In light of the widespread use of electric vehicles for urban distribution, this paper delves into the electric vehicle routing problem (EVRP): specifically addressing multiple trips per vehicle, diverse vehicle types, and simultaneous pickup and delivery. The primary objective is to minimize the overall cost, which encompasses travel expenses, waiting times, recharging costs, and fixed vehicle costs. The focal problem is formulated as a heterogeneous and multi-trip electric vehicle routing problem with pickup and delivery (H-MT-EVRP-PD). Additionally, we introduce two heuristic algorithms to efficiently approximate solutions within a reasonable computational time. The variable neighborhood search (VNS) algorithm and the adaptive large neighborhood search (ALNS) algorithm are presented and compared based on our computational experiences with both. Through solving a series of large-scale real-world instances for the H-MT-EVRP-PD and smaller instances using an exact method, we demonstrate the efficacy of the proposed approaches.

The position analysis of a nine-link Barranov truss is finished by using Dixon resultants together with Sylvester resultants. Above all, using vector method in complex plane to construct four constraint equations and transform them into complex exponential form, then three constraint equations are used to construct a $6×6$ Dixon matrix, which contains two variables to be eliminated. We extract the greatest common divisor (GCD) of two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the fourth constraint equation can be used to construct a Sylvester resultant. A $50deg$ univariate polynomial equation is obtained from the determinant of Sylvester resultant. Other variables can be computed by Euclidean algorithm and Gaussian elimination. Lastly, a numerical example confirms that the analytical solution number of the Barranov truss is 50. It is the first time to complete analytical solutions of this kind of Barranov truss.

Highway less than truckload (LTL) transportation vehicles and cargos matching problem is a joint optimization problem of typical vehicle routing and loading, which is also a hot issue of operational research. This article based on the demand of virtual logistics platform, for the problem of the highway LTL transportation, the matching model of the idle vehicle and the transportation order is set up and the corresponding genetic algorithm is designed. Then the algorithm is implemented by Java. The simulation results show that the solution is satisfactory.

For a spherical four-bar linkage, the maximum number of the spherical RR dyad (R: revolute joint) of five-orientation motion generation can be at most 6. However, complete real solution of this problem has seldom been studied. In order to obtain six real RR dyads, based on Strum’s theorem, the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method. Moreover, the Grashof condition and the circuit defect condition are taken into account. Given the relationships between the design parameters and the aforementioned two conditions, two objective functions are constructed and optimized by the adaptive genetic algorithm(AGA). Two examples with six real spherical RR dyads are obtained by optimization, and the results verify the feasibility of the proposed method. The paper provides a method to synthesize the complete real solution of the five-orientation motion generation, which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.

Online shopping platform in rural distribution difficulties, leading to rural online shopping market and logistics market development is slow. At present, China Post and other private courier companies are not possible to do. So we need to build distribution alliances. Reasonable profit allocation mechanism is the key to the stable development of this distribution alliance. So we proposed the Shapley Value Method and the ANP Improved Model to allocate profits. Finally, the rationality of the method is proved by numerical analysis before and after using the corrected Shapley Value.