Controller design with a evolutionary multi-objective optimization approach

The huge bandwidth of optical fibres is exploited through wavelength division multiplexing technology, which introduces new complexities in the routing problem. In this context, the wavelength converter allocation problem has become a key factor to minimize blocking. The wavelength converter allocation problem has been treated as a mono-objective problem minimizing the number of wavelength converters or minimizing blocking; however, both criteria are in conflict with each other. Therefore, the wavelength converter allocation problem is studied here in a pure multi-objective optimization context for more appropriate decision making. This work proposes a multi-objective optimization approach based on an evolutionary algorithm which simultaneously minimizes blocking and the number of wavelength converters. Extensive simulations on three real optical networks show promising results in the sense that our algorithm generates the trade-off curve between blocking and the number of converters needed, and outperforms a recently proposed approach.

Precision component displacement, processing, and manipulation in an industrial environment require the high-precision positioning and orientation of industrial robots. However, industrial robots’ positioning includes uncertainties due to assembly and manufacturing tolerances. It is therefore required to use calibration techniques for industrial robot parameters. One of the major sources of uncertainty is the one associated with industrial robot geometrical parameter values. In this paper, using multi-objective meta-heuristic optimization approaches and optical metrology measurements, more accurate Denavit–Hartenberg (DH) geometrical parameters of an industrial robot are estimated. The sensor data used to perform this calibration are the absolute 3D position readings using a highly accurate laser tracker (LT) and industrial robot joint angle readings. Other than position accuracy, the mean absolute deviation of the DH parameters from the manufacturer’s given parameters is considered as the second objective function. Therefore, the optimization problem investigated in this paper is a multi-objective one. The solution to the multi-objective optimization problem is obtained using different evolutionary and swarm optimization approaches. The evolutionary optimization approaches are nondominated sorting genetic algorithms and a multi-objective evolutionary algorithm based on decomposition. The swarm optimization approach considered in this paper is multi-objective particle swarm optimization. It is observed that NSGAII outperforms the other two optimization algorithms in terms of a more diverse Pareto front and the function corresponding to the positional accuracy. It is further observed that through using NSGAII for calibration purposes, the root mean squared for positional error has been improved significantly compared with nominal values.

This paper presents an application of a constrained multiobjective evolutionary algorithm for the design of active suspension controllers for light rail vehicles with the aim of providing superior ride comfort within the suspension's stroke limitation. A multibody dynamic model of a three‐car train is derived and the control parameters are optimized. Force cancellation, skyhook damper, and track‐following are used to synthesize the active controller. Selection of the active suspension parameters is aided by an evolutionary computation algorithm to get the best compromise between ride quality and suspension deflections due to irregular gradient tracks. An evolutionary multiobjective optimization approach accompanied with the Pareto set is proposed to deal with the complicated control design problem.

This paper describes the development and application of a new multi-objective evolutionary optimization approach for the design and upgrading of water distribution systems with multiple pumps and service reservoirs. The optimization model employs a pressure-driven analysis simulator that accounts for the minimum node pressure constraints and conservation of mass and energy. Pump scheduling, tank siting and tank design are integrated seamlessly in the optimization without introducing additional heuristic procedures. The computational solution of the optimization problem is entirely penalty-free, thanks to pressure-driven analysis and the inclusion of explicit criteria for tank depletion and replenishment. The model was applied to the Anytown network that is a benchmark optimization problem. Many new solutions were achieved that are cheaper and offer superior performance compared to previous solutions in the literature. Detailed and extensive simulations of the solutions achieved were carried out. Spatial and temporal variations in water quality were investigated by simulating the chlorine residual and disinfection by-products in addition to water age. The hydraulic requirements were satisfied; efficiency of pumps was consistently high; effective operation of the new and existing tanks was achieved; water quality was improved; and overall computational efficiency was high. The formulation is entirely generic.

This paper presents an approach for finding regions Of specified gain margins (GM) and phase margins (PM) in the parameter space of a single-input single-output (SISO) control system with adjustable parameters. The method uses the Nyquist stability criterion of encirclement of a point in the polar plot. The necessary of the specified GM or PM regions in the parameter space are fully treated by mapping a point related to specified GM or PM in the polar plane into the parameter space. A general problem with previous mapping techniques is identified where points in the parameter space do not necessarily satisfy the required GM or PM. A searchbased technique is proposed to address this problem. Three examples illustrate the theoretical development. I. Introduction G AIN margin (GM) and phase margin (PM) are perhaps the two most important and widespread accepted criteria in analysis and design of practical control systems. These criteria are related to the open-loop transfer function of systems. In the robust stabilization problem of control systems, however, parameter space methods generally consider the closed-loop characteristic equation of the system.13 Parameter space techniques were initially studied by Vishnegradesky for a third-order system using a graphical technique that was popularized by Nimark and was referred to as D-partition or D-decomposition46 in its early development. This method actually establishes a direct correlation between the variable parameters of the closed-loop characteristic equation and the various important stability regions, e.g., open left half of the complex plane (OLHP). The method is directly suitable for graphical representation, in which case it is convenient to consider two parameters at a time. The idea of correlating the free parameters of the open-loop transfer function of a system and the relative stability regions appears to have been initially given in Ref. 7. Unfortunately , the method was not developed in detail, and the idea of isolating the GM region in the parameter plane was not correct. A recent improvement to the idea was presented by introducing the gain-phase margin tester into the system,8 which attempted to isolate specified GM and PM regions in the parameter space to allow a choice of the adjustable parameters. However, it is argued here that in this latter approach all the possible of the relative stability regions are not in fact considered, and some and possibly all points in the relative stability region do not necessarily satisfy the actual specified relative stability margin. In particular, the so called singular boundaries of the D-partition method6 need to be considered. Finally, arising through frequency loci with re-entrant or convoluted characteristics also need to be considered with care. In this paper, a method for accounting for the

In this paper, we present a surrogate-based multi-objective evolutionary optimization approach to optimize airfoil aerodynamic designs. Our approach makes use of multiple surrogate models which operate in parallel with the aim of combining their features when solving a costly multi-objective optimization problem. The proposed approach is used to solve five multiobjective airfoil aerodynamic optimization problems. We compare the performance of a multi-objective evolutionary algorithm with surrogates with respect to the same approach without using surrogates. Our preliminary results indicate that our proposal can achieve a substantial reduction in the number of objective function evaluations, which has obvious advantages for dealing with expensive objective functions such as those involved in aeronautical optimization problems.

A hybrid optimization approach for PI controller tuning based on gain and phase margin specifications

This study proposes a comprehensive optimization framework that integrates single- and multi-objective algorithms for solving complex problems in structural mechanics. A genetic algorithm (GA) and non-dominated sorting genetic algorithm II (NSGA-II) are developed and validated through multiple mechanical case studies, including truss structures, beam vibration and fluid-structure interactions. An isogeometric analysis (IGA) approach is incorporated to improve the accuracy of boundary representation. The numerical results demonstrate the robustness and precision of the proposed methods compared to existing literature, providing an efficient and reliable optimization strategy for practical engineering applications.

Implementing green projects is critical to achieve the green and sustainable development goal. This paper investigates a green project planning with the realistic consideration of multiple objectives including minimizing the total cost and maximizing the total emission reduction. The realistic multi-objective problem in engineering optimization aims to find a best solution for real-world use instead of finding a set of Pareto-optimal solutions. To handle this problem, we develop a weight sets-based multi-objective evolutionary optimization approach to find the best solution for realistic use. The approach integrates a single-objective evolutionary optimization process, novel solution encoding and decoding heuristics, and a non-dominated sort technique. Based on real-world data from a seaport in China, experiments were conducted to validate the proposed optimization approach. Results show that the proposed approach can effectively solve the real-world multi-objective green project planning problem because the solution found by our approach is one of the Pareto optimal solutions generated by the NSGA-II.

Municipalities across the United States face the challenge of sanitary sewer overflows (SSOs), events which pose serious public health and environmental problems. SSOs are unintentional discharges of untreated sewage from the sewer system that can occur as a result of rain derived infiltration and inflow (RDII). SSOs can be reduced by decreasing RDII into the collection system, increasing conveyance capacity, and lessening peak flow through detention storage facilities. However, the sheer length of sanitary sewer systems makes the implementation of these controls very costly. Thus, a novel approach is required to a posteriori design cost-effective rehabilitation options. This study describes a multiobjective evolutionary optimization approach to design a rehabilitation strategy for SSOs reduction in the eastern subsewershed of the San Antonio Water System (SAWS) sewer network. The subsewershed consists of 3,304 conduits connected via 3,155 manholes to form a network that is 160.8 miles long and services an area covering 20.4 square miles with an approximate population of 36,000 inhabitants. The hydraulic behavior of the system is simulated using the EPA Storm Water Management Model (EPA-SWMM) hydraulic model, and the number of SSOs is calculated as the number of nodes that oveflow during the 5 year–6 hours design storm. The optimization method utilized was the Nondominated Sorting Genetic Algorithm (NSGA II) to generate near Pareto-optimal solutions that express tradeoffs between the number of SSOs and cost. The NSGA II was implemented in JAVA, where each individual is represented as a set of vectors that is composed of three sets of genes. The decision variables include the number of pipe segments to be replaced, the location of the first link to be replaced, and the amount of commercial diameter increase from existing pipe diameter. The use of the optimization approach is expected to generate more efficient solutions in comparison to typical engineering approaches that look into solving a localized SSOs problems in sanitary sewer networks.

Exposure to noise is a significant problem for communities that exist near airports. The distribution of noise exposure can be positively affected by changes in the procedures that aircraft follow in the vicinity of an airport (e.g. rate of ascent, ground track, etc.). When considering such changes, a decision maker often has to weigh the objective of lower noise impact against 'more practical' considerations such as fuel consumption and time-of-flight. This study presents a method of numerical optimization which seeks to find the optimal-tradeoff set (Pareto front) of flight procedures given information about an airport and the surrounding population and geography. This front will only include procedures such that an aggregate noise metric cannot be improved without detriment to a more practical objective. A contemporary multi-objective evolutionary algorithm is used as the basis of the optimization effort. Results from a simulated military airfield near Asheville, NC are shown. Ways in which decision makers are empowered by having access to a Pareto front are discussed.

The mean-variance framework for portfolio selection should be revised when investor’s concern is the downside risk. This is especially true when the asset returns are not normal. In this paper, we incorporate value-at-risk (VaR) in portfolio selection and the mean-VaR framework is proposed. Due to the twoobjective optimization problem faced by the meanVaR framework, an evolutionary multi-objective approach is applied to construct the mean-VaR efficient frontier. In particular, the NSGA-II is considered here. From the empirical analysis it is found that the risk-averse investor might inefficiently allocate his wealth if his decision is based on the mean-variance framework.

Aiming at the static unstable Hypersonic vehicle, a method for designing H∞ autopilot to satisfy gain margin and phase margin is proposed. Structured H∞ synthesis is used to synthesize the autopilot under the fixed structure. The gain margin and phase margin were constrained by using H∞ norm of the complementary of the scaled plant. The requirement for the gain margin and phase margin is represented by the distance between the open loop Nyquist curve and the circle that represents the gain margin and phase margin in the complex plane. The distance is adjusted by tuning the parameter of performance specifications automatically to reduce the conservatism of the controller. The present method is applicable to both static stable vehicle and static unstable vehicle, and a three loops acceleration tracking autopilot is design. The numerical simulations have demonstrated that the autopilot satisfys the performance specifications, gain margin and phase margin simultaneously.

Design proportional–integral–derivative (PID) controllers for unstable first-order plus time delay (FOPTD) and unstable second-order plus time delay (SOPTD) systems with/without a zero is proposed by direct synthesis method. For unstable FOPTD system, a series PID controller is considered. The derivative time of series PID controller is made equal to 0.5 times time delay to cancel the numerator zero with the pole of the loop transfer function (product of process transfer function and controller transfer function). The reduced characteristic equation is compared with the desired characteristic equation to get PI settings. The conventional PID controller parameters are obtained from series PID controller. For unstable SOPTD systems, PID controller with a first-order lead/lag compensator is considered. The controllers designed by the proposed method are implemented on various transfer function models, nonlinear model equations of bioreactor and on inverted pendulum (IP) set-up to show the efficiency of the proposed method. The performance of the proposed controllers is compared with the controllers reported in the recent literature in terms of IAE. The robustness of the controller is determined by the maximum magnitude of sensitivity function, phase margin and gain margin.

Most combinatorial problems are complex and very hard to solve. That is why, lots of methods focus on the optimization according to a single criterion. The combining of several criteria presents additional complexity and new problems.