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

Electrochemical detection of biofilms

[Excerpt] Biofilms are the result of adhesion and growth of microorganisms, creating microenvironments - a polymeric matrix - where several microbial reactions take place [1]. Usually, biofilms are divided in two groups: the ones that are beneficial, as in wastewater treatment or production of specific products, and the detrimental biofilms such as the ones that appear in drinking water pipes and heat exchangers. In any case it is very important to detect the biofilm as soon as possible, to increase its growth or to avoid the risks associated with its presence. The ideal detector must allow the easy detection of biofilms in the early stages of formation and on line. Electrochemical techniques are well known for their role in analytical chemistry, allowing the determination and quantification of a large number of organic, inorganic and biological compounds. These techniques have largely proved to provide an efficient means for detection in situ and on line of a variety of compounds [2]. [...

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

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

Using a genetic algorithm to solve a bi-objective WWTP process optimization

When modeling an activated sludge system of a wastewater treatment plant (WWTP), several conflicting objectives may arise. The proposed formulation is a highly constrained bi-objective problem where the minimization of the investment and operation costs and the maximization of the quality of the effluent are simultaneously optimized. These two conflicting objectives give rise to a set of Pareto optimal solutions, reflecting different compromises between the objectives. Population based algorithms are particularly suitable to tackle multi-objective problems since they can, in principle, find multiple widely different approximations to the Pareto-optimal solutions in a single run. In this work, the formulated problem is solved through an elitist multi-objective genetic algorithm coupled with a constrained tournament technique. Several trade-offs between objectives are obtained through the optimization process. The direct visualization of the trade-offs through a Pareto curve assists the decision maker in the selection of crucial design and operation variables. The experimental results are promising, with physical meaning and highlight the advantages of using a multi-objective approach

Hybrid genetic pattern search augmented Lagrangian algorithm : application to WWTP optimization

An augmented Lagrangian algorithm is presented to solve a global optimization problem that arises when modeling the activated sludge system in a Wastewater Treatment Plant, attempting to minimize both investment and operation costs. It is a heuristic-based algorithm that uses a genetic algorithm to explore the search space for a global optimum and a pattern search method for the local search refinement. The obtained results have physical meaning and show the effectiveness of the proposed method