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Aquila Optimization Algorithm (AQUILA) is a newly emerged metaheuristic optimizer for solving global optimization problems, which is based on intrinsic hunting behaviors of the foraging aquila individuals. However, this stochastic optimization method suffers from some algorithm-specific drawbacks, such as premature convergence to the local optimum points over the search hyperspace due to the lack of solution diversity in the population. To conquer this algorithmic deficiency, an ensemble of Wavelet mutation operators has been implemented into the standard AQUILA to enhance the explorative capabilities of the algorithm by diversifying the search domain as much as possible. Furthermore, a brand-new local search scheme empowered by the synergetic interactions of elite opposition-based learning and a simple-yet-effective exploitative manipulation equation is introduced into the base AQUILA to intensify on the previously visited promising regions. The proposed learning schemes are stochastically applied to the obtained solutions from the base Aquila algorithm to refine the overall solution quality and amend the premature convergence problem. It is also aimed to investigate whether the collective application of Wavelet mutation operators with different types entails a significant improvement in the general search effectivity of the algorithm rather than their individual efforts. Numerical experiments made on a suite of unconstrained unimodal and multimodal benchmark functions reveal that this hybridization with AQUILA has improved the general solution accuracy and stability to very high standards, outperforming its contemporary counterparts in the comparative statistical analysis. Furthermore, an exhaustive benchmark analysis has been performed on fourteen constrained real-world complex engineering problems.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

As a constrained optimization strategy, model predictive control (MPC) is widely used in the optimal dispatch of microgrids. Rolling optimization and feedback correction strategy can effectively deal with the impact due to the system uncertainty and model mismatch which ensures the stable operation of the microgrid. Due to the uncertainty of distributed power sources, MPC can be applied to solve the problem of renewable energy output in microgrid for fishery. This paper reviews the optimal dispatch of microgrid for fishery based on model predictive control. Firstly, this article introduces the basic principles and classification of model predictive control, and then explains the remaining problems and research directions. The characteristics of the microgrid optimal dispatching problem are described, and the analysis are focused on how MPC solves the uncertain problems in the microgrid optimal dispatching. Finally, perspectives and the future research direction of model predictive control in microgrid energy dispatch is reviewed.

This paper presents an inertial neural network to solve the source localization optimization problem with l 1 -norm objective function based on time of arrival (TOA) localization technique. The convergence and stability of the inertial neural network are analyzed by the Lyapunov function method. An inertial neural network iterative approach is further used to find a better solution among the solutions with different inertial parameters. Furthermore, the clock asynchronization is considered in the TOA l 1 -norm model for more general real applications, and the corresponding inertial neural network iterative approach is addressed. The numerical simulations and real data are both considered in the experiments. In the simulation experiment, the noise contains uncorrelated zero-mean Gaussian noise and uniform distributed outliers. In the real experiment, the data is obtained by using the ultra wide band (UWB) technology hardware modules. Whether or not there is clock asynchronization, the results show that the proposed approach always can find a more accurate source position compared with some of existing algorithms, which implies that the proposed approach is more effective than the compared ones.

Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. In other situations, collocated measurements of variables from the same, yet unknown, distribution are characterized with separate models that may not respect the relatedness of the measurements. One way to preserve this imprecision or relatedness in a geostatistical mapping framework is to characterize the measurements as intervals rather than single numbers. To effectively analyze the interval-valued data, this paper develops an interval-valued kriging based on the modification of a previous attempt and the recent development of the random sets theory. Numerical implementation of our interval-valued kriging is provided using a penalty-based constrained optimization algorithm. An interval-valued kriging of design ground snow loads in Ohio, USA, demonstrates the applicability and advantages of the proposed methodology.

This paper presents a dynamic neural network based adaptive impedance control method for redundant robots under multiple physical constraints. In order to provide optimal contact performance without an accurate environment model, an adaptive impedance learning method is proposed to establish the optimal interaction between robot and environment. In the inner loop, a theoretical framework of constraint optimization is constructed, and then a dynamic neural network is established to compensate the nonlinear dynamics, and compliance to physical limitations is also satisfied. These limitations include joint angle restriction, angular velocity restriction, angular acceleration restriction, and torque restriction. Theoretical analysis proves the stability of the closed loop system. Numerical results show the effectiveness of the proposed control scheme.

The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory; however, it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints. In this paper, a modified shape approximation low-thrust model is presented, and a novel constrained optimization algorithm is developed to solve this problem. The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit. In particular, a transformed high-order polynomial model based on finite Fourier series is proposed, which can be characterized as a multi-constraint optimization problem. Then, a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory. The key performance indicators of the index include minimum flight time, low fuel consumption and bi-objective optimization of the two. Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques. Besides, the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set. Furthermore, we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.

A key issue in evolutionary constrained optimization is how to achieve a balance between feasible and infeasible solutions. The quality of generated solutions in decomposition-based multi-objective evolutionary algorithms (MOEAs) depends strongly on the weights’ setting. To fully utilize both the promising feasible and infeasible solutions, this paper proposes two-type weight adjustments based on MOEA/D for solving highly constrained many-objective optimization problems (CMaOPs). During the course of the search, the number of infeasible weights is dynamically reduced, to guide infeasible solutions with better convergence to cross the infeasible barrier, and also to lead infeasible solutions with better diversity to locate multiple feasible subregions . Feasible weights are evenly distributed and keep unchanged throughout the evolution process, which aims to guide the population to search Pareto optimal solutions . The effectiveness of the proposed algorithm is verified by comparing it against six state-of-the-art CMaOEAs on three sets of benchmark problems. Experimental results show that the proposed algorithm outperforms compared algorithms on majority problems, especially on highly constrained optimization problems . Besides, the effectiveness of the proposed algorithm has also been verified on an antenna array synthesis problem .

The present study proposes an optimal design methodology of tuned liquid sloshing dampers (TLSDs) installed in wind-excited benchmark tall building. The TLSDs design parameters were determined using proposed optimal design methodology based on nonlinear constraint optimization technique. Top floor peak acceleration was considered as the objective function and maximum value of sloshing depth of liquid as a nonlinear constraint for the design purpose. The classical nonlinear shallow water wave theory was used for the simulation of liquid sloshing, and the basic equations of nonlinear liquid sloshing were solved using the Lax Finite Difference Scheme. The governing equations of motion of combined structure-TLSDs system were expressed as state-space variables and structural response was numerically simulated. The findings were presented and assessed on the basis of a comparison between power spectral density functions, time history analysis, root mean square, peak response, and performance criteria for benchmark building with and without TLSDs. The off-tuning effect of TLSDs due to ± 15 % uncertainty in the building stiffness was also investigated. Further, an attempt has been made to present the control effectiveness of TLSDs in time–frequency domain (wavelet scalogram) using continuous wavelet transformation technique. The optimal TLSDs design based on the proposed methodology was found to be quite effective in serviceability-based design of benchmark tall building under wind loads and can be very useful for the practical design of TLSDs.

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-aCA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC’06, and the IEEE CEC’19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-aCA + mIS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms.

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive.

Thickening-dewatering process is widely used for solid–liquid separation in mineral processing plants. Usually, the feed quantity of the thickener is an uncertain variable, so the underflow concentration of the thickener cannot be accurately predicted, which may result in improper operation and high security risk. This paper proposes a stochastic chance-constrained optimization framework for the thickening-dewatering process with the uncertain feed quantity. Firstly, a feed quantity predictive model is established by gray correlation analysis (GCA) and partial least squares (PLS) to reduce the uncertainty of the feed quantity. Then, the stochastic chance-constrained optimization model of the thickening-dewatering process is established to minimize the energy economic index (EEI). In order to solve the stochastic chance-constrained optimization model, the nonlinear time-of-use electricity price function in the objective is linearized, and then the stochastic chance-constrained optimization model is transformed into a deterministic model. The cases study illustrate that the optimization framework can reduce the EEI and the security risk of the thickening-dewatering process.

The frequency constrained design of large-scale structures is a complex optimization problem with many local optima. In order to tackle this problem, in this paper, a chaotic version of a newly-established metaheuristic algorithm, the so-called Water Strider Algorithm (WSA), is introduced. This version repetitively diversifies solutions and then focuses on promising areas during the course of iterations. The chaotic algorithm involves two types of succession states, namely explorative and exploitative states, and it probabilistically switches between them using the Circle map with a quasi-cyclic behavior. To examine the effectiveness of this algorithm, it is applied to structural optimization of large-scale structures with multiple frequency constraints such as 600-, 1180- and 1410-bar dome trusses. The results show that the new version outperforms its basic version as well as some other well-established algorithms in the literature. The statistical measures reveal that it is reasonably capable of providing a satisfactory performance in terms of both obtaining lighter designs and convergence speed.

This paper proposes a continuous-time enhanced variant of Beetle Antennae Search (BAS), a metaheuristic algorithm that mimics the food searching nature of beetles. Beetles register the smell of the food on their two antennae, and based on the intensity of smell, they move left or right. Likewise, discrete-time BAS computes the value of objective function three times and moves toward the optimal solution. However, the computation of objective function three times in each iteration known as a “virtual particle,” makes it computationally expensive, inefficient, and time-consuming, especially while dealing with complex systems, e.g., redundant manipulators. Our proposed, Enhanced Beetle Antennae Search with Zeroing Neural Network (BASZNN) algorithm overcomes this problem by introducing a delay factor in objective function and input. This delay allows BASZNN to compute objective function value once, making it computationally robust and efficient. BASZNN includes the flexible random searching nature of BAS and the parallel processing nature of ZNN, making it computationally fast and less time-consuming, especially for complex problems. As a testbed, we employed BASZNN on two types of problems: Unconstrained (unimodal, multimodal) and Constrained (real-world) and compared the results with state-of-the-art metaheuristic algorithms.

To solve constrained optimization problems (COPs), it is crucial to guide the infeasible solution to a feasible region. Gradient-based repair (GR) is a successful repair strategy, where the forward difference is often used to estimate the gradient. However, GR has major deficiencies. First, it is difficult to deal with individuals falling into the local optima. Second, large amounts of fitness evaluations are required to estimate the gradient. In this paper, we proposed a new repair strategy, random direction repair (RDR). RDR generates a set of random directions, and calculates the repair direction and the repair step size of infeasible individual to reduce its constraint violation. Since the introduction of randomness, RDR could deal with individuals falling into the local optima. Furthermore, RDR only requires a few number of fitness evaluation. To demonstrate the performance of RDR, RDR was embedded into two state-of-the-art evolutionary continuous constrained optimization algorithms, tested on the Congress on Evolutionary Computation 2017 constrained real-parameter optimization benchmark. Experimental results demonstrated that RDR combined with evolutionary algorithms are highly competitive.

Nonconvex distributed constrained optimization over multi-agent systems plays an increasingly important role in control community. However, the duality gap for a nonconvex distributed constrained optimization problem is not always zero. This brings some difficulties for the algorithm design and convergence analysis about such problems. In this paper, to eliminate the duality gap, the original distributed optimization problem is converted to an equivalent distributed one by using a partial power reformulation. Next, for solving this equivalence problem, a continuous-time algorithm is proposed over the multi-agent system where each agent exchanges local information with other agents under an undirected communication graph. It is proved that the proposed continuous-time algorithm locally converges to a strict local optimal solution of the considered original nonconvex distributed optimization problem. Numerical examples show the validness of the presented algorithm. Finally, the algorithm is applied for optimal placement.

The Frank-Wolfe algorithm is a method for constrained optimization relying on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational advantage of solving linear minimizations instead of projections. However, the discussions supporting this advantage are often incomplete. We review the complexity bounds for both tasks on several sets commonly used in optimization. Projection methods onto the l p -ball, p ∈ ] 1 , 2 [ ∪ ] 2 , + ∞ [ , and the Birkhoff polytope are also proposed.

In this paper, a novel algorithm KTLBO is presented to achieve computationally expensive constrained optimization. In KTLBO, Kriging is adopted to develop dynamically updated surrogate models for costly objective and inequality constraints. A data managing method aiming at solving expensive constrained problems is developed to archive, classify and update expensive samples, where a penalty function is set to adaptively select elite individuals. Moreover, based on the Teaching-Learning-based Optimization (TLBO), a Kriging-assisted two-phase optimization framework is presented to alternately conduct local and global searches. In Kriging-assisted Teaching and Learning Phases, two different prescreening operators considering the probability of feasibility are respectively proposed to select the high-quality samples around the present best solution and the samples exhibiting better space-filling performance, as an attempt to balance exploitation of surrogates and exploration of unknown area. In brief, KTLBO retains the meta-heuristic search mechanism of TLBO while adopting Kriging to accelerate its search, thereby acting as a novel idea for surrogate-assisted constrained optimization. Lastly, KTLBO is compared with 6 well-known methods on 27 benchmark cases, and then its significant advantages in expensive constrained optimization are verified. Furthermore, KTLBO is adopted to design the structure of a Blended-Wing-Body underwater glider, and the satisfactory solution is yielded.

In this paper, we propose decision analysis methods for determining the optimal number of agents of a service system where the system rates (arrival, service, and abandonment) are modeled as dependent random variables. In doing so, we take the Bayesian point of view of inference and obtain joint posterior distributions of the system rates. We solve the proposed stochastic staffing decision problem with augmented probability simulation based optimization methods. The novelty of our approach stems from the use of dependent system rates to determine optimal staffing in a constrained optimization setting for stochastic service systems. We demonstrate the implications of ignoring dependence and uncertainty in system rates on simulated data for general service systems, and illustrate the application of the proposed methodology on call center operations.

This paper presents a number of power grid network design and optimization techniques that consider the electromigration (EM) effects for multi-segment interconnect wires. First, we consider a new EM immortality constraint due to EM void saturation volume for multi-segment interconnects. It helps reduce conservativeness in the EM-aware on-chip power grid design. Along with the EM nucleation phase immortality constraint, we show that both EM immortality constraints can be naturally integrated into the existing programming based power grid optimization framework. Second, to mitigate the overly conservativeness of the immortality constrained optimization methods, we further explore three strategies: we first size up failed wires to meet one of the immortality conditions subject to the design rules; second, we consider the EM-induced aging effects on power supply networks for a target lifetime, which allows some short-lived wires to fail and optimizes the remaining wires; third, we propose a large change sensitivity-based optimization scheme to perform localized fixing based on recently proposed coupled EM-IR drop analysis method. Numerical results on a number of IBM-format power grid networks demonstrate that the new method can reduce more power grid area compared to the existing EM immortality constrained optimizations. Moreover, the new method is able to optimize power grids with nucleated wires, which would not be possible with the existing methods. Results also show the sensitivity-based localized power girds fixing can fix EM-induced IR drop violations in a few minutes for synthesized power grid networks from ARM core designs.

Orthogonal collocation on finite elements (OCFE) has been used universally to approximate ODEs to date. For PDEs, this contribution presents a novel discretization scheme applying the methodology of OCFE to discretize both space and time domain simultaneously, named as space–time orthogonal collocation on finite elements (ST-OCFE). Due to the existence of boundary conditions, the selection of discrete points and the constitution of discretized algebraic equations are different in space and time domain. Furthermore, for solving optimal control problems constrained by PDEs, a discretize-then-optimize algorithm based on ST-OCFE and quasi-sequential approach is proposed. The formulation of discretized optimization problems and the procedure of sensitivity computation are deduced. In the algorithm, diverse types of PDEs, state constraints, and general control parameterization are considered. The proposed method has the advantages of generality, higher numerical accuracy, and easy handling of state constraints, as demonstrated by three examples.

In this study, we present a neural network that consists of nodes with heterogeneous sensitivity. Each node in a network is assigned a variable that determines the sensitivity with which it learns to perform a given task. The network is trained via a constrained optimization that maximizes the sparsity of the sensitivity variables while ensuring optimal network performance. As a result, the network learns to perform a given task using only a few sensitive nodes. Insensitive nodes, which are nodes with zero sensitivity, can be removed from a trained network to obtain a computationally efficient network. Removing zero-sensitivity nodes has no effect on the performance of the network because the network has already been trained to perform the task without them. The regularization parameter used to solve the optimization problem was simultaneously found during the training of the networks. To validate our approach, we designed networks with computationally efficient architectures for various tasks such as autoregression, object recognition, facial expression recognition, and object detection using various datasets. In our experiments, the networks designed by our proposed method provided the same or higher performances but with far less computational complexity.

To enhance the machining efficiency, curved thin-walled parts in the aerospace and automobile industries are often formed to the near-net shapes and then subtractive manufactured to their design shapes. The billets for the manufacturing process may lack of the removal material in some regions due to low forming accuracy, which would increase the rejection rate of these parts. However, there is a chance that some rejected billets can be saved by using partial tolerance ranges to compensate the shape errors of the raw billets. Aiming to reduce the rejection rate and save the production cost, this paper attempts to develop a novel approach for constructing process shape of curved thin-walled part, in which its nominal shape was slightly changed within their tolerance ranges to avoid the undercut during the machining process. Firstly, a registration algorithm was used to find an optimal position between the design shape and the on-machine measurement points. Afterwards, a non-linear constrained optimization model was established to search for the feasible points in the tolerance ranges, in which the profile occupancy, thickness occupancy and non-uniformity of machining allowances were carefully considered. Finally, a new process shape was constructed based on these feasible points, which could be used for adaptive machining of curved thin-walled part. The results of a case study validated the feasibility of the proposed process shape construction approach.

The synthesis problem of a cyber-physical system (CPS) is to find an input signal under which the system’s behavior satisfies a given specification. Our setting is that the specification is a formula of signal temporal logic, and furthermore, that the specification is a conjunction of different and often conflicting requirements. Conjunctive synthesis is often challenging for optimization-based falsification—an established method for CPS analysis that can also be used for synthesis—since the usual framework (especially how its robust semantics handles Boolean connectives) is not suited for finding delicate trade-offs between different requirements. Our proposed method consists of a combination of optimization-based falsification and constrained optimization. Specifically, we show that the state-of-the-art multiple constraint ranking method can be combined with falsification powered by CMA-ES optimization; its performance advantage for conjunctive synthesis is demonstrated in experiments.

Auxetic foams were fabricated using thermo-mechanical process. Image analysis was performed to find Poisson’s ratio values. Compression tests were performed to generate stress–strain data. Experimental data is used to determine the parameters for a variant of Ogden model (proposed by Ciambella et al., 2015) for negative Poisson’s ratio (auxetic) material. Experimental data of two different auxetic foams (fabricated using 2.06 and 2.98 compression factors) are used. Constrained optimization was performed in MATLAB to determine the best values of the model parameters. This material model can be used in finite element simulations to study the behavior of auxetic foams in various cushioning applications.

One of the most important aspects of visual perception is the inference of 3D shape from a 2D retinal image of the outside world. The existence of several valid mapping functions from object to data makes this inverse problem ill-posed and therefore computationally difficult. In human vision, the retinal image is a 2D projection of the 3D world. The visual system imposes certain constraints on the family of solutions in order to uniquely and efficiently solve this inverse problem. This work specifically focused on the minimization of standard deviations of 3D angles (MSDA) for 3D perception. Our goal was to use a Deep Convolutional Neural Network based on biological principles derived from visual area V4 to achieve 3D reconstruction using constrained minimization of MSDA. We conducted an experiment using novel shapes with human subjects to collect data and test the model. The performance of the network largely agreed with how humans estimated novel 3D shapes. The results show that the constraint of MSDA in 3D shape can be implemented in a neural network and produce human-like results. Additional visual constraints can be added to the network in the future to fully test the theory of visual constraints as a basis of 3D shape perception.

Athletes in many sports can potentially earn significant amounts of prize money from taking less time to complete a given distance than their competitors. Time is literally money in these cases. The objective of an athlete is to choose an optimal race strategy that minimizes race time without becoming prematurely exhausted. If the first part of a race is completed too quickly, the fatigue generated makes the second part of the race slow and painful. If completed too slowly, the second part will be fast but it cannot make up for the time lost earlier on. Either way, the total time taken to complete the entire distance will not be as fast as it could otherwise have been. This optimal decision problem has long been debated by athletes, coaches, and more recently by physicists and applied mathematicians. We show that this optimal choice problem can be solved with solutions that are both simple enough for them to be of practical use but flexible enough for them to be personalized for an athlete. We use the 800 m running race to demonstrate how our technique works since it is a well known ideal example of an event that combines both the elements of speed and endurance.

In this paper, a new stochastic optimizer, which is called slime mould algorithm (SMA), is proposed based on the oscillation mode of slime mould in nature. The proposed SMA has several new features with a unique mathematical model that uses adaptive weights to simulate the process of producing positive and negative feedback of the propagation wave of slime mould based on bio-oscillator to form the optimal path for connecting food with excellent exploratory ability and exploitation propensity. The proposed SMA is compared with up-to-date metaheuristics using an extensive set of benchmarks to verify its efficiency. Moreover, four classical engineering problems are utilized to estimate the efficacy of the algorithm in optimizing constrained problems. The results demonstrate that the proposed SMA benefits from competitive, often outstanding performance on different search landscapes. The source codes of SMA are publicly available at http://www.alimirjalili.com/SMA.html and https://tinyurl.com/Slime-mould-algorithm .

In part I of this series of articles, the concept of overall system reliability was presented for two applications: reliable estimation of variables for steady state linear flow processes, and reliable fault detection and diagnosis for any process. In this part, systematic generation of the proposed system-wide reliability expression is discussed. In particular, an approach for generating the system reliability using the sum of disjoint product method is presented. This serves as the objective function to be maximized in various constrained optimization formulations for sensor network design, which are also proposed in this work for both applications. A heuristic is proposed to solve the resulting nonlinear integer programming problems. The sensor network design formulations are applied to two benchmark case studies: (1) Tennessee Eastman process, (2) Steam metering process. Results indicate the utility of the proposed sensor network design approach in designing optimal sensor networks that maximize system reliability.

We estimate costs associated with mothballing, restarting, abandoning and maintaining peaking power plants. We develop a real options model to explain switching and maintenance behavior of plant managers. The constrained optimization approach to estimate crucial costs accommodates non-parametric dynamics for the expectations of the plant managers regarding future profitability. The empirical analysis is based on the status of power plants reported annually to the United States Energy Information Administration (EIA) during 2001–2009. We arrive at economically meaningful estimates of maintenance costs and switching costs, and discuss these in light of rates used in the Pennsylvania-New Jersey-Maryland capacity market.

After the discovery of adversarial examples and their adverse effects on deep learning models, many studies focused on finding more diverse methods to generate these carefully crafted samples. Although empirical results on the effectiveness of adversarial example generation methods against defense mechanisms are discussed in detail in the literature, an in-depth study of the theoretical properties and the perturbation effectiveness of these adversarial attacks has largely been lacking. In this paper, we investigate the objective functions of three popular methods for adversarial example generation: the L-BFGS attack, the Iterative Fast Gradient Sign attack, and Carlini & Wagner's attack (CW). Specifically, we perform a comparative and formal analysis of the loss functions underlying the aforementioned attacks while laying out large-scale experimental results on ImageNet dataset. This analysis exposes (1) the faster optimization speed as well as the constrained optimization space of the cross-entropy loss, (2) the detrimental effects of using the signature of the cross-entropy loss on optimization precision as well as optimization space, and (3) the slow optimization speed of the logit loss in the context of adversariality. Our experiments reveal that the Iterative Fast Gradient Sign attack, which is thought to be fast for generating adversarial examples, is the worst attack in terms of the number of iterations required to create adversarial examples in the setting of equal perturbation. Moreover, our experiments show that the underlying loss function of CW, which is criticized for being substantially slower than other adversarial attacks, is not that much slower than other loss functions. Finally, we analyze how well neural networks can identify adversarial perturbations generated by the attacks under consideration, hereby revisiting the idea of adversarial retraining on ImageNet., Accepted for publication in Pattern Recognition Letters, 2020

This paper presents a new procedure for optimal allocation and optimal sizing of a battery energy storage system (BESS) for primary frequency support in an isolated power system. For the BESS allocation, a transmission bus system with larger frequency decline is recognized and the BESS sizing is performed by a constrained optimization strategy based on a new modified metaheuristic, called Developed Harris Hawks Optimization (DHHO). The simulation results of the suggested DHHO are compared with Bat Optimization Algorithm (BOA) and Genetic Algorithm (GA) from the literature to show the method efficiency. The final results showed higher precision with lower required iterations for the suggested DHHO method. Also, the proposed DHHO gives lower investment costs for BESS with lower power and energy requirement toward the other compared methods.

In this paper, the distributed constrained optimization problem over a directed graph is considered. We assume that the digraph has a row-stochastic adjacency matrix, which corresponds to the case when agents assign weights to the received information individually. We present an algorithm that converges to the optimal solution even with a time-varying stepsize which is not attenuated to zero. The choice of stepsizes is relatively easy. The usable type of stepsizes is added. The diminishing or constant stepsizes can be used in our algorithm. Equality constraints and set constraints are also considered in this paper. Convergence analysis of the proposed algorithm relies on a conversion theorem between column-stochastic and row-stochastic matrices. Finally, the results of the numerical simulation are provided to verify the effectiveness of the proposed algorithm.

Despite many attempts to establish material grindability in a milling process, it remains very difficult to predict the milling performance. In this study, impact milling tests were carried out under varying operational conditions in a UPZ100 impact pin mill. The product size distribution and fineness of milled alumina particle are reported and analyzed. A multiscale framework coupling discrete element method (DEM) and population balance model (PBM) is proposed to predict the milling performance of the mill. The impact velocity and impact frequency information from DEM is utilized to inform the mill operation parameters of the PBM model at the process scale, whilst the material grindability parameters are evaluated using constrained optimization to match a milling test. The predictions of the product size distribution show very good agreement with the experimental results. This indicates that the multiscale model is promising for optimizing the design and operation of mills.

Camera calibration is a basic and crucial problem in photogrammetry and computer vision. Although existing calibration techniques exhibit excellent precision and flexibility in classical cases, most of them need from 5 to 10 calibration images. Unfortunately, only a limited number of calibration images and control points can be available in many application fields such as criminal investigation, industrial robot and augmented reality. For these cases, this paper presented a two-step calibration based on soft constraint optimization, which is motivated by "no free lunch" theorem and error analysis. The key steps include (1) homography estimation with weighting function, (2) Initialization based on a simplified model, and (3) soft constraint optimization in terms of reprojection error. The proposed method provides direct access to geometric information of the object from very few images. After extensive experiments, the results demonstrate that the proposed algorithm outperforms Zhang's algorithms from the point of view of the success ratio, accuracy and precision.

This paper proposes an advanced decentralized method where an Automated Guided Vehicle (AGV) can optimally insert charging stations into an already assigned optimal tour of task locations. In today's industrial AGV systems, advanced algorithms and techniques are used to control the whole fleet of AGVs robustly and efficiently. While in academia, much research is conducted towards every aspect of AGV control. However, resource management or battery management is still one aspect which is usually omitted in research. In current industrial AGV systems, AGVs operate until their resource level drops below a certain threshold. Subsequently, they head to a charging station to charge fully. This programmed behaviour may have a negative impact on the manufacturing systems performance. AGVs lose time charging at inconvenient moments while this time loss could be avoided. Using the approach, an AGV can choose independently when it will visit a charging station and how long it will charge there. A general constrained optimization algorithm will be used to solve the problem and the current industrial resource management will be used as a benchmark. We use a simple extension of the Traveling Salesman Problem (TSP) representation to model our approach. The paper follows a decentral approach which is in the interest of the authors. The result of the proposal is a compact and practical method which can be used in today's operative central or decentral controlled AGV systems.

Automatic summarization is typically aimed at selecting as much information as possible from text documents using a predefined number of words. Extracting complete sentences into a summary is not an optimal way to solve this problem due to redundant information that is contained in some sentences. Removing the redundant information and compiling a summary from compressed sentences should provide a much more accurate result. Major challenges of compressive approaches include the cost of creating large summarization corpora for training the supervised methods, the linguistic quality of compressed sentences, the coverage of the relevant content, and the time complexity of the compression procedure. In this work, we attempt to address these challenges by proposing an unsupervised polynomial-time compressive summarization algorithm. The proposed algorithm iteratively removes redundant parts from original sentences. It uses constituency-based parse trees and hand-crafted rules for generating elementary discourse units (EDUs) from their subtrees (standing for phrases) and selects ones with a sufficient tree gain. We define a parse tree gain as a weighted function of its node weights, which can be computed by any extractive summarization model capable of assigning importance weights to terms. The results of automatic evaluations on a single-document summarization task confirm that the proposed sentence compression procedure helps to avoid redundant information in the generated summaries. Furthermore, the results of human evaluations confirm that the linguistic quality—in terms of readability and coherency—is preserved in the compressed summaries while improving their coverage. However, the same evaluations show that compression in general harms the grammatical correctness of compressed sentences though, in most cases, this effect is not significant for the proposed compression procedure.

Fast charging has gained an increasing interest in the convenient use of Lithium-ion batteries. This paper develops a constrained optimization based fast charging control strategy, which is capable of meeting needs in terms of charging time, energy loss, and safety-related charging constraints. To solve it with less computational effort, a two-layer optimization strategy is proposed, where a charging time region contraction method is utilized to search the minimum expected charging time in the top layer, and the bottom layer uses the barrier method to calculate the corresponding optimal charging current with the charging time given by the top layer. Through utilizing this two-layer optimization method, the optimal charging current can be obtained that leads to the shortest charging period while guaranteeing the charging constraints with relatively low computational complexity. Extensive simulation results are provided to validate the proposed optimal fast charging control strategy, which well outperforms the constant current-constant voltage method.

This paper extends a hierarchical control approach for power balancing in a meshed DC microgrid while minimizing the power losses in the central transmission network. The control strategy is divided into three layers in hierarchical framework: i) the high level solves a continuous-time optimization problem which minimizes the DC-bus power loss and the electricity cost from the external grid power purchase through the combined use of differential flatness with B-splines parametrization; ii) the middle level employs a tracking Model Predictive Control (MPC) method which mitigates the discrepancies among the optimal and the actual profiles; iii) the low level controller handles the switching activity of the converters. The proposed approach is validated in simulation for a specific meshed DC microgrid system.

The sequencing and line balancing of manual mixed-model assembly lines are challenging tasks due to the complexity and uncertainty of operator activities. The control of cycle time and the sequencing of production can mitigate the losses due to non-optimal line balancing in the case of open-station production where the operators can work ahead of schedule and try to reduce their backlog. The objective of this paper is to provide a cycle time control algorithm that can improve the efficiency of assembly lines in such situations based on a specially mixed sequencing strategy. To handle the uncertainty of activity times, a fuzzy model-based solution has been developed. As the production process is modular, the fuzzy sets represent the uncertainty of the elementary activity times related to the processing of the modules. The optimistic and pessimistic estimates of the completion of activity times extracted from the fuzzy model are incorporated into a model predictive control algorithm to ensure the constrained optimization of the cycle time. The applicability of the proposed method is demonstrated based on a wire-harness manufacturing process with a paced conveyor, but the proposed algorithm can handle continuous conveyors as well. The results confirm that the application of the proposed algorithm is widely applicable in cases where a production line of a supply chain is not well balanced and the activity times are uncertain.

The purpose of this paper is to propose a new approach to the Min-Max Model Predictive Control (MMMPC) of Linear Time-Invariant Discrete-time Polytopic (LTIDP) systems. The purpose is to simplify the treatment of complex issues like stability and feasibility analysis of robust MPC as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two Degrees Of Freedom (2DOF) control scheme where the output r(k) of the feedforward Input Estimator (IE) is used as input forcing a stable closed-loop system Σf. Σf is the feedback connection of an LTIDP plant Σp with an LTI dynamic controller Σg. The task of Σg is to guarantee the quadratic stability of Σf, as well as the fulfillment of hard constraints on some physical variables of Σf for any input r(k) satisfying an ”a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on-line minimization of a worst case finite-horizon quadratic cost functional and is applied to Σf according to the usual receding horizon strategy. Rather than resorting to an ”ad hoc” software, the numerical complexity issue is here addressed reducing the number of both decision variables and constraints involved in the on-line constrained optimization procedure. This is obtained modeling r(k) as a B-spline function, which is known to be a universal approximator which also admits a parsimonious parametric representation. This allows us to reformulate the minimization of the worst case cost functional as a box-constrained Robust Least Squares (RLS) estimation problem which can be efficiently solved using Second Order Cone Programming (SOCP).

This paper designs the predictive pursuit-evasion game-based orbit control method for the chasing spacecraft to approach a space uncooperative maneuvering target. Firstly, the trajectory planning algorithm combines RRT⁎ and cubic splines to generate a feasible reference trajectory in the relative motion space for the chaser, which enables to deal with the boundary constraints and avoid collisions with the attachments of target. Then, based on the dynamics model, input constrains and objective functions, the pursuit-evasion game model between the target and the chaser is formulated, in which each one acts independently to satisfy its own objective function. With the game formulation, a predictive pursuit-evasion game controller for the chaser is designed to track reference trajectory. Under the frame of model predictive control, the multiple objective constraint optimization can be transferred into to quadratic programming problem to handle input constraints. By predicting opponent’s best move and changing its optimal strategy for its benefit iteratively, the saddle points of the game can be obtained without opponent’s maneuvering. Numerical simulations verify the effectiveness of the predictive pursuit-evasion game control method for approaching an uncooperative target.

The adoption of fractional calculus in control systems has enabled the synthesis of new controllers with fractional-order derivatives and integrals. Several optimization-based methods for tuning of linear fractional-order controllers have been explored. However, few have considered the stability of the closed-loop system during optimization. This paper presents a model-driven method for tuning of fractional-order controllers based on a heuristic optimization technique and the experimental use of Nyquist’s stability criterion to enforce closed-loop stability of fractional-order systems. The proposed frequency domain tuning method enables tuning of linear fractional-order controllers with few to medium number of parameters. The method can handle both fractional-order linear and integer-order linear plant models and controllers. To assist the experimental use of Nyquist’s stability criterion, a function for drawing a Logarithmic amplitude polar diagram has been developed. Simulation results of the method applied to a nanopositioning system in atomic force microscopy suggest that the proposed method can be used for optimization of fractional-order controllers while enforcing closed-loop stability. Given that the system can be stabilized with the given controller. Matlab code building on the FOTF toolbox and global optimization toolbox is provided.

Constrained optimization is a highly important field of engineering as most real-world optimization problems are associated with one or several constraints. Such problems are often challenging to solve due to their complexity and high nonlinearity. Differential evolution (DE) is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems and has shown to be very efficient when solving constrained global optimization problems. In this paper we investigate the performance of several DE variants existing in the literature such as the traditional DE, the composite DE (CoDE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (jDE and SaDE), for handling constrained structural optimization problems. The performance of each DE variant is quantified by using three well-known benchmark structures in 2D and 3D. It is shown that JADE, which updates control parameters in an adaptive way, truly exhibits superior performance and outperforms the other DE variants in all the cases examined.

Mars life support system models consist of numerous mission-critical, interrelated, and scenario-specific parameters. The large size and involved nature of these models make them computationally expensive, with parameters that are subject to several sources of uncertainty. Accurately characterizing these uncertainties and their impact on overall model predictions is crucial for decision-support and mission optimization. This paper focuses on uncertainty quantification of a model of a space crop cultivation system, which is one of several systems that are required on a long-duration manned Mars mission. The model performs constrained optimization of the equivalent system mass (ESM) metric, which augments shipped mass costs with those of pressurized volume, demanded power, thermal control, and needed crew time. This paper uses surrogate modeling for fast quantification of the effect of probabilistic uncertainty in mission-critical parameters of semi-empirical equations that describe crop growth and equipment operation. This work shows sparse polynomial chaos-Kriging (PCK) yields a computationally cheap-to-evaluate surrogate for the minimum ESM that accounts for probabilistic uncertainty in 86 model parameters. This surrogate model accelerates a global sensitivity analysis that elucidates which crop growth and equipment operation parameters are critical to mission outcome variability. The PCK surrogate model realizes a 100-fold computational speed gain in the estimation of the probability distribution of the minimum ESM.

In this paper, we propose a novel method for estimating depth values by stereo cameras through a curved transparent medium that causes refraction. Our method takes both the surface shape of the medium and the refraction into account. We model that the rays from the stereo cameras are refracted by a curved transparent medium whose inner surface is represented by a parametric model, assuming that the medium has constant thickness. The parameters of the model are estimated using a constrained optimization simply by attaching several markers on the inner surface. The depth value is then estimated by the triangulation considering the refraction based on the model. The experimental results show that our method yields consistently high error reduction rates with respect to the baseline method without considering the refraction caused by the medium. In addition, our method provides satisfactory estimates for various shapes of the medium.

This work studies chance constrained optimization of boundary-value parabolic partial differential equations (CCPDE) with random data, where the PDE model is treated as equality constraint and chance constraints are imposed on inequality constraints involving state variables. Since such a CCPDE problem is generally non-smooth, non-convex and difficult to solve directly, we use our recently proposed smoothing approximation method to solve the problem. As a result, the probability function of the chance constraints is approximated in two different ways by a family of differentiable functions. This leads to two smooth parametric optimization problems IAτ and OAτ, where the feasible sets of IAτ are always subsets (inner approximation) and the feasible sets of OAτ always supersets (outer approximation). The feasible sets of IAτ (resp. OAτ ) converge asymptotically to the feasible set of the CCPDE. Moreover, any limit point of a sequence of optimal solutions of IAτ (resp. OAτ ) is a stationary point of CCPDE. The viability of the approximation approach is numerically demonstrated by optimal thermal cancer treatment as a case study.

The paper describes one of the key steps in creating a bio-inspired galloping robot, namely parametric optimization of a multi-link leg mechanism. We introduce the cascaded constrained optimization procedure for finding optimal values for geometric parameters of a femur, knee, and foot segments for given design constraints and various gait specifications. The presented approach is computationally efficient and guarantees convergence to the unique solution. Steps on free parameters, constraints, and cost function selection are discussed. The efficiency of the proposed procedure is illustrated via a series of simulations. The proposed approach can also be implemented for the design of wearable robots like upper and lower-limb exoskeletons and rehabilitation systems that should follow sometimes sophisticated human-like trajectories.

Interior-point or barrier methods handle nonlinear programs by sequentially solving barrier subprograms with a decreasing sequence of barrier parameters. The specific barrier update rule strongly influences the theoretical convergence properties as well as the practical efficiency. While many global and local convergence analyses consider a monotone update that decreases the barrier parameter for every approximately solved subprogram, computational studies show a superior performance of more adaptive strategies. In this paper we interpret the adaptive barrier update as a reinforcement learning task. A deep Q-learning agent is trained by both imitation and random action selection. Numerical results based on an implementation within the nonlinear programming solver WORHP show that the agent successfully learns to steer the barrier parameter and additionally improves WORHP’s performance on the CUTEst test set.