Dynamic Modeling and Multi-Objective Energy Optimization of Nepalese Manufacturing Systems Using AI and Numerical Differential Equation Methods

Abstract

Manufacturing plants in Nepal need operating decisions that lower energy cost without compromising delivery, yet few analytical tools link plant dynamics, electricity tariffs and optimisation in a transparent and reproducible way. This paper develops and tests such a workflow on a representative electrically heated batch-processing line. A six-state ordinary-differential-equation (ODE) model couples process temperature, order backlog, energy, cost, throughput and cumulative del.ay. Seven numerical integrators (Euler, Heun, RK4, RK45, DOP853, Radau and BDF) are verified against a high-accuracy reference; multilayer-perceptron, random-forest and gradient-boosting surrogates are trained on Latin-hypercube simulations; and NSGA-II is used to minimise specific energy consumption, energy cost per unit and a backlog-delay index. Fixed-step RK4 with a two-minute step reproduced reference objectives to within 3.4×10−5 relative error across 30 random designs, whereas a loose adaptive tolerance (10−3) produced temperature errors above 3 °C. A neural surrogate reached R2 ≥ 0.998 from 3,000 simulations. Setpoint temperature explained 76–89% of output variance (first-order Sobol indices). A compromise operating point cut energy per unit by 8.7% and cost per unit by 9.5% relative to a conventional baseline, and a “no-regret” point cut 8.1% and 9.1% with no delay penalty; energy and cost gains held in all 2,000 parameter-uncertainty draws. Surrogate-assisted search with 400 simulations did not outperform random sampling at equal budget. Because plant parameters are assumed rather than measured, the numerical values are illustrative; the contribution is the verified workflow and the trade-off structure it exposes.