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Computational Intelligence Based Methodologies for Modeling and Optimization. Somnath Nandi Asst. Professor Dept. of Petroleum and Petrochemical Engineering MIT - Pune. Contents. Modeling Artificial Neural Networks Optimization Genetic Algorithms Differential Evolution Case Study
Dept. of Petroleum and Petrochemical Engineering
MIT - Pune
- Process behavior described in terms of the appropriate mass, momentum and energy balance equations together with the pertinent chemical engineering principles.
- Mathematical formulation describing the physico-chemical phenomena underlying in the process is formulated followed by model fitting.
- Regression techniques based on the least squares minimization
- It provides a valuable insight into the process behavior
- It possesses extrapolation ability
- Owing to the complex nature of many processes, the underlying physico-chemical phenomenon is seldom fully understood
- Collection of the requisite phenomenological information is costly, time-consuming and tedious
- Nonlinear behavior common for many processes leads to complex nonlinear models, which in most cases are not amenable to analytical solutions; thus, computationally intensive numerical methods must be utilized for obtaining solutions
- Process behavior is modeled using appropriately chosen empirical equations, for instance, polynomial expressions.
- Model can be constructed solely from the process input-output data without explicitly invoking the process phenomenology.
- An appropriate functional form that possibly fits the process data is selected in advance following which the unknown model parameters are estimated using a suitable function fitting procedure.
- AI is science and engineering of making “intelligent” systems, especially intelligent computer programs
- Related to task of using computers to understand the “human intelligence”
- Intelligence can be broadly defined as computational part of our ability to efficiently achieve goals in the world.
(i) nonlinear function approximation (i.e., process modeling),
(ii) pattern recognition and classification,
(iii) data reduction and compression,
(iv) signal processing,
(v) noise reduction.
min f (x) Goal function
g (x) = 0 Equality constraints
h (x) < 0 Inequality constraints
(1) critical analysis of the process or design,
(2) insight about what appropriate performance objectives are (what is to be accomplished),
(3)use of past experience, sometimes called engineering judgment.
A function exhibiting different types of stationary points.
a-inflection point (scalar equivalent to a saddle point);
Minimize f1(x) (1)
Minimize f2(x) (2)
With respect to x
Subject to xL ≤ x ≤ xU (3)
h (x) = 0 (4)
g (x) ≤ 0 (5)
- Survival of the fittest
- Evolution of species with time
Let us consider the maximization problem:
- Variable xi are first coded into binary strings
- Length of string is determined based on desired accuracy of solution
- GA are based on survival-of-the-fittest
- Naturally suitable for solving maximization problems
- Minimization are transformed to suitable maximization ones
- Fitness function is a measure of goodness of the string
- Our target is to keep on increasing the overall fitness functions of all the strings
- Genetic operators perform duty to manipulate binary strings so that fitness function is keep on increasing on successive iterations
- Reproduction / Selection
- New strings are created
- It exchanges information among
strings of mating pool
- 2 strings are picked at random
- Point of crossover is probabilistically chosen
- It changes 1 to 0 and vice versa
- Small probability pm generally < 0.1
- Need is to create a point in the neighborhood of the current point
- Performs local search around current solution
- It maintains diversity of population
- Real variables are directly used
- Optimal point of any desired accuracy obtained
- To keep versatility of population
- Give more chance to a poor performer to enhance its skills
- Population in a GA simulation is adaptively divided into separate subpopulation, corresponding to each optimum point by use of sharing functions
- Can get all the solutions of Pareto Optimal front in one shot
– Cumene Synthesis
- Phenol Production
– MMA Synthesis
- Polyethylene Plant
- Nylon Manufacture
- Generate new vector by adding weighted difference of two vectors to third
- Mix new vector with target vector to yield trial vector
- Replace target vector with trial vector if latter is strictly superior
Somewhat slow during initial iterations
Benzene + Isopropyl Alcohol Cumene + Water
Cumene + Isopropyl Alcohol p-Di-isopropyl Benzene + Water
p-Di-isopropyl Benzene m-Di-isopropyl Benzene (isomerization)
2 Isopropyl alcohol Di-isopropyl ether + Water
- population size (Npop) = 25
- crossover probability (pcross) = 0.82
- mutation probability (pmut) = 0.05
- maximum number of generations (Ngen) = 100
Published in Chemical Engineering Journal, Vol. 97, No. 2 – 3, pg: 115 – 129 (2004)