## 1 Introduction
Generally, optimization-based control methods include PMP, QP, DP, and convex optimization [6]. The PMP algorithm is applied to achieve the energy management adaptively for the GM Chevrolet Volt [33]. Nevertheless, a complex Hamilton function and the local optimum solution need to be solved and determined. In Ref. [22], the energy management strategy is optimized by the QP algorithm to reduce the engine fuel consumption, whereas this algorithm does not consider the influence of the initial SOC variation. In Ref. [17], the DP based energy management strategy is constructed, which considered the discretization resolution of the relevant variables and the boundary constraint of their feasible regions. Currently, convex optimization has been substantially applied to energy management optimization of traditional HEVs and PHEVs [24; 34; 35; 36]. In Ref. [34], a convex programming-based power management strategy of a PHEV, which covers expenditures of electricity charged from the grid, fuel consumed during on-road driving, and battery aging. In Ref. [36], a novel convex modeling approach is presented which allows for battery sized and energy management of a plug-in hybrid powertrain based on a semidefinite program. However, some fixed control parameters, such as the engine-on power, cannot be estimated by the convex optimization [37]. In order to calculate these variables, randomized heuristic searching algorithm are applied, such as genetic algorithm (GA), simulated annealing (SA). Compared with GA algorithm, the SA algorithm is simpler and with higher efficiency, which can search the optimal solution more quickly. Due to these merits, the SA algorithm has been applied in the research of energy management for HEVs and PHEVs [22; 38; 39]. Compared with the optimization-based method, the optimal control parameters of analytic method and rule-based energy management strategy for PHEV can be obtained difficultly. Even the intelligent based method for PHEV has been widely applied, nevertheless, the intelligent based control method is complex and difficult to find the optimal solutions. The optimization-based method can obtain the global optimal solutions, improve the vehicle's control performance and engine fuel economy. Motivated by these, we plan to compare the performance among different methods. In this paper, there typical methods including the CD/CS method, the DP method, and an intelligent method, i.e., SA combing with the convex optimization are employed to compare the fuel economy for a parallel PHEV. As shown in Figure 1, the parallel PHEV can be powered by the engine and motor together. Since the gearbox can select the gear ratio according to the power and speed demand from the driveline, there exist two degrees of freedom in the vehicle, which increases certain complexity to decouple the powertrain dynamics. In order to simplify the problem, an automated gear shift rule strategy is adopted considering the vehicle speed. By this manner, the degrees of freedom changes from two to one and the problem becomes easier to solve. In this paper, the optimization purpose is to minimize the fuel consumption in a certain trip. Based on analysis of the energy flow and the vehicle working modes, the vehicle driveline system is simplified and translated into a series of quadratic equations, which can effectively express the relationship between the engine fuel rate and the battery power at different power demand and velocity. The SA algorithm is implemented to search the optimal engine-on power, in which the optimal sequence of battery power is optimized simultaneously by CP. With considering the referred discussions, the optimal engine-on power is quickly searched by the SA algorithm and then the battery power command is calculated by convex optimization algorithm based on the interior point method. Highway Fuel Economy Driving Schedule (HWFET), New European Driving Cycle (NEDC), and Urban Dynamometer Driving Schedule (UDDS) are selected as test cycles to verify the performance of the proposed algorithm.