A Parallel Evolution Strategy for Acoustic Full-Waveform Inversion

In this work, we propose another alternative to find an initial velocity model for the acoustic FWI without any physical knowledge. Motivated by the recent growth of high performance computing (HPC), we tackle the high non-linearity of the problem to minimize, using global optimization methods which are easy to parallelize, in particular, evolution strategies. The first contribution adapt evolution strategies to the FWI setting where the cost function evaluation is the most expensive part. The second contribution is the parameterization of the regarded problem, by being able to represent the model, as faithfully as possible, while limiting the number of parameters needed, since each additional parameter is an additional dimension to explore. The last contribution is to propose a highly parallel evolution strategy adapted to the FWI setting. The initial results on the Salt Dome velocity model using low frequency range, show that great improvement can be done to automate the FWI

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Alternative Restart Strategies for CMA-ES

This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing