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The paper presents the creation of a general mathematical model of a two-step optimization problem which finds the most energy efficient route where the battery and the electric engine of an electric-bicycle are used to minimum. In the first step, a multi-criteria problem is solved which finds the most efficient mode of operation of the battery and the engine in every segment part of the complete route. To solve this task a scalarization method is used (also known as weighted sum method). In the second step, a common most efficient route is found by applying a network optimization model. To find the solution a method of dynamic optimization is used Bellman's Principle. The major part of the paper is dedicated to the mathematical models, the approaches and the demonstration of the models’ workability. For this reason, the generation of data is based on the a priori known information as well as on information which is periodic and stochastic in the time and space.

Route optimization for long durability battery life during e-bike cycling