Incorporating Human Preferences in Decision Making for Dynamic Multi-Objective Optimization in Model Predictive Control

We present a new two-step approach for automatized a posteriori decision making in multi-objective optimization problems, i.e., selecting a solution from the Pareto front. In the first step, a knee region is determined based on the normalized Euclidean distance from a hyperplane defined by the furthest Pareto solution and the negative unit vector. The size of the knee region depends on the Pareto front’s shape and a design parameter. In the second step, preferences for all objectives formulated by the decision maker, e.g., 50–20–30 for a 3D problem, are translated into a hyperplane which is then used to choose a final solution from the knee region. This way, the decision maker’s preference can be incorporated, while its influence depends on the Pareto front’s shape and a design parameter, at the same time favorizing knee points if they exist. The proposed approach is applied in simulation for the multi-objective model predictive control (MPC) of the two-dimensional rocket car example and the energy management system of a building

Optimización multi-objetivo en procesos biotecnológicos : aplicación al cultivo de células vegetales en suspensión de Thevetia peruviana

RESUMEN: La productividad de los bioprocesos es un compromiso entre dos objetivos en conflicto, la maximización de la velocidad de crecimiento de la biomasa y la minimización del consumo de sustrato. En este trabajo, se resuelve un problema de optimización multi-objetivo para mejorar la productividad del cultivo en suspensión de células vegetales de la especie Thevetia peruviana. La solución del problema multi-objetivo permitió determinar las concentraciones iniciales óptimas de sustrato y biomasa para garantizar la máxima productividad. La optimización se lleva a cabo utilizando un modelo mecanistico, que incluye una representación de los procesos intracelulares que tienen lugar en las células vegetales. Las mejores soluciones se eligieron del frente de Pareto teniendo en cuenta el criterio experto. Los resultados indican que se recomienda una concentración inicial de inóculo de 3.91g/L y una concentración inicial de sacarosa de 23.63g/L como condiciones iniciales para obtener una productividad de biomasa de 1.57g/L*día con un consumo aceptable de sacarosa. Se llevó a cabo la validación experimental del óptimo encontrado y la productividad obtenida fue de 1.52g/L usando una concentración de inóculo inicial de 4.27g/L y una concentración inicial de sacarosa de 25.44g/L. Los resultados sugieren que la metodología propuesta puede ampliarse para aumentar la productividad en términos de producción de metabolitos a partir de estos cultivos de células vegetales y otras especies vegetales.ABSTRACT: Bioprocesses productivity is a compromise between two conflicting objectives, maximization of biomass growth rate and minimization of substrate consumption. In this work, a model based multi-objective optimization problem is solved for improving the process productivity in plant cell suspension cultures of Thevetia peruviana. A solution of the multi-objective problem allowed determining the optimal initial concentrations of substrate and biomass for assuring maximal productivity. Model-based optimization is carried out using a mechanistic model, which includes a representation of the intracellular processes taking place on the plant cells. The best solutions were chosen from the Pareto front in agreement with expert criterion. Results indicate that an initial inoculum concentration of 3.91g/L and an initial sucrose concentration of 23.63g/L, are recommended as initial conditions for obtaining a biomass productivity of 1.57g/L*day with an acceptable sucrose uptake. Experimental validation of the optimal found was carried out and the productivity obtained was 1.52g/L using an initial inoculum concentration of 4.27g/L and an initial sucrose concentration of 25.44g/L. Results suggest that the proposed methodology can be extended to increase the productivity in terms of metabolite production from this plant cell cultures and other plant species

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Hybrid Evolutionary-based Sparse Channel Estimation for IRS-assisted mmWave MIMO Systems

The intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) communication system has emerged as a promising technology for coverage extension and capacity enhancement. Prior works on IRS have mostly assumed perfect channel state information (CSI), which facilitates in deriving the upper-bound performance but is difficult to realize in practice due to passive elements of IRS without signal processing capabilities. In this paper, we propose a compressive channel estimation techniques for IRS-assisted mmWave multi-input and multi-output (MIMO) system. To reduce the training overhead, the inherent sparsity of mmWave channels is exploited. By utilizing the properties of Kronecker products, IRS-assisted mmWave channel is converted into a sparse signal recovery problem, which involves two competing cost function terms (measurement error and sparsity term). Existing sparse recovery algorithms solve the combined contradictory objectives function using a regularization parameter, which leads to a suboptimal solution. To address this concern, a hybrid multiobjective evolutionary paradigm is developed to solve the sparse recovery problem, which can overcome the difficulty in the choice of regularization parameter value. Simulation results show that under a wide range of simulation settings, the proposed method achieves competitive error performance compared to existing channel estimation methods