The traveling salesman problem (TSP), a typical non-deterministic polynomial (NP) hard problem, has been used in many engineering applications. Genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. However, it has some issues for solving TSP, including quickly falling into the local optimum and an insufficient optimization precision. To address TSP effectively, this paper proposes a hybrid Cellular Genetic Algorithm with Simulated Annealing (SA) Algorithm (SCGA). Firstly, SCGA is an improved Genetic Algorithm (GA) based on the Cellular Automata (CA). The selection operation in SCGA is performed according to the state of the cell. Secondly, SCGA, combined with SA, introduces an elitist strategy to improve the speed of the convergence. Finally, the proposed algorithm is tested against 13 standard benchmark instances from the TSPLIB to confirm the performance of the three cellular automata rules. The experimental results show that, in most instances, the results obtained by SCGA using rule 2 are better and more stable than the results of using rule 1 and rule 3. At the same time, we compared the experimental results with GA, SA, and Cellular Genetic Algorithm (CGA) to verify the performance of SCGA. The comparison results show that the distance obtained by the proposed algorithm is shortened by a mean of 7% compared with the other three algorithms, which is closer to the theoretical optimal value and has good robustness.

Aiming at the scheduling problem of logistics distribution vehicles, an enhanced artificial electric field algorithm (SC-AEFA) based on the sine cosine mechanism is proposed. The development of the SC-AEFA was as follows. First, a map grid model for enterprise logistics distribution vehicle path planning was established. Then, an enhanced artificial electric field algorithm with the sine cosine mechanism was developed to simulate the logistics distribution vehicle scheduling, establish the logistics distribution vehicle movement law model, and plan the logistics distribution vehicle scheduling path. Finally, a distribution business named fresh enterprise A in the Fuzhou Strait Agricultural and Sideline Products Trading Market was selected to test the effectiveness of the method proposed. The theoretical proof and simulation test results show that the SC-AEFA has a good optimization ability and a strong path planning ability for enterprise logistics vehicle scheduling, which can improve the scheduling ability and efficiency of logistics distribution vehicles and save transportation costs.

Ordinary differential equations (ODEs) have a wide range of potential applications in science and engineering with regard to nonlinear dynamic systems. Frequently, there is a focus upon locating unique solutions to ODEs, with non-unique solutions being viewed as potentially problematic. However, some have recognized the importance of examining the character of non-unique solutions as well in order to properly understand the behaviour of physical systems. In some areas of engineering, notably control theory, the latter concern has become pressing. In this paper, by studying the asymptotic stability of second-order ordinary differential systems, we present a theorem creatively and prove it strictly by two lemmas. Using the criteria for non-unique solutions of first-order ordinary differential equations at points of equilibrium, we can solve engineering problems effectively. The applicability of this novel approach to the solution of engineering problems is provided through an example relating to the optimization of finite time controllers.

The ILAHS (inhomogeneous linear algebraic hybrid system) is a kind of classic hybrid system. For the purpose of optimizing the design of ILAHS, one important strategy is to introduce equivalence to reduce the states. Recent advances in the hybrid system indicate that approximate trace equivalence can further simplify the design of ILAHS. To address this issue, the paper first introduces the trajectory metric $d_{trj}$ for measuring the deviation of two hybrid systems’ behaviors. Given a deviation $\epsilon \ge 0$ , the original ILAHS of ${\mathcal{H}}_1$ can be transformed to the approximate ILAHS of ${\mathcal{H}}_2$ , then in trace equivalence semantics, ${\mathcal{H}}_2$ is further reduced to ${\mathcal{H}}_3$ with the same functions, and hence ${\mathcal{H}}_1$ is $\epsilon$ -approximate trace equivalent to ${\mathcal{H}}_3$ . In particular, $\epsilon =0$ is a traditional trace equivalence. We implement an approach based on RealRootClassification to determine the approximation between the ILAHSs. The paper also shows that the existing approaches are only special cases of our method. Finally, we illustrate the effectiveness and practicality of our method on an example.

Error coefficients are ubiquitous in systems. In particular, errors in reasoning verification must be considered regarding safety-critical systems. We present a reasoning method that can be applied to systems described by the polynomial error assertion (PEA). The implication relationship between PEAs can be converted to an inclusion relationship between zero sets of PEAs; the PEAs are then transformed into first-order polynomial logic. Combined with the quantifier elimination method, based on cylindrical algebraic decomposition, the judgment of the inclusion relationship between zero sets of PEAs is transformed into judgment error parameters and specific error coefficient constraints, which can be obtained by the quantifier elimination method. The proposed reasoning method is validated by proving the related theorems. An example of intercepting target objects is provided, and the correctness of our method is tested through large-scale random cases. Compared with reasoning methods without error semantics, our reasoning method has the advantage of being able to deal with error parameters.