Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation

When a Genetic Algorithm (GA), or a stochastic algorithm in general, is employed in a statistical problem, the obtained result is affected by both variability due to sampling, that refers to the fact that only a sample is observed, and variability due to the stochastic elements of the algorithm. This topic can be easily set in a framework of statistical and computational tradeoff question, crucial in recent problems, for which statisticians must carefully set statistical and computational part of the analysis, taking account of some resource or time constraints. In the present work we analyze estimation problems tackled by GAs, for which variability of estimates can be decomposed in the two sources of variability, considering some constraints in the form of cost functions, related to both data acquisition and runtime of the algorithm. Simulation studies will be presented to discuss the statistical and computational tradeoff question.Comment: 17 pages, 5 figure

Designing a manufacturing cell system by assigning workforce

Purpose: In this paper, we have proposed a new model for designing a Cellular Manufacturing System (CMS) for minimizing the costs regarding a limited number of cells to be formed by assigning workforce. Design/methodology/approach: Pursuing mathematical approach and because the problem is NP-Hard, two meta-heuristic methods of Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms have been used. A small randomly generated test problem with real-world dimensions has been solved using simulated annealing and particle swarm algorithms. Findings: The quality of the two algorithms has been compared. The results showed that PSO algorithm provides more satisfactory solutions than SA algorithm in designing a CMS under uncertainty demands regarding the workforce allocation. Originality/value: In the most of the previous research, cell production has been considered under certainty production or demand conditions, while in practice production and demand are in a dynamic situations and in the real settings, cell production problems require variables and active constraints for each different time periods to achieve better design, so modeling such a problem in dynamic structure leads to more complexity while getting more applicability. The contribution of this paper is providing a new model by considering dynamic production times and uncertainty demands in designing cells.Peer Reviewe

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Consensus-Based Optimization with Truncated Noise

Consensus-based optimization~(CBO) is a versatile multi-particle metaheuristic optimization method suitable for performing nonconvex and nonsmooth global optimizations in high dimensions. It has proven effective in various applications while at the same time being amenable to a theoretical convergence analysis. In this paper, we explore a variant of CBO, which incorporates truncated noise in order to enhance the well-behavedness of the statistics of the law of the dynamics. By introducing this additional truncation in the noise term of the CBO dynamics, we achieve that, in contrast to the original version, higher moments of the law of the particle system can be effectively bounded. As a result, our proposed variant exhibits enhanced convergence performance, allowing in particular for wider flexibility in choosing the parameters of the method as we confirm experimentally. By analyzing the time-evolution of the Wasserstein-$2$ distance between the empirical measure of the interacting particle system and the global minimizer of the objective function, we rigorously prove convergence in expectation of the proposed CBO variant requiring only minimal assumptions on the objective function and on the initialization. Numerical evidences clearly demonstrate the benefit of truncating the noise in CBO.Comment: 23 page