Dynamic optimization of chemical processes using ant colony framework
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:such thatgiven where u is the control variable bounded umax and umin.andwhere and 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
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Present address: Indian Institute of Technology, Bombay, India.