design solutions for an explicit representation of a process most often performed implicitly with iterative calculations.We demonstrate the capabilities of a mixed-integer nonlinear algorithm, MINLPBB, to find optimal sizing and reinforcing for cast-in-place beam and column elements in multistory RC structures. Problem instances contain up to 678 variables, of which 214 are integer, and 844 constraints, of which 582 are nonlinear. We solve problems to local optimality within a reasonable amount of computational time, and we find an average cost savings over typical-practice design solutions of 13 percent.
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