Numerical and Evolutionary Optimization – NEO 2017

This chapter presents an empirical comparison of six deterministic parameter control schemes based on a sinusoidal behavior that are incorporated into a differential evolution algorithm called “Differential Evolution with Combined Variants” (DECV) to solve constrained numerical optimization problems. Besides, the feasibility rules and the ε-constrained method are adopted as constraint-handling techniques.

Two parameters are considered in this work, F (related with the mutation operator) and CR (related with the crossover operator). Two DECV versions (rand-best) and (best-rand) are assessed. From the above elements, 24 different variants are tested in 36 well-known benchmark problems (in 10 and 30 dimensions). Two performance measures used in evolutionary constrained optimization (successful percentage and average number of evaluations in successful runs) are adopted to evaluate the performance of each variant. Five experiments are proposed to compare (1) those variants with the feasibility rules, (2) those variants with the \( \varepsilon \)-constrained method, (3) the most competitive variants from the previous two experiments, (4) the convergence plots of those most competitive variants and (5) the significant statistical differences of feasible final results among variants.

The obtained results suggest that an increasing oscillation of F and CR values, starting around 0.5 and then moving between 0 and 1, is suitable for the (rand-best) DECV variant. In contrast, a decreasing oscillation of both parameter values is suitable for the (best-rand) DECV variant. The convergence behavior observed in the most competitive variants indicates the convenience of the increasing oscillation of both parameters, coupled with the rand-best DECV version, to promote a faster convergence. The \( \varepsilon \)-constrained method showed to be more competitive with this type of parameter control than the feasibility rules. Finally, no significant differences among variants were observed based on final feasible results.

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.

In traditional, single objective, optimisation local optima may be found by gradient search. With the recently introduced hypervolume indicator (HVI) gradient search, this is now also possible for multi-objective optimisation, by steering the whole Pareto front approximation (PFA) in the direction of maximal improvement. However, so far it has only been evaluated on simple test problems. In this work the HVI gradient is used for the real world problem of building spatial design, where the shape and layout of a building are optimised. This real world problem comes with a number of constraints that may hamper the effectiveness of the HVI gradient. Specifically, box constraints, and an equality constraint which is satisfied by rescaling. Moreover, like with regular gradient search, the HVI gradient may overstep an optimum. Therefore, step size control is also investigated. Since the building spatial designs are encoded in mixed-integer form, the use of gradient search alone is not sufficient. To navigate both discrete and continuous space, an evolutionary multi-objective algorithm (EMOA) and the HVI gradient are used in hybrid, forming a so-called memetic algorithm. Finally, the effectiveness of the memetic algorithm using the HVI gradient is evaluated empirically, by comparing it to an EMOA without a local search method. It is found that the HVI gradient method is effective in improving the PFA for this real world problem. However, due to the many discrete subspaces, the EMOA is able to find better solutions than the memetic approach, albeit only marginally.

In this Chapter, we address the problem of identifying and fitting more than one ellipse simultaneously, from a set of data points in the plane. This problem is an active research area with many applications in engineering and biology. Numerous studies attempted to solve this problem by detecting, fitting, and extracting the ellipses in a one-by-one approach from the set of data points. Although the one-by-one approach is effective and useful for many applications, recent studies have show that this approach is ill posed which led to the proposal of novel methods such as PEARL. PEARL is a multi-model fitting algorithm which minimizes an energy function. The PEARL algorithm requires to be initialized with random solutions. In this work we show that the performance of the PEARL algorithm, to solve the multi-ellipse fitting problem, can be improved by initializing it in a smarter way with solutions taken from a multi-objective genetic algorithm. Numerical results show that our approach can solve challenging data points instances, with high amount of outliers, and also with overlapping and nested ellipses.

Based on the design of a proportional integral controller, the intention is to eliminate the existing error between the level of planned inventory and the actual level in the different parts of the supply chains of goods and services. It is considered necessary to increase the performance of this indicator to optimize the inventory holding costs by improving the profitability of the companies of the multiple chains. A PI controller was developed according with the material balance equation, adjusted to the dynamic models of the supply chains. Likewise, the network elements were classified into producers and non-producers and saturation functions were assigned to each group. Subsequently, the system was simulated incorporating two types of deterministic demands: the first one constant in time and the second one with a variation by season. A linear relationship between the supply volumes was also established for those segments of the chain that have more than one supplier at the same time. It can be argued as a result of this simulation that the control system designed for the supply networks solves the problems of regulation and monitoring. As a consequence of this effect, the satisfaction of the demand of the end customer of the chain is guaranteed, maintaining in an optimal state the levels of inventory as long as the models used in the planning process are adequate.

In the design of linear (model) predictive controllers (MPC), tuning plays a very important role. However, there is a problem not yet fully resolved: how to determine the best strategy for the selection of the optimal tuning parameters in order to obtain good performance with a large feasibility region, but maintaining a low computational load of the control algorithm? Because these objectives determine the proper functioning of the controller and are committed to each other, adjusting the controller parameters becomes a difficult task. The main contribution of this paper is to revise a method that uses the Nondominated Sorting Genetic Algorithm II (NSGA-II) for the parameter selection of a predictive control algorithm that has been parameterized with Laguerre functions (LOMPC) in order to explore the efficiency and provide statistical significance of the algorithm. Numerical simulations show that NSGA-II is a useful tool to obtain consistently good solutions for the selection of MPC tuning parameters.

The optimization of controller parameters or gains is a challenge usually approached using empirical methods that consume valuable time, without the certainty that the obtained gains actually produce the desired behaviour of the controlled plant. There are several analytical and numerical methodologies to find the parameters for PID controllers, however currently there is not enough available information regarding the application of optimization methods for nonlinear controllers. The present work describes the application of the maximum descent method to find the gains of IDA-PBC controller for a ball and beam system. The proposed methodology involves implementing a mathematical model to describe the system’s dynamics, the design of a objective function to measure how closely the plant follows the desired behaviour, and finally the evaluation of a set of gains obtained by the numerical method. The dynamic model and the optimization algorithm were implemented in C language in order to reduce the computer time compared to the use of frameworks such as MATLAB. Numerical simulations to validate the effectiveness of the proposed methodology are included.

The chapter describes an alternative of fuzzy-based sliding mode control (FSMC) with a self-adjusting fuzzy system. The introduced auto-tuner is based on the relay control approach where a limit cycle is exhibited at the output of the closed-loop system. The amplitude of oscillations is considered in order to move the centers of membership functions such that the absence of oscillations is assured for the fuzzy controller. Finally, numerical simulations verify the feasibility of the proposed algorithm.

This work focuses on the application of a discontinuous controller combined with a type of modal control using hybrid optimization techniques to tune the parameters of the controller. The case study is a civil structure with three floors, on which the performance of the control scheme is evaluated by applying an external harmonic force at the ground floor of the structure. The active control is designed to reduce the displacement of the civil structure and the vibrations of the overall system. The Differential Evolution method with the Interior Point Algorithm are used to tune the parameters of the proposed controller, with the goal of maximizing performance relative to hand-tuned parameters. The numerical results are presented comparing the performance of the control in open and closed loop, considering the optimized values of the control parameters.

Of interest is the characterization of a cancellous bone immersed in an acoustic fluid. The bone is placed between an ultrasonic point source and a receiver. Cancellous bone is regarded as a porous medium saturated with fluid according to Biot’s theory. This model is coupled with the fluid in an open pore configuration and solved by means of the Finite Volume Method. Characterization is posed as a Bayesian parameter estimation problem in Biot’s model given pressure data collected at the receiver. As a first step we present numerical results in 2D for signal recovery. It is shown that as point estimators, the Conditional Mean outperforms the classical PDE-constrained minimization solution.

The optimization of analog integrated circuits has been a challenge due to the fact that there are not rules or systematic guidelines to bias and size the transistors and other elements in the circuit under design. This Chapter reviews the design of generic operational amplifiers by using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology and shows the optimization of three different low-dropout (LDO) voltage regulators that consists of an operational amplifier and passive circuit elements. We highlight that if one performs a sensitivity analysis for each LDO, then a reduced set of design variables can be selected to create the chromosome for performing a multi-objective optimization by the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II). In addition, the computed sensitivities are used to reduce the search spaces for the design variables of the MOS transistors to accelerate the optimization process. Finally, from the feasible solutions of the three LDOs, a process-voltage and temperature (PVT) analysis is performed to guarantee that the designed LDO is robust to variations.

The water quality problem is a world-wide challenge for human development. Traditionally, since the 1960’s water quality evaluation has been promoted through the application of various quality or pollution indexes. However, these indexes present excessive divergence and little complementarity that have not allowed to advance toward a unified system of globalized application due to the quantity, the range and the complexity of parameters. We propose a Takagi-Sugeno type fuzzy system to classify and make decisions about treated water reuse for direct or indirect contact activities. The fuzzy system design is based on expert knowledge, and considers guidelines established in mexican and international standards about pollution and water quality indexes. The coefficients in some rule consequents of the fuzzy system were determined by solving an optimization problem through a genetic algorithm. The classification performance of the fuzzy system was verified using real data of a water treatment plant through a leave-one-out cross validation and with an analysis of variance for the pollution indexes assessments.

Vertical structures such as buildings, bridges and trusses are subjected to strong changes with respect to their original state of design due to different external disturbances. Seismic waves are leading sources of disturbances giving rise to lateral displacements, as well as vertical and angular deformations, which increase the risk of structural failure compromising the structure integrity. In order to prevent catastrophic failures in structures and its subsequent side effects, in this work we propose a scheme for the attenuation of the vibration effects in vertical structures by means of a control system based on a Mamdani-type fuzzy inference system. The fuzzy rules of the controller were designed such that the close loop system is guaranteed to satisfy the Lyapunov stability criterion. Numerical simulations were performed to evaluate the best performance and effectiveness of fuzzy control, considering that the controller is placed at different levels of the building and inducing as perturbations signals that approximate a seismic event. The results show that the proposed controller attenuates the vibration in the structure accomplishing the control objective.

In this paper, the design and implementation of two methods for I/Q imbalance compensation is presented, based on a low cost phase measurement approach. The design methodology for an I/Q imbalance correction system is presented based on a DSP-FPGA board. The first method employs some trigonometric properties. The second employs Volterra series to model the non-linear behavior of the I/Q imbalance. The system performance is verified using a complex signal with phase and amplitude imbalance. The implemented systems have the advantage of having low implementation cost and a high design flexibility, which allows for future revisions or enhancement. The Stratix III FPGA board from Altera is employed for the practical implementation and results verification of the system. A comparison between methods is introduced for correcting (I or Q) branches respectively to guarantee amplitude and phase balancing condition in the modulator output. Experimental results are implemented employing an FPGA by using DSP-Builder to bit true VHDL hardware description of proposed model. This work can be considered as a low cost alternative for I/Q imbalance correction given that it does not require additional measurement equipment nor uses complex algorithms.

Best practices in social media have been recently a major concern for organizations, since they are an important key in online social networks to develop a comprehensive strategy both on e-commerce and on traditional business. This paper makes use of Data Envelopment Analysis (DEA) (Charnes et al. 1978) for measuring the economic performance of organizations that lead to best practices using online social networks in their business and strategic processes. In particular, we apply a DEA CRS input-oriented model on a dataset of thirteen hotel organizations in Mazatlán, México, to measure efficiency from the period of 2012 to 2013. The results show that management styles and technology adoption have a great impact on efficiency as well on the creation of competitive strategies. Also, hotel organizations that are willing to use the information obtained from online social networks to create new products or services and aggressively invest on these networks to reach new markets are increasing their market share and show the best performance.