Uncertainty on multi-objective optimization problems

In general, parameters in multi-objective optimization are assumed as deterministic with no uncertainty. However, uncertainty in the parameters can affect both variable and objective spaces. The corresponding Pareto optimal fronts, resulting from the disturbed problem, define a cloud of curves. In this work, the main objective is to study the resulting cloud of curves in order to identify regions of more robustness and, therefore, to assist the decision making process. Preliminary results, for a very limited set of problems, show that the resulting cloud of curves exhibits regions of less variation, which are, therefore, more robust to parameter uncertainty.The authors would like to thank FCT - Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) that supported in part this work

Stochastic algorithms assessment using performance profiles

Optimization with stochastic algorithms has become a relevant approach, specially, in problems with complex search spaces. Due to the stochastic nature of these algorithms, the assessment and comparison is not straightforward. Several performance measures have been proposed to overcome this difficulty. In this work, the use of performance profiles and an analysis integrating a trade-off between accuracy and precision are carried out for the comparison of two stochastic algorithms. Traditionally, performance profiles are used to compare deterministic algorithms. This methodology is applied in the comparison of two stochastic algorithms - genetic algorithms and simulated annealing. The results highlight the advantages and drawbacks of the proposed assessment.The authors would like to thank FCT - Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) that supported in part this wor

Heuristic pattern search for bound constrained minimax problems

This paper presents a pattern search algorithm and its hybridization with a random descent search for solving bound constrained minimax problems. The herein proposed heuristic pattern search method combines the Hooke and Jeeves (HJ) pattern and exploratory moves with a randomly generated approxi- mate descent direction. Two versions of the heuristic algorithm have been applied to several benchmark minimax problems and compared with the original HJ pat- tern search algorithm

Percolation Effects in Very High Energy Cosmic Rays

Most QCD models of high energy collisions predict that the inelasticity $K$ is an increasing function of the energy. We argue that, due to percolation of strings, this behaviour will change and, at $\sqrt{s} \simeq 10^4$ GeV, the inelasticity will start to decrease with the energy. This has straightforward consequences in high energy cosmic ray physics: 1) the relative depth of the shower maximum $\bar{X}$ grows faster with energy above the knee; 2) the energy measurements of ground array experiments at GZK energies could be overestimated.Comment: Correction of equation (19) and figures 3 and 4. 4 pages, 4 figure

On optimizing a WWTP design using multi-objective approaches

In this paper, the multi-objective formulation of an optimization problem arising from an activated sludge (AS) system of a wastewater treatment plant (WWTP) design optimization is solved through a multi-objective genetic algorithm. Two multi-objective approaches are proposed. First, a solution to the WWTP design is provided, regardless of its location, date of construction or the involved unit operations. The variables that mostly influence the cost of the system define the objectives and are simultaneously optimized. Second, two crucial objectives for the correct operation of the AS system are simultaneously optimized: the investment and operation costs are minimized and the effluent quality is maximized. Since the objectives are conflicting, several trade-offs between objectives are obtained through the optimization process. The direct visualization of the trade-offs through Pareto curves assists the decision-maker in the selection of crucial design and operation variables. The numerical results show that the proposed methodology produces improved results with physical meaning when compared with previous work.Fundação para a Ciência e a Tecnologia (FCT

A hybrid genetic pattern search augmented Lagrangian method for constrained global optimization

Hybridization of genetic algorithms with local search approaches can enhance their performance in global optimization. Genetic algorithms, as most population based algorithms, require a considerable number of function evaluations. This may be an important drawback when the functions involved in the problem are computationally expensive as it occurs in most real world problems. Thus, in order to reduce the total number of function evaluations, local and global techniques may be combined. Moreover, the hybridization may provide a more effective trade-off between exploitation and exploration of the search space. In this study, we propose a new hybrid genetic algorithm based on a local pattern search that relies on an augmented Lagrangian function for constraint-handling. The local search strategy is used to improve the best approximation found by the genetic algorithm. Convergence to an $\varepsilon$-global minimizer is proved. Numerical results and comparisons with other stochastic algorithms using a set of benchmark constrained problems are provided.FEDER COMPETEFundação para a Ciência e a Tecnologia (FCT

On the factor structure of the Dissociative Experiences Scale:ontribution with an Italian version of the DES-II

Aim of the study: Notwithstanding its clinical and empirical relevance, there is no consensus on how to conceptualize dissociation. This may be partly due to the conflicting results yielded on the factor structure of the gold-standard selfreport measure of dissociation (the Dissociative Experiences Scale-Revised; DES-II, Carlson and Putnam, 1993). In an attempt to advance research on this topic, we sought to explore the factorial structure of an Italian version of the DES-II. Material and methods: A sample of 320 subjects (122 inmates and 198 community participants) was administered the Italian version of the DES-II. Results: The Italian version of the DES-II showed good psychometric properties and replicated a two-factor structure. Items content seemed to support the distinction into two qualitatively different forms of dissociative experiences, described as detachment and compartmentalization phenomena. In line with the expectations, participants in the inmate sample reported higher rates of dissociative experiences than community participants, on both dimensions. Conclusions: This study provides further support for the validity of the Italian version of the DES-II for use with community and inmate samples. Furthermore, we corroborated previous evidence on a two-factor structure of the DES-II, which is consistent with theoretical assumptions describing two distinct, albeit overlapping, dissociative dimensions (i.e., detachment and compartmentalization)

Optimização de um sistema de lamas activadas por um algoritmo genético

Apresenta-se, neste artigo, um problema de optimização relacionado com um processo biológico de tratamento de águas residuais. A formulação matemática que surge da modelação de um sistema de lamas activadas de uma ETAR é optimizado, em termos de custos de investimento e custos operacionais, através de um algoritmo genético. É usado o modelo ASM1 para as lamas activadas, um dos modelos matemáticos mais difundidos e aceites pela comunidade científica. Para o sedimentador secundário é usado um modelo que combina as normas ATV e o modelo da dupla exponencial. Trata-se de uma formulação matemática de elevada complexidade. O modelo está disponível em MatLab e AMPL, e foi resolvido por uma heurística que garante convergência para um óptimo global do problema. Esta heurística baseia-se num algoritmo genético que implementa elitismo