Optimization In Parameter Space Research Articles

A review of practice of using evolutionary algorithms for neural network synthesis and training

The object of this research is the application of evolutionary algorithms for the synthesis and training of neural networks. The paper aims to select and review the existing experience on using evolutionary algorithms as competitive methods to conventional approaches in neural network training and creation, and to evaluate such existing solutions for further development of this field. The essence of the obtained results lies in the successful application of genetic algorithms in conjunction with neural networks to optimize parameters, architecture, and weight coefficients of the networks. The genetic algorithms allowed improving the performance and accuracy of neural networks, especially in cases where backpropagation algorithms faced difficulties in finding optimal solutions. These results can be attributed to the fact that genetic algorithms are efficient methods for global optimization in parameter space. They help avoid local minima and discover more reliable and stable solutions. The obtained findings can be practically utilized to enhance the performance and quality of neural networks in various classification and prediction tasks. The use of genetic algorithms enables the selection of optimal weight coefficients, network connections, and identification of significant features from the dataset. However, they come with the limitation of additional time costs for evaluating the entire population according to the selection criteria. It is worth noting that the application of genetic algorithms is not a universal method for all tasks, and the algorithm parameters should be individually tuned for each specific problem. Further research could focus on refining the combination methods of genetic algorithms and neural networks, as well as exploring their application in new domains and tasks.

Structured controller synthesis through block-diagonal factorization and parameter space optimization

Constraints on the feedback structure arise in many control systems due to implementing cost, hardware limitations and operational reliability. The parameter space method aims to solve the robust structured controller design problems based on a convex reformulation technique. Despite its attractiveness, the structural constraints are limited to be either decentralized or linear dependence among entries within the same row or column in the current literature. And the global optimal solution is yet to be guaranteed, since a non-convex constraint is introduced in the parameter space after reformulating it as the output feedback synthesis problem. In this paper, we extend the parameter space method to a more generalized structured optimal control problem, such that the linear dependence can occur among its arbitrary entries. A bilinear factorization to the feedback gain matrix is proposed by a special Kronecker product decomposition. Subsequently, an equivalent transformation is proposed to convert this structured control design problem to a controller synthesis problem under decentralized full-state feedback. Thereby, the prior non-convex constraint in the parameter space is removed and the globally optimal structured controller is synthesized by convex programming. Examples such as integrated design and formation control demonstrate its practical appeals.

Few-Shot Quality-Diversity Optimization

In the past few years, a considerable amount of research has been dedicated to the exploitation of previous learning experiences and the design of Few-shot and Meta Learning approaches, in problem domains ranging from Computer Vision to Reinforcement Learning based control. A notable exception, where to the best of our knowledge, little to no effort has been made in this direction is Quality-Diversity (QD) optimization. QD methods have been shown to be effective tools in dealing with deceptive minima and sparse rewards in Reinforcement Learning. However, they remain costly due to their reliance on inherently sample inefficient evolutionary processes. We show that, given examples from a task distribution, information about the paths taken by optimization in parameter space can be leveraged to build a prior population, which when used to initialize QD methods in unseen environments, allows for few-shot adaptation. Our proposed method does not require backpropagation. It is simple to implement and scale, and furthermore, it is agnostic to the underlying models that are being trained. Experiments carried in both sparse and dense reward settings using robotic manipulation and navigation benchmarks show that it considerably reduces the number of generations that are required for QD optimization in these environments.

Parameter Space Optimization Towards Constrained Controller Design With Application to Tray Indexing

Tray indexing driven by timing belt actuator is widely used in the industry, where high-precision profile tracking is essential to guarantee good production quality. To avoid humming sound and chip dislodged, an autonomous S-curve trajectory is used as the reference profile and the jerk resulting from the control input chattering needs to be well controlled. To implement the optimal tracking control with respect to an S-curve profile and maintain a guaranteed adequate level of performance towards the perturbation, the composite system is constructed by augmenting the S-curve trajectory with the system model and an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> guaranteed cost optimization problem is formulated. The system performance in terms of tracking accuracy and jerk minimization is quantified as the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm, and it aims to minimize the upper bound to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm over the uncertain domain. However, due to structural constraints on the composite gain matrix as well as robustness requirement, the algebraic Riccati equations cannot be used. This article presents the theoretical results where all the stabilizing constrained gain matrices can be parameterized over an extended matrical set. Efficient numerical procedures are developed to obtain the ε-optimum with guaranteed robustness by linear programming and outer linearization in an iterative framework. Numerical optimization and experiments are conducted to validate the theoretical results and the practical appeal of the proposed approach.

Parameter space optimization towards integrated mechatronic design for uncertain systems with generalized feedback constraints

There is an increasing trend to apply integrated mechatronic design approaches in precision engineering to synthesize key mechanical and controller parameters simultaneously. However, such technique is yet to be mature, due to the constraints imported by mechanical design and feedback control, as well as the existence of model uncertainties. In this work, we treat the integrated mechatronic design problem as a controller optimization problem with structural constraints. We start from the case when the composite feedback gain matrix (CFGM) has some elements either being zero or with equal or opposite relationships. First, algorithms are proposed to factorize the CFGM. Secondly, the feedback constraints are transformed from the state space to an extended parameter space. In this way, the design problem is reformulated as minimizing the ℋ2-norm upper bound of the closed-loop system transmittance from the exogenous disturbance to the regulated variables over the intersection of convex and non-convex domains. Eventually, cutting-plane-based numerical procedures are developed to obtain a global optimal solution, and the closed-loop robust stability is ensured with guaranteed performance. An illustrative example on a flexure-linked biaxial gantry stage is presented to reveal the practical appeal of the proposed approach. This approach is extensively applicable to a class of optimal control problems, such as controller synthesis problem with prescribed sparsity pattern, decentralized control problem with/without structural constraints, etc.

A combined steepest descent and genetic algorithm (SD/GA) approach for the optimization of solvation parameters

An accurate solvation model is essential for computer modeling of protein folding and other biomolecular self-assembly processes. Compared to explicit solvent models, implicit solvent models, such as the Poisson-Boltzmann (PB) with solvent accessible surface area model (PB/SA), offer a much faster speed—the most compelling reason for the popularity of these implicit solvent models. Since these implicit solvent models typically use empirical parameters, such as atomic radii and the surface tensions, an optimal fit of these parameters is crucial for the final accuracy of properties such as solvation free energy and folding free energy. In this paper, we proposed a combined approach, namely SD/GA, which takes the advantage of both local optimization with the steepest descent (SD), and global optimization with the genetic algorithm (GA), for parameters optimization in multi-dimensional space. The SD/GA method is then applied to the optimization of solvation parameters in the non-polar cavity term of the PB/SA model. The results show that the newly optimized parameters from SD/GA not only increase the accuracy in the solvation free energies for ∼200 organic molecules, but also significantly improve the free energy landscape of a β-hairpin folding. The current SD/GA method can be readily applied to other multi-dimensional parameter space optimization as well.

Optimizing cosmological surveys in a crowded market

Optimizing the major next-generation cosmological surveys (such as SNAP, KAOS, etc.) is a key problem given our ignorance of the physics underlying cosmic acceleration and the plethora of surveys planned. We propose a Bayesian design framework which (1) maximizes the discrimination power of a survey without assuming any underlying dark-energy model, (2) finds the best niche survey geometry given current data and future competing experiments, (3) maximizes the cross section for serendipitous discoveries and (4) can be adapted to answer specific questions (such as ``is dark energy dynamical?''). Integrated parameter-space optimization (IPSO) is a design framework that integrates projected parameter errors over an entire dark energy parameter space and then extremizes a figure of merit (such as Shannon entropy gain which we show is stable to off-diagonal covariance matrix perturbations) as a function of survey parameters using analytical, grid or MCMC techniques. We discuss examples where the optimization can be performed analytically. IPSO is thus a general, model-independent and scalable framework that allows us to appropriately use prior information to design the best possible surveys.