The solution of non-linear geophysical inverse problems presents several challenges mainly related to the possibility of convergence toward a local minimum of the objective function. For this reason, global optimization methods are often preferred over linearized approaches especially in case of objective functions with complex topology (i.e. many local minima). In particular, over the last decade the continuously increasing power of modern parallel architectures has considerably encouraged the application of these global methods to solve many geophysical optimization problems (Sen and Stoffa, 2013). Since the ‘70s, tens of global algorithms have been implemented (for a synthetic list see Hosseini and Al Khaled 2014). However, many of these methods have found applications in engineering optimizations (i.e. computer engineering, industrial engineering, mechanical engineering) and only a small subset of them has been employed to tackle geophysical exploration problems. In this context, genetic algorithms, simulated annealing and particle swarm are undoubtedly the most popular (Sajeva et al. 2017). Notably, the performances of these global methods are different for different optimization problems and strongly depend on the shape of the objective function and on the model space dimension (i.e. the number of unknowns). For this reason, in this work we are interested in comparing the performances of three global optimization algorithms: The Firefly Algorithm (FA), the Imperialist Competitive Algorithm (ICA) and the Quantum Particle Swarm Optimization (QPSO). These methods have been introduced in the last few years and have found very limited popularity in the geophysical community so far. In particular, as the authors are aware of, there are no applications of ICA and FA approaches in the context of seismic exploration problems. The three methods are first tested on two multi-minima analytic objective functions often used to test optimization algorithms. Then, the three algorithms are compared on the residual statics corrections, which is a highly non-linear geophysical optimization problem characterized by an objective function with multiple minima. We remind, that the performances of a stochastic method in solving a particular problem may critically depend on the choice of the control parameters. Generally, it is difficult to give hard and fast rules that may work with a wide range of applications, although some guidelines and rules of thumb can be dictated by experience. The control parameters used in the following tests have been determined from a trial-and-error procedure with the aim of balancing the rate of convergence with the accuracy of the final solution.

Comparing Firefly Algorithm, Imperialist Competitive Algorithm and Quantum Particle Swarm Optimization on analytic objective functions and residual statics corrections

Mattia Aleardi
;
PIERINI, SILVIO
2018

Abstract

The solution of non-linear geophysical inverse problems presents several challenges mainly related to the possibility of convergence toward a local minimum of the objective function. For this reason, global optimization methods are often preferred over linearized approaches especially in case of objective functions with complex topology (i.e. many local minima). In particular, over the last decade the continuously increasing power of modern parallel architectures has considerably encouraged the application of these global methods to solve many geophysical optimization problems (Sen and Stoffa, 2013). Since the ‘70s, tens of global algorithms have been implemented (for a synthetic list see Hosseini and Al Khaled 2014). However, many of these methods have found applications in engineering optimizations (i.e. computer engineering, industrial engineering, mechanical engineering) and only a small subset of them has been employed to tackle geophysical exploration problems. In this context, genetic algorithms, simulated annealing and particle swarm are undoubtedly the most popular (Sajeva et al. 2017). Notably, the performances of these global methods are different for different optimization problems and strongly depend on the shape of the objective function and on the model space dimension (i.e. the number of unknowns). For this reason, in this work we are interested in comparing the performances of three global optimization algorithms: The Firefly Algorithm (FA), the Imperialist Competitive Algorithm (ICA) and the Quantum Particle Swarm Optimization (QPSO). These methods have been introduced in the last few years and have found very limited popularity in the geophysical community so far. In particular, as the authors are aware of, there are no applications of ICA and FA approaches in the context of seismic exploration problems. The three methods are first tested on two multi-minima analytic objective functions often used to test optimization algorithms. Then, the three algorithms are compared on the residual statics corrections, which is a highly non-linear geophysical optimization problem characterized by an objective function with multiple minima. We remind, that the performances of a stochastic method in solving a particular problem may critically depend on the choice of the control parameters. Generally, it is difficult to give hard and fast rules that may work with a wide range of applications, although some guidelines and rules of thumb can be dictated by experience. The control parameters used in the following tests have been determined from a trial-and-error procedure with the aim of balancing the rate of convergence with the accuracy of the final solution.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/934967
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