Application of sequential quadratic programming based on active set method in cleaner production

Li Xia,Jianyang Ling,Rongshan Bi,Wenying Zhao,Shuguang Xiang,Zhen Xu

doi:10.1007/s10098-021-02207-8

Abstract

On the platform of general chemical process simulation software (it was named Optimization Engineer, OPEN), a general optimization algorithm for chemical process simulation is developed using C + + code. The algorithm is based on sequential quadratic programming (SQP). We adopt the activity set algorithm and the rotation axis algorithm to generate the activity set to solve the quadratic programming sub-problem. The active set method can simplify the number of constraints and speed up the calculation. At the same time, we used limited memory BFGS algorithm (L-BFGS) to simplify the solution of second derivative matrix. The special matrix storage mode of L-BFGS algorithm can save the storage space and speed up the computing efficiency. We use exact penalty function and traditional step-size rule in the algorithm. These two methods can ensure the convergence of the algorithm, a more correct search direction and suitable search step. The example shows that the advanced optimization function can meet the requirements of General Chemical Process Calculation. The number of iterations can reduce by about 6.0%. The computation time can reduce by about 6.5%. We combined this algorithm with chemical simulation technology to develop the optimization function of chemical engineering simulation. This optimization function can play an important role in the process optimization calculation aiming at energy saving and green production.

Highlights

As one of the pillar industries of economic development, the chemical industry has the characteristics of high energy consumption and high pollution
The limited memory BFGS algorithm (L-BFGS) algorithm is similar to the BFGS algorithm, but the L-BFGS algorithm needs less memory to store matrix
The active set method obtains the feasible points of the QP sub-problem, which makes the optimization problem easier to converge, and the calculation speed is faster

Summary

Introduction

As one of the pillar industries of economic development, the chemical industry has the characteristics of high energy consumption and high pollution. The search steps are usually determined by the value functions in the algorithm, such as the l1 value function and the Fletcher value function Both methods have simple forms and ideal numerical results, and are suitable for chemical simulation and optimization. The calculation steps of the algorithm are as follows: 1) Obtain the objective function and constraint function input by the user; 2)Use general chemical process simulation and optimization software process simulation function to calculate the objective function and constraint function value; 3) Find the gradient, given the initial identity matrix Bk; 4) Solve the sub-problem (3) with the active set method, and get dk; 5) Calculate the convergence and output the result; otherwise, proceed to the step; 6) Use l1 value function and Armijo criterion; 7) Let k:=k+1, continue to step 3. The activity set method is a feasible point method, which can avoid unnecessary computation and iterative search

Conclusion

Findings

Methods and