How good are evolutionary algorithms with equality constraints?
I must add the objective function is specified as the sum of absolutes.
I need/ want to use equality constraints to guide the solution.
Some of the optimization coefficients (variable cells), when summed, must equal to a certain value.
Probably it depends on the ability of producing such coefficients. If the number of coefficients is constant, then you can alleviate this restriction by reducing one dimension. E.g. a+b+c is constant, so optimize the objective function by varying a and b; while c is set to (a+b+c)-(a+b). So, in this case, the performance of such evol.algo with restriction is as good as without restriction. If the number of coefficients is not constant, then the problem might be much more complex.
Thank you for the question and replies so far. My experience is that evolutionary algorithms (metaheuristics) are good for inequality constraints but not so for equality constraints. So, it is better to eliminate equality constraints to reduce the problem dimension before using evolutionary algorithms. When one equality constraint is eliminated to calculate one (dependent) variable, then inequality constraints may have to be added if there are lower and/or upper bounds on the (dependent) variable.
See the following book chapter for our study on using differential evolution for solving optimization problems with equality constraints.
Sharma S. and Rangaiah G.P., Improved Constraint Handling Technique for Multi-Objective Optimization with Application to Two Fermentation Processes in “Multi-Objective Optimization in Chemical Engineering: Developments and Applications” edited by G.P. Rangaiah and A. Bonilla-Petriciolet, John Wiley, 2013.
Thank you for the question. It's not possible to find a problem with inequalities constraints, even if we've an inequalities constraints, we can transform these in equalities constraints in introducing the slacks variables and this introducing will not influence the result. It's good to generalize the problem, and I conclude the evolutionnary algorithm are good for the problem in equalities constraints.
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