CODEWITHSUNDEEP
algorithmmatlab
Ehsa
Ehsa

Reputation: 121

Multi objective convex optimization using genetic algorithm or cvx tool

I have solved a single objective convex optimization problem (actually related to reducing interference reduction) using cvx package with MATLAB. Now I want to extend the problem to multi objective one. What are the pros-cons of solving it using genetic algorithm in comparison to cvx package? I haven't read anything about genetic algorithms and it came about by searching net for multiobjective optimization.

Upvotes: 1

Views: 826

Answers (1)

Sunghee Yun
Sunghee Yun

Reputation: 820

The optimization algorithms based on derivatives (or gradients) including convex optimization algorithm essentially try to find a local minimum. The pros and cons are as follows.

Pros: 1. It can be extremely fast since it only tries to follow the path given by derivative. 2. Sometimes, it achieves the global minimum (e.g., the problem is convex).

Cons: 1. When the problem is highly nonlinear and non-convex, the solution depends on initial point, hence there is high probability that the solution achieved is far from the global optimum. 2. It's not quite for multi-objective optimization problem.

Because of the disadvantages described above, for multi-objective optimization, we generally use evolutionary algorithm. Genetic algorithms belong to evolutionary algorithm.

Evolutionary algorithms developed for multi-objective optimization problems are fundamentally different from the gradient-based algorithms. They are population-based, i.e., maintain multiple solutions (hundreds or thousands of them) where as the latter ones maintain only one solution.

NSGA-II is an example: https://ieeexplore.ieee.org/document/996017, https://mae.ufl.edu/haftka/stropt/Lectures/multi_objective_GA.pdf, https://web.njit.edu/~horacio/Math451H/download/Seshadri_NSGA-II.pdf

The purpose of the multi-objective optimization is find the Pareto surface (or optimal trade-off surface). Since the surface consists of multiple points, population-based evolutionary algorithms suit well.

(You can solve a series of single objective optimization problems using gradient-based algorithms, but unless the feasible set is convex, it cannot find them accurately.)

Upvotes: 1

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