Elsevier

Computers & Chemistry

Volume 25, Issue 6, November 2001, Pages 583-595
Computers & Chemistry

Dynamic optimization of chemical processes using ant colony framework

https://doi.org/10.1016/S0097-8485(01)00081-XGet rights and content

Abstract

Ant colony framework is illustrated by considering dynamic optimization of six important bench marking examples. This new computational tool is simple to implement and can tackle problems with state as well as terminal constraints in a straightforward fashion. It requires fewer grid points to reach the global optimum at relatively very low computational effort. The examples with varying degree of complexities, analyzed here, illustrate its potential for solving a large class of process optimization problems in chemical engineering.

Introduction

Optimal design and control of industrially important chemical processes rely on dynamic optimization. Biegler (1984) and Logsdon and Biegler (1989) have been very successful in applying collocation based nonlinear programming techniques for optimal design of some chemical systems. Goh and Teo (1998) used control parameterization technique to solve a general class of optimization problems. Dadebo and McAuley (1995) used iterative dynamic programming method to solve several constrained dynamic optimization problems. Luus et al. (1992) while solving a bifunctional catalyst problem has shown that there exists as many as 25 local optima for this problem. Their work suggests that it would be improper to rely on a single optimization technique for successfully obtaining a global optimum. It is now well established that evolutionary algorithms like Genetic Algorithms and Simulated Annealing can be used for obtaining global optimum for a very large class of optimization problems. These have recently been used for molecular catalyst design, heat and mass exchange networks, heat integrated unit operations and batch scheduling problems (Cardoso et al., 1994, Stair and Fraga, 1995, McLeod et al., 1997, Garad and Fraga, 1998, Jung et al., 1998, Tayal et al., 1999). In this work we introduce ‘Ant Colony’ framework, a new evolutionary technique, for dynamic optimization problems encountered in chemical process design. This algorithm was applied to solve six benchmark examples with varying degree of complexities. A brief account of the ant colony technique is provided in the next section before subsequently adapting it to dynamic optimization problems.

Section snippets

Ant colony algorithm — an overview

Proposed by Marco Dorigo and coworkers (Colorni et al., 1991, Dorigo et al., 1996), the algorithm has since been applied to a variety of problems like, quadratic assignment problem (Maniezzo et al., 1994, Gambardella et al., 1999), travelling salesman problem (Dorigo and Gambardella, 1997), heat and power system optimization (Chou and Song, 1997), communication networks (Di Caro and Dorigo, 1998), batch scheduling problem (Jayaraman et al., 2000), continuous function optimization (Mathur et

Problem formulation

The structure of a typical dynamic optimization problem is given below:OptimizeF(x̄,u)such thatdxidt=Gi(x̄,u),i=1,2,…ngiven x̄(0), where u is the control variable bounded umax and umin.umin≤u≤umax0≤t≤tfH(x̄,u)≤0,andI(x̄,u)=0.where H(x̄,u) and I(x̄,u) are inequality and equality constraints involving state and control variable(s), respectively.

Ant colony algorithm

The step by step description of the ant algorithm for solving the dynamic optimization problems is given below:

Results and discussion

The ant colony algorithm was tested on six examples from the literature. The details of the problems are provided in Table 1. The examples were chosen in a manner to illustrate the ability of the ant system to cater to the problems of varying levels of difficulty. For each problem, 25 runs were taken in order to ensure that the seed used for the random number generator did not bear any influence on the quality of the results obtained. To treat constraints, the penalty function approach was

Conclusions

In this work, we have illustrated the utility of the ant colony algorithm for solving dynamic optimization problems. The algorithm is very simple and is able to take care of problems with state as well as terminal constraints. The computational requirements are very nominal. The penalty factor approach has been used for treating the constraints giving excellent results with very small or no violation of the constraints. Dynamic optimization problems involving applications of the optimal control

References (30)

  • L.T. Biegler

    Comput. Chem. Engng

    (1984)
  • S.A. Dadebo et al.

    Comput. Chem. Engng

    (1995)
  • D.J. Gunn et al.

    Chem. Engng Sci.

    (1965)
  • V.K. Jayaraman et al.

    Comput. Chem. Engng

    (2000)
  • A.S. McLeod et al.

    J. Catal.

    (1997)
  • J.G. Renfro et al.

    Comput. Chem. Engng

    (1987)
  • D. Tieu et al.

    Comput. Chem. Engng

    (1995)
  • M.F. Cardoso et al.

    Ind. Engng Chem. Res.

    (1994)
  • Chou, C.S., Song, Y.S., 1997. Ant Colony — Tabu Approach for Combined Heat and Power Economic Dispatch. 32nd University...
  • A. Colorni et al.

    Distributed optimization by ant colonies

  • G. Di Caro et al.

    J. Artif. Intell. Res.

    (1998)
  • M. Dorigo et al.

    IEEE Trans. Evol. Comput.

    (1997)
  • M. Dorigo et al.

    IEEE Trans. Sys. Man. Cybernetics

    (1996)
  • L.M. Gambardella et al.

    J. Op. Res. Soc.

    (1999)
  • A. Garad et al.

    Comput. Chem. Engng

    (1998)
  • Cited by (99)

    • Hybrid stochastic optimization method for optimal control problems of chemical processes

      2017, Chemical Engineering Research and Design
      Citation Excerpt :

      In order to raise the productivity, profitability and/or efficiency of chemical processes, many contributions have been devoted to their improvement using computer aided chemical process engineering approaches. Thus, mathematical modeling of chemical process systems, dynamic optimization, and system control have been becoming basic tools to optimization design and operate production facilities in the chemical process industry sector (Rajesh et al., 2001; Balsa-Canto et al., 2001; Babu and Angira, 2006; Pham, 2012; Qian et al., 2012, 2013; Chen et al., 2014). However, because of nonlinearity which is characteristic of the chemical processes and the existence of equality and/or inequality control input constraints, it is very difficult to choose the optimal operating strategies.

    • Multi-objective differential evolution with performance-metric-based self-adaptive mutation operator for chemical and biochemical dynamic optimization problems

      2017, Applied Soft Computing Journal
      Citation Excerpt :

      And the times of independent runs are set to be 20 in all experiments. This problem is considered as a single objective optimization in most cases and its objective is to achieve the maximal concentration of B. For example, values of 0.610775, 0.6104, and 0.61045 are achieved by Asgari et al. [61], Zhang et al. [62], and Rajesh et al. [63], respectively. Additionally, this problem has also been considered as a MOP has been solved by Jia et al. [36] and Chen et al. [37].

    View all citing articles on Scopus
    1

    Present address: Indian Institute of Technology, Bombay, India.

    View full text