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This paper proposes the Shrike Optimization Algorithm (SHOA) as a swarm intelligence optimization algorithm. Many creatures, who live in groups and survive for the next generation, randomly search for food; they follow the best one in the swarm, a phenomenon known as swarm intelligence. While swarm-based algorithms mimic the behaviors of creatures, they struggle to find optimal solutions in multi-modal problem competitions. The swarming behaviors of shrike birds in nature serve as the main inspiration for the proposed algorithm. The shrike birds migrate from their territory in order to survive. However, the SHOA replicates the survival strategies of shrike birds to facilitate their living, adaptation, and breeding. Two parts of optimization exploration and exploitation are designed by modeling shrike breeding and searching for foods to feed nestlings until they get ready to fly and live independently. This paper is a mathematical model for the SHOA to perform optimization. The SHOA benchmarked 19 well-known mathematical test functions, 10 from CEC-2019 and 12 from CEC-2022’s most recent test functions, for a total of 41 competitive mathematical test functions and four real-world engineering problems with different conditions, both constrained and unconstrained. The statistical results obtained from the Wilcoxon ranking sum and Fridman test show that SHOA has a significant statistical superiority in handling the test benchmarks compared to competitor algorithms in multi-modal problems. The results for engineering optimization problems show the SHOA outperforms other nature-inspired algorithms in many cases.

Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise robustness. First, if the input HS image is highly noisy, even if the balance between sparse and piecewise-smooth regularizations for abundance maps is carefully adjusted, noise may remain in the estimated abundance maps or undesirable artifacts may appear. Second, existing methods do not explicitly account for the effects of stripe noise, which is common in HS measurements, in their formulations, resulting in significant degradation of unmixing performance when such noise is present in the input HS image. To overcome these limitations, we propose a new robust HS unmixing method based on constrained convex optimization. Our method employs, in addition to the two regularizations for the abundance maps, regularizations for the HS image reconstructed by mixing the estimated abundance maps and endmembers. This strategy makes the unmixing process much more robust in highly noisy scenarios, under the assumption that the abundance maps used to reconstruct the HS image with desirable spatio-spectral structure are also expected to have desirable properties. Furthermore, our method is designed to accommodate a wider variety of noise including stripe noise. To solve the formulated optimization problem, we develop an efficient algorithm based on a preconditioned primal-dual splitting method, which can automatically determine appropriate stepsizes based on the problem structure. Experiments on synthetic and real HS images demonstrate the advantages of our method over existing methods.

An Error-Bound Particle Swarm Optimization (EB-PSO) is proposed in this work. The objective function is evaluated for each particle in each iteration. The velocity update equation is modified by introducing two new parameters $\zeta _{1}$ and $\zeta _{2}$ . These parameters varies exponentially, within the bounds ( $\zeta _{1,min}$ , $\zeta _{2,min}$ ) and ( $\zeta _{1,max}$ , $\zeta _{2,max}$ ), with respect to the number of iterations. Initially, a higher value of $\zeta _{2}$ and minimum value of $\zeta _{1}$ is chosen to facilitate a global search. Once the global error ( $\varepsilon _{2}$ ) is less than the desired value, $\zeta _{1}$ is allowed to increase from its minimum value and $\zeta _{2}$ is held constant at $\zeta _{2,max}$ . This leads to local exploitation of the search space. The proposed algorithm is implemented on Python platform. To verify the effectiveness of the proposed EB-PSO algorithm in analog circuit sizing, a case study on the performance and optimization of two-stage op-amp is presented, whose validation is done in Cadence-Virtuoso environment at 45-nm CMOS technology. The results show that the proposed EB-PSO algorithm converges in 11 iterations for two-stage op-amp, whereas it takes 23, 29, and 41 iterations to converge for conventional GA, DE, and PSO algorithms respectively.

This work introduces a Partition Bound Particle Swarm Optimization (PB-PSO) algorithm to enhance convergence rates in analog circuit optimization. Two new parameters, $\zeta _{1}$ and $\zeta _{2}$ , are incorporated to adaptively update particle velocities based on iteration numbers. The parameter $\zeta _{1}$ depends on the non-linear convergence factor ( $\alpha $ ) and the number of iterations, $N$ . The results indicate that $\zeta _{1}$ ’s optimal value occurs with $\alpha = 4.~\zeta _{2}$ partitions iterations into two regions, aiding local and global search. The PB-PSO algorithm, implemented in Python, demonstrates higher convergence rates than existing methods, with successful designs verified through Cadence-Virtuoso circuit simulations. The proposed PB-PSO algorithm converges in 15 and 13 iterations for differential amplifier and two-stage op-amp respectively. For a case study of two-stage amplifier, it achieves a gain of 60.4 dB with a phase margin of 79.76°, meeting input specifications within constraints. The figure of merit was then evaluated using the obtained parameters, which turns out to be 0.275 $V^{-2}$ .

Traditional approaches for multi-agent navigation consider the environment as a fixed constraint, despite the obvious influence of spatial constraints on agents' performance. Yet hand-designing conducive environments is inefficient and potentially expensive. The goal of this article is to consider the obstacle layout of the environment as a decision variable in a system-level optimization problem. In other words, we aim to find an automated solution that optimizes the obstacle layout to improve the performance of multi-agent navigation, under a variety of realistic constraints. Towards this end, we propose novel problems of unprioritized and prioritized environment optimization, where the former considers agents unbiasedly and the latter incorporates agent priorities into optimization. We show, through formal proofs, under which conditions the environment can change to guarantee completeness (i.e., all agents reach goals), and analyze the role of agent priorities in the environment optimization. We proceed to impose constraints on the environment optimization that correspond to real-world restrictions on obstacle changes, and formulate it mathematically as a constrained stochastic optimization problem. Since the relationship between agents, environment and performance is challenging to model, we leverage reinforcement learning to develop a model-free solution and a primal-dual mechanism to handle constraints. Distinct information processing architectures are integrated for various implementation scenarios, including online/offline optimization and discrete/continuous environment. Numerical results corroborate the theory and demonstrate the validity and adaptability of our approach.

This work extends a near feasibility threshold (NFT) based adaptive penalty function for constrained multiobjective optimization. The NFT zone adjoining the feasible region is considered as good one, where infeasible solutions are relatively less penalized. The modified penalty function, denoted by TAP with five different settings of NFT is embedded in a renowned multiobjective evolutionary algorithm based on decomposition, MOEA/D. This offers five constrained variants, namely CMOEA/D-TAP1 to CMOEA/D-TAP5, of the base algorithm. These variants are tested on well-known constrained multiobjective benchmark test suits, the CTP series and the CF series. The proposed variants are compared with the four best performing algorithms through HV (hyper volume) metric statistics for CTP series, and with seven state-of-the-art algorithms through Wilcoxon rank sum test employed to mean values of both HV and IGD (inverted generational distance) metrics for CF series. Simulation results reflect that overall performance of the newly introduced variants is better than the competitors for the taken benchmark test suits.

The Multi-Swarm approach allows the use of multiple configurations between two or more populations of particles, where each one can present different approaches (e.g. lbest, gbest, Unified, Guaranteed-Convergence) directed towards improving the optimization process. This article presents a proposal for local/global stochastic interconnection applied to the context of the Multi-Swarm algorithm, as well as for incrementing a local search method for refining previously obtained solutions. Two proposals are introduced for this new Multi-Swarm PSO (MSO). The first one is the inclusion of “counterpart particles”, which establishes a sub-topology between inter-swarm particles, accessed by migration and evaluability rules. The other involves using customized crossover operators and is based on the BLX scheme (Blend Crossover) with direction information used as a reference for establish a subspace search around the particles. Performance and robustness of the new approaches were assessed by ten constrained engineering design optimization problems (COPs), as is compared to other solutions already published in the scientific literature. Results indicate significant performance improvements for all 10 COPs when compared to concurrent-based MSOs. By making available new references from other swarms, the counterpart particles approach tends to improve the optimization process in the search space, while an intermediate layer of local search based on a modified directed BLX crossover should provide an extra search around the particle, and thus, refining previously obtained solutions.

This article proposes a lateral vehicle trajectory planning and control algorithm using a model predictive control (MPC) scheme for an automated perpendicular parking system. Previous work showed that approximated clothoid-based local path planning using a virtual towing distance provides low computational time and the stability of lateral vehicle motion in a parking system. However, this approach cannot function in certain parking situations and may cause undesirable steering maneuvers due to state-dependent planning. We present a new approximated clothoid path based on lateral vehicle kinematics to cope with these problems. Using the proposed kinematic model, we formulate an MPC problem for path planning. Then, the proposed lateral vehicle trajectory planning becomes an MPC problem under constraints. Besides, we show that lateral vehicle motion for vertical parking can be implemented using simple kinematic lateral motion control. Experimental results show that the vehicle with the proposed method moves smoothly and completes the given parking mission under constraints, even under tight parking space conditions. [ABSTRACT FROM AUTHOR]

This article presents an automated, model-free, data-driven method for the safe tuning of PID cascade controller gains based on Bayesian optimization. The optimization objective is composed of data-driven performance metrics and modeled using Gaussian processes. The safety requirement is imposed via a barrier-like term in the objective, which is introduced to account for operational changes in the system. We further introduce a data-driven constraint that captures the stability requirements from system data. Numerical evaluation shows that the proposed approach outperforms relay feedback autotuning and quickly converges to the global optimum, thanks to a tailored stopping criterion. We demonstrate the performance of the method through simulations and experiments. For experimental implementation, in addition to the introduced safety constraint, we integrate a method for automatic detection of the critical gains and extend the optimization objective with a penalty depending on the proximity of the current candidate points to the critical gains. The resulting automated tuning method optimizes system performance while ensuring stability and standardization. [ABSTRACT FROM AUTHOR]

This article proposes a control and modulation strategy for medium-voltage (MV) drives that exhibits excellent steady-state and transient behavior. Specifically, optimized pulse patterns (OPPs) and direct model predictive control are employed so that the associated advantages of both, such as minimum stator current total demand distortion (TDD) and fast transients, respectively, are fully exploited. To do so, the current reference trajectory tracking and modulation problems are addressed in a coordinated manner in the form of a constrained optimization problem that utilizes the knowledge of the stator current evolution—as described by its gradient—within the prediction horizon. Solving this problem yields the optimal real-time modification of the offline-computed OPP, which guarantees that very low—and close to its theoretical minimum value—stator current TDD is produced at steady state, and very short settling times during transients. To highlight the effectiveness of the proposed strategy, a variable speed drive system consisting of a three-level neutral point clamped inverter and an MV induction machine serves as a case study. [ABSTRACT FROM AUTHOR]

A generator of classes of multidimensional test problems for benchmarking continuous constrained global optimization methods is proposed. It is based on the generator of test classes for global optimization proposed in 2003 by Gaviano, Kvasov, Lera, and Sergeyev and extends the previous generation procedure from the box-constrained case to the case of nonlinear constraints. The user has the possibility to fix the difficulty of tests in an intuitive way by choosing several types of constraints. A detailed information (including the global solution) for each of 100 problems in each generated class is provided to the user. The generator is particularly suited for testing black-box optimization algorithms that normally address low or medium dimensional problems with hard to evaluate objective functions. [ABSTRACT FROM AUTHOR]

Most commercially available optical see-through head-mounted displays (OST-HMDs) utilize optical combiners to simultaneously visualize the physical background and virtual objects. The displayed images perceived by users are a blend of rendered pixels and background colors. Enabling high fidelity color perception in mixed reality (MR) scenarios using OST-HMDs is an important but challenging task. We propose a real-time rendering scheme to enhance the color contrast between virtual objects and the surrounding background for OST-HMDs. Inspired by the discovery of color perception in psychophysics, we first formulate the color contrast enhancement as a constrained optimization problem. We then design an end-to-end algorithm to search the optimal complementary shift in both chromaticity and luminance of the displayed color. This aims at enhancing the contrast between virtual objects and the real background as well as keeping the consistency with the original displayed color. We assess the performance of our approach using a simulated OST-HMD environment and an off-the-shelf OST-HMD. Experimental results from objective evaluations and subjective user studies demonstrate that the proposed approach makes rendered virtual objects more distinguishable from the surrounding background, thereby bringing a better visual experience. [ABSTRACT FROM AUTHOR]

During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, we focus on computing the depth of the interference, so that these false positive interferences can be removed, and attention can be properly focused on the actual design. Specifically, we focus on efficiently computing the penetration depth between two polyhedra, which is a well-studied problem in the computer graphics community. We formulate the problem as a constrained five-variable global optimization problem, and then derive an equivalent unconstrained, two-variable nonsmooth problem. To solve the optimization problem, we apply a popular stochastic multistart optimization algorithm in a novel way, which exploits the advantages of each problem formulation simultaneously. Numerical results for the algorithm, applied to 14 randomly generated pairs of penetrating polytopes, illustrate both the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy fault tolerance algorithm is proposed for quarter vehicle active suspensions based on multi-objective constrained optimizations, which improves the riding comfort and driving safety. The objective function approach the optimal solutions via integrating multi-objective constraints as cost functions. By introducing the barrier function, the nonlinear active suspensions with multi-objective constraints are transformed into pure feedback systems without constraints. The problem is rather complicated yet challenging if the actuator faults are taken into account in quarter vehicle. The actuator faults are solved by the utilization of proportional actuation method. The unknown smooth dynamics based on physical truth are identified by exploiting the fuzzy logic knowledge. Meanwhile, the signals received in the suspensions do not violate the constraint boundary. Finally, the simulation results show that the algorithm is effective.

In complex indoor environments, there is often no Line of Sight (LOS) path between the transmitter and the receiver due to walls, moving people, and many other obstacles. Traditional localization method based on LOS measurement is no longer available which provides lower localization accuracy in Non-Line of Sight (NLOS) environments. In response to this problem, this paper proposes a joint localization algorithm for scatterers and target user based on indoor prior information in NLOS scenarios. The algorithm makes use of the prior localization information of the access point (AP) and the wall to determine the position of the scatterers and target user simultaneously. Since the established constrained optimization problem is non-convex which is a difference of convex (DC) problem, it is transformed into a convex one based on a Taylor series expansion (TSE) method before it is solved. At the same time, as only a single AP signal can be received normally, the proposed method is then extended to the scenario with only one AP. Simulation and real-world testing results both show that not only the proposed method based on multiple APs, but also the method based on a single AP achieve high positioning accuracy, which are better than the existing positioning methods mentioned in this article as well. [ABSTRACT FROM AUTHOR]

Model predictive control is a promising technique for electric drives as it enables optimization for multiple parameters and offers reliable operation with nonlinear systems. In this article, a novel approach is presented that aims to harness the advantages of both finite and continuous set model predictive methods in converter-fed ac drive control. The proposed method requires the calculation of only seven predicted states. These states are then assigned cost function values. Using a quadratic regression model, the cost function is mapped to the entire modulation region. After solving a constrained optimization problem on this cost function mapping, the optimal voltage vector is obtained, which is then applied via pulsewidth modulation. The presented method can also be applied to multilevel converter structures without the need to calculate predictions for additional voltage vectors. Therefore, the proposed method does not increase in complexity with the utilized converter topology. Furthermore, the method offers a fixed switching frequency operation and an exact noniterative solution to the optimization problem due to the formulation of the regression model. As a case study, simulation and experimental results verify the operation of the predictive torque control for permanent magnet synchronous machines with the proposed method. [ABSTRACT FROM AUTHOR]

Conventional radars repeat the transmission of the same waveform after a predefined interval of time called pulse-repetition-interval (PRI). This technique helps estimate the range and Doppler shift of the targets and suppress clutter. However, in dual-function radar communication (DFRC), a different symbol waveform is transmitted after each PRI. Depending on the number of targets, radar receiver output yields several peaks representing different targets’ ranges. Each peak comes with its side-lobes called range-side-lobes (RSL). In DFRC, due to different symbol waveform transmission, peaks and RSLs do not remain coherent, making Doppler shift estimation and clutter suppression challenging tasks. In most of the available literature, iterative receive filters have been designed for DFRC to minimize RSLs and achieve coherent output for different waveforms. However, the proposed receive filter does not guarantee coherent output for more than two waveforms. In contrast, we proposed two novel closed-form algorithms to design receive filters for DFRC that guarantee coherent output response for several waveforms and suppress RSLs. Simulation results demonstrate that the proposed receivers achieve full coherency, and the RSLs are significantly lower than the conventional method. Furthermore, the advantage of achieving coherent output response is shown in target detection and bit-error-rate improvement. [ABSTRACT FROM AUTHOR]

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is formulated as the marginalized maximum likelihood (or type-II ML) estimation of the variance hyperparameters of a joint sparsity inducing Gaussian prior on the source signals. We derive conditions under which the resulting nonconvex constrained optimization perfectly recovers the nonzero support of a joint-sparse Gaussian source ensemble with arbitrarily high probability. The support error probability decays exponentially with the number of MMVs at a rate that depends on the smallest restricted singular value and the nonnegative null space property of the self Khatri-Rao product of the sensing matrix. Our analysis confirms that nonzero supports of size as high as $O(m^{2})$ are recoverable from $m$ measurements per sparse vector. Our derived sufficient conditions for support consistency of the proposed constrained type-II ML solution also guarantee the support consistency of any global solution of the multiple sparse Bayesian learning (M-SBL) optimization whose nonzero coefficients lie inside a bounded interval. For the case of noiseless measurements, we further show that a single MMV is sufficient for perfect recovery of the $k$ -sparse support by M-SBL, provided all subsets of $k + 1$ columns of the sensing matrix are linearly independent. [ABSTRACT FROM AUTHOR]

Data centers are facilities with large number of servers providing cloud services. The increasing number of data centers in the last years has generated environmental concern due to the large amount of energy consumed by them. This also includes some auxiliary services such as the cooling equipment which is known to be very costly. For that reason, efficient data center strategies are needed in order to provide an acceptable quality of service (QoS) and suitable temperature for every server while using the least amount of resources possible. This article presents some strategies to deal with the unified workload and temperature problem that appears in the data center. As the system is modeled as a queue and the control variables have an hybrid nature, some highly parallelizable particle-based optimization algorithms are proposed to solve the optimization problem. Numerical simulations are provided in order to illustrate the effectiveness of the strategy. These simulations also show the improvements obtained from the GPU computing. Finally, a probabilistic evaluation approach is developed in order to provide certificates on the probability of constraint satisfaction without increasing the computational burden of the online problem. Note to Practitioners—This article addresses the problem of deciding in real-time the number of active servers in a data center that is required to meet the quality of service (QoS) demands while keeping energy consumption at a minimum. The temperature set point of the cooling equipment must also be taken into account, as it is advisable to use the minimum cooling that keeps the servers running in safe conditions. The management strategy proposed is based on predictive control. In this way, the number of active servers and temperature set point will be chosen so that the future energy consumption is minimized while guaranteeing that QoS and safety demands are met under different possible operating conditions. Furthermore, the proposed management strategy can be tuned depending on the QoS that it is desirable to provide. The proposed strategy will lead to energy-consumption improvements while having guarantees on the data center performance. [ABSTRACT FROM AUTHOR]

In this article, we investigate the problem of dynamically estimating the instantaneous position, orientation, velocity, and angular velocity of an arbitrarily shaped object during its free flight based on image frames taken simultaneously by two high-speed cameras. Aerodynamic effects, including drag, lift, and Magnus forces, are modeled to describe the object’s flight. Observables are derived from combining dynamics with a camera projection model assuming two-view geometry, via the use of multiple quaternions. The state of the composed system can then be estimated via constrained Kalman filtering, to which a solution is presented for the case of multiple quadratic constraints. To keep track of appearing and disappearing visual features during flight, the estimation algorithm employs a graph matching-based technique to maintain a set of evolving hypotheses through evaluation, pruning, and addition. Experiments conducted over various objects have either provided validation against motions independently estimated using multiple accelerometers, or formed verification by matching flight images against projections based on the state estimates. [ABSTRACT FROM AUTHOR]

In this article, we present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon our novel optimality conditions for unconstrained control effort minimization. We design linear-complexity operations on this representation to conduct spatial–temporal deformation under various planning requirements. Smooth maps are utilized to exactly eliminate geometrical constraints in a lightweight fashion. A variety of state-input constraints are supported by the decoupling of dense constraint evaluation from sparse parameterization and the backward differentiation of flatness map. As a result, this framework transforms a generally constrained multicopter planning problem into an unconstrained optimization that can be solved reliably and efficiently. Our framework bridges the gaps among solution quality, planning efficiency, and constraint fidelity for a multicopter with limited resources and maneuvering capability. Its generality and robustness are both demonstrated by applications to different flight tasks. Extensive simulations and benchmarks are also conducted to show its capability of generating high-quality solutions while retaining the computation speed against other specialized methods by orders of magnitude. [ABSTRACT FROM AUTHOR]

This article presents a maximum torque per ampere strategy for a five-phase synchronous reluctance drive. The approach is developed considering general machine parameters and is formalized as a constrained optimization problem. The optimal solution is found analytically by using Lagrange’s multipliers method and is based on the computation of the eigenvalues and eigenvectors of the inductance derivatives matrix. The proposed approach is evaluated both numerically and experimentally. It is also compared with other current references control strategies, effectively showing a reduction of the machine rms currents for the same developed torque. The same approach can also be extended to machines with a different number of phases. [ABSTRACT FROM AUTHOR]

To achieve the global optimization of efficiency and power density of interleaved buck/boost converter (IBBC) for transportation electrification, a numerical optimization method is proposed based on the penalty and barrier theory. In this method, converter volume is the optimization objective, and efficiency and flux density are the constraints. To formulate the optimization objective and constraints, comprehensive modeling for IBBC is conducted, which decouples master–slave relationships among variables in the modeling process. Then, the penalty and barrier theory is performed on the optimization objective and constraints and an integrated optimization function is established, thus converting the constrained numerical optimization problem to an unconstrained one. Hereafter, a modified backtracking search method is employed for the minimization of the integrated optimization function, and Pareto fronts of efficiency and volume are obtained. Finally, a 60-kW IBBC converter was constructed and the power density reaches 9.65 kW/L, whereas the highest efficiency is 98.6%. Compared with an unoptimized converter, efficiency and power density are improved by 0.3% and 0.65 kW/L, respectively. [ABSTRACT FROM AUTHOR]

Up to date, the existing methods for nonlinear optimization with time-dependent parameters can be classified into two types: 1) static methods are capable of handling inequality constraints but may generate large lagging errors in the solution of the intrinsically time-dependent constrained nonlinear optimization (TDCNO) problem due to the hypothesis of short-time invariance and 2) time-variant methods, e.g., zeroing neural networks, are able to remedy the lagging error but fail to solve the TDCNO problem under inequality constraints. To resolve this contradiction, a noise-suppressing neural dynamics (NSND) model is proposed to solve the TDCNO problem subject to both equality and inequality constraints via the nonlinear complementary problem (NCP) function. The proposed method allows inequality constraints for unknown variables, removes the short-time invariance hypothesis, and further eliminates lagging errors during the solving process in the presence of noises. Besides, the rapid convergence, global stability, and noise processing of the NSND model are verified by the theoretical analyses. Simulation results of illustrative examples, including dimensionality reduction on principal component analyses (PCA) and a robot motion control, show that the NSND model outperforms the existing models for the TDCNO problem. [ABSTRACT FROM AUTHOR]

In wireless networks, the optimization problems generally have complex constraints and are usually solved via utilizing the traditional optimization methods that have high computational complexity and need to be executed repeatedly with the change of network environments. In this paper, to overcome these shortcomings, an unsupervised deep unrolling framework based on projection gradient descent (PGD), i.e., unrolled PGD network (UPGDNet), is designed to solve a family of constrained optimization problems. The set of constraints is divided into two categories according to the coupling relations among optimization variables and the convexity of constraints. One category of constraints includes convex constraints with decoupling among optimization variables, and the other category of constraints includes non-convex or convex constraints with coupling among optimization variables. Then, the first category of constraints is directly projected onto the feasible region, while the second category of constraints is projected onto the feasible region using a neural network. Finally, an unrolled sum rate maximization network (USRMNet) is designed based on UPGDNet to solve the weighted SR maximization problem for the multiuser ultra-reliable low latency communication system. Numerical results show that USRMNet has a comparable performance with low computational complexity and an acceptable generalization ability in terms of the user distribution. [ABSTRACT FROM AUTHOR]

Handling nonlinear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and nonlinear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this article, we adopt the framework of estimation of distribution algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with nonlinear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning, and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint-handling methods. Conducted experiments confirm the speed, robustness, and efficiency of the proposed algorithm in tackling various problems with linear and nonlinear constraints. [ABSTRACT FROM AUTHOR]

In addition to the search for feasible solutions, the utilization of informative infeasible solutions is important for solving constrained multiobjective optimization problems (CMOPs). However, most of the existing constrained multiobjective evolutionary algorithms (CMOEAs) cannot effectively explore and exploit those solutions and, therefore, exhibit poor performance when facing problems with large infeasible regions. To address the issue, this article proposes a novel method, called DD-CMOEA, which features dual stages (i.e., exploration and exploitation) and dual populations. Specifically, the two populations, called mainPop and auxPop, first individually evolve with and without considering the constraints, responsible for exploring feasible and infeasible solutions, respectively. Then, in the exploitation stage, mainPop provides information about the location of feasible regions, which facilitates auxPop to find and exploit surrounding infeasible solutions. The promising infeasible solutions obtained by auxPop in turn help mainPop converge better toward the Pareto-optimal front. Extensive experiments on three well-known test suites and a real-world case study fully demonstrate that DD-CMOEA is more competitive than five state-of-the-art CMOEAs. [ABSTRACT FROM AUTHOR]

Expensive constrained optimization refers to problems where the calculation of the objective and/or constraint functions are computationally intensive due to the involvement of complex physical experiments or numerical simulations. Such expensive problems can be addressed by Gaussian process-assisted evolutionary algorithms. In many problems, the (single) objective and constraints are correlated to some extent. Unfortunately, existing works based on the Gaussian process for expensive constrained optimization treat the objective and multiple constraints as being statistically independent, typically for the ease of computation. To fill this gap, this article investigates the correlation among the objective and constraints. To be specific, we model the correlation amongst the objective and constraint functions using a multitask Gaussian process prior, and then mathematically derive a constrained expected improvement acquisition function that allows the correlation among the objective and constraints. The correlation between the objective and constraints can be captured and leveraged during the optimization process. The performance of the proposed method is examined on a set of benchmark problems and a real-world antenna design problem. On problems with high correlation amongst the objective and constraints, the experimental results show that leveraging the correlation yields improvements in both the optimization speed and the constraint-handling ability compared with the method that assumes the objective and constraints are statistically independent. [ABSTRACT FROM AUTHOR]

Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction (reducing the number of support vectors) appears to be necessary, which gives rise to the topic of the sparse SVM. Motivated by this problem, the sparsity constrained kernel SVM optimization has been considered in this paper in order to control the number of support vectors. Based on the established optimality conditions associated with the stationary equations, a Newton-type method is developed to handle the sparsity constrained optimization. This method is found to enjoy the one-step convergence property if the starting point is chosen to be close to a local region of a stationary point, thereby leading to a super-high computational speed. Numerical comparisons with several powerful solvers demonstrate that the proposed method performs exceptionally well, particularly for large-scale datasets in terms of a much lower number of support vectors and shorter computational time. [ABSTRACT FROM AUTHOR]

A local constrained multiobjective Bayesian optimization (LoCoMOBO) method is introduced to address automatic sizing and tradeoff exploration for analog and RF integrated circuits (ICs). LoCoMOBO applies to constrained optimization problems utilizing multiple Gaussian process (GP) models that approximate the objective and constraint functions locally in the search space. It searches for potential pareto optimal solutions within trust regions of the search space using only a few time-consuming simulations. The trust regions are adaptively updated during the optimization process based on feasibility and hypervolume metrics. In contrast to mainstream Bayesian optimization approaches, LoCoMOBO uses a new acquisition function that can provide multiple query points, therefore allowing for parallel execution of costly simulations. GP inference is also enhanced by using GPU acceleration in order to handle highly constrained problems that require large sample budgets. Combined with a framework for schematic parametrization and simulator calls, LoCoMOBO provides improved performance tradeoffs and sizing results on three real-world circuit examples, while reducing the total runtime up to $\times 43$ times compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

System design tools are often only available as input–output blackboxes: for a given design as input, they compute an output representing system behavior. Blackboxes are intended to be run in the forward direction. This article presents a new method of solving the “inverse design problem,” namely, given requirements or constraints on output, find an input that also optimizes an objective function. This problem is challenging for several reasons. First, blackboxes are not designed to be run in reverse. Second, inputs and outputs can be discrete and continuous. Third, finding designs concurrently satisfying a set of requirements is hard because designs satisfying individual requirements may conflict with each other. Fourth, blackbox evaluations can be expensive. Finally, evaluations can sometimes fail to produce an output due to nonconvergence of underlying numerical algorithms. This article presents CNMA, a new method of solving the inverse problem that overcomes these challenges. CNMA tries to sample only the part of the design space relevant to solving the inverse problem, leveraging the power of neural networks, mixed-integer linear programs, and a new learning-from-failure feedback loop. This article also presents a parallel version of CNMA that improves the efficiency and quality of solutions over the sequential version and tries to steer it away from local optima. CNMA’s performance is evaluated against conventional optimization methods for seven nonlinear design problems of 8 (two problems), 10, 15, 36 and 60 real-valued dimensions and one with 186 binary dimensions. Conventional methods evaluated are stable, off-the-shelf implementations of the Bayesian optimization with the Gaussian Processes, Nelder–Mead, and Random Search. The first two do not even produce a solution for problems that are high dimensional, having both discrete and continuous variables or whose blackboxes fail to return values for some inputs. CNMA produces solutions for all problems. When conventional methods do produce solutions, CNMA improves upon their performance by 1%–87%. [ABSTRACT FROM AUTHOR]

This article presents a real-time realization of a continuous-control-set model predictive current controller for the two types of permanent magnet synchronous machines: 1) surface-mounted permanent magnet synchronous machine (SMPMSM) and 2) interior permanent magnet synchronous machine (IPMSM). The constrained optimization problem is solved online using a slack formulation of the primal-dual interior-point method. The proposed controller is tested on a 14.5 kW SMPMSM based on the linear time-invariant (LTI) model of the machine and on a 0.5 kW IPMSM. For the latter, we present in detail how the nonlinear first-principles modeling yields the fastest possible transient as well as an offset-free steady-state performance. The experimental results were obtained at sampling times typically used in the electrical drive applications (125 and 100 $\mu$ s for the two machines, respectively). [ABSTRACT FROM AUTHOR]

A growing number of organizations are hosting their software applications in distributed data centers (DCs) in the cloud, for faster response time and higher energy efficiency. The dramatic increase of user tasks, however, poses a significant challenge on DC providers to retain users’ expectations on both aspects. To tackle this challenge, this work first formulates the problem into a constrained biobjective optimization problem. A biobjective algorithm, named simulated-annealing-based adaptive differential evolution (SADE), is presented to simultaneously reduce both the response time of tasks and energy cost. Meanwhile, a method of minimal Manhattan distance is adopted to search for a final knee, for achieving a good balance between response time minimization and energy cost reduction. Experimental results on real-life datasets, i.e., the electricity prices and tasks collected from a Google cluster trace, have proved that SADE yields less task response time and lower energy cost compared with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

A colored traveling salesman problem (CTSP) as a generalization of the well-known multiple traveling salesman problem utilizes colors to distinguish the accessibility of individual cities to salesmen. This work formulates a precedence-constrained CTSP (PCTSP) over hypergraphs with asymmetric city distances. It is capable of modeling the problems with operations or activities constrained to precedence relationships in many applications. Two types of precedence constraints are taken into account, i.e., 1) among individual cities and 2) among city clusters. An augmented variable neighborhood search (VNS) called POPMUSIC-based VNS (PVNS) is proposed as a main framework for solving PCTSP. It harnesses a partial optimization metaheuristic under special intensification conditions to prepare candidate sets. Moreover, a topological sort-based greedy algorithm is developed to obtain a feasible solution at the initialization phase. Next, mutation and multi-insertion of constraint-preserving exchanges are combined to produce different neighborhoods of the current solution. Two kinds of constraint-preserving $k$ -exchange are adopted to serve as a strong local search means. Extensive experiments are conducted on 34 cases. For the sake of comparison, Lin–Kernighan heuristic, two genetic algorithms and three VNS methods are adapted to PCTSP and fine-tuned by using an automatic algorithm configurator-irace package. The experimental results show that PVNS outperforms them in terms of both search ability and convergence rate. In addition, the study of four PVNS variants each lacking an important operator reveals that all operators play significant roles in PVNS. [ABSTRACT FROM AUTHOR]

Most off-highway constructions and agriculture equipment use hydraulics, which has unmatched power density, for power transmission and throttling as a means for control. A novel hybrid hydraulic–electric architecture (HHEA) has recently been proposed to improve efficiency for high-power machines that would have been cost-prohibitive to electrify directly. HHEA uses a set of common pressure rails (CPRs) to transmit the majority of power hydraulically and small electric motor drives to modulate that power and to achieve precise control. This article proposes a computationally efficient Lagrange multiplier method (LMM) for computing the optimal sequence of pressure rail selections to minimize energy use. This is needed to evaluate HHEA’s energy-saving potential and for iterative architecture design and sizing. An interesting complication is that the cost function is not fully defined until the candidate control sequence is fully specified. This issue is dealt with by decomposing the original problem into a set of sub-problems with additional constraints that can be solved efficiently. Computational effort can be further reduced if actuators are optimized individually instead of together. However, additional steps are required to prevent the constraint functions from becoming discontinuous with respect to the Lagrange multipliers, which is necessary for meeting the constraints. A case study of a construction machine demonstrates the efficacy of the method and shows that the HHEA reduces energy consumption by 68%–73% compared to the baseline load-sensing architecture. [ABSTRACT FROM AUTHOR]

Noncooperative game-theoretic methods have been widely utilized in system-level engineering applications as they are capable of aggregating interests, information, and behaviors of many independent, self-interested entities with conflicting objectives via payoffs. Another major advantage is the existence of adaptive learning dynamics that involve realistic, constrained decision making, and converge to Nash equilibrium. If players are not fully rational (e.g., constrained or regulated), such convergence is generally not guaranteed except in some special games, such as potential games (PGs). Within each PG, there exists a potential function that connects the global objective with players’ payoffs and actions such as optimizers of the global objective align with Nash equilibrium. Therefore, PGs have been widely utilized in many engineering domains and recently to power grids. This article summarizes the state-of-the-art existing literature on applying various PG models in power grids and provides an overlook of potential models and algorithms that have not received sufficient attention but possess unique capabilities to solve existing challenges in power grids. [ABSTRACT FROM AUTHOR]

Considering the requirement of avoiding obstacles in different planetary landing missions, this article presents a generalized method dealing with the obstacle avoidance constrained landing trajectory optimization problem with vectorized strategy, i.e., vector trajectory method (VTM). By introducing a trajectory direction constraint with vectorized description, the character of the obstacle avoidance trajectory can be more specifically depicted. Moreover, by satisfying proper trajectory direction constraint, the lander's particular performances, such as the observation to the target or probability of a safe flight, can be improved. To this end, the VTM and relevant theorem are first developed, revealing the relationship between the two aspects of obstacle avoidance constraint (i.e., distance constraint and trajectory direction constraint). Then, both aspects of constraints are uniformly transformed as the auxiliary angle magnitude constraint with the vectorized strategy, which significantly simplifies the solving procedure of obstacle avoidance constrained trajectory optimization problem. Finally, the proposed VTM is illustrated in detail through the examples with the planetary landing background of atmospheric entry and powered descent landing. [ABSTRACT FROM AUTHOR]

Placing robotsoutside controlled conditions requires versatile movement representations that allow robots to learn new tasks and adapt them to environmental changes. The introduction of obstacles or the placement of additional robots in the workspace and the modification of the joint range due to faults or range-of-motion constraints are typical cases, where the adaptation capabilities play a key role for safely performing the robot’s task. Probabilistic movement primitives (ProMPs) have been proposed for representing adaptable movement skills, which are modeled as Gaussian distributions over trajectories. These are analytically tractable and can be learned from a small number of demonstrations. However, both the original ProMP formulation and the subsequent approaches only provide solutions to specific movement adaptation problems, e.g., obstacle avoidance, and a generic, unifying, probabilistic approach to adaptation is missing. In this article, we develop a generic probabilistic framework for adapting ProMPs. We unify previous adaptation techniques, for example, various types of obstacle avoidance, via-points, and mutual avoidance, in one single framework and combine them to solve complex robotic problems. Additionally, we derive novel adaptation techniques such as temporally unbound via-points and mutual avoidance. We formulate adaptation as a constrained optimization problem, where we minimize the Kullback–Leibler divergence between the adapted distribution and the distribution of the original primitive,while we constrain the probability mass associated with undesired trajectories to be low. We demonstrate our approach on several adaptation problems on simulated planar robot arms and seven-degree-of-freedom Franka Emika robots in a dual-robot-arm setting. [ABSTRACT FROM AUTHOR]

Spatial dose non-uniformity is a key variation of concern in ion implantation. These non-uniformities are often compensated for by adjusting the implantation times spent at each point on the wafer: areas with a low uncompensated dose are assigned more implantation time, while those with a greater dose are assigned reduced times. In this paper, we present a machine learning based method that rapidly learns a set of compensating implantation times in order to achieve a desired uniformity.We propose an iterative tuning approach comprised of two components. The first component is an empirical Bayesian forward model that infers the relationship between the implantation times and the implantation dose profile. The model is updated as new implantations are performed and measured, enabling progressive accuracy improvements during tuning. The second component is an optimization method that selects compensating times by solving a constrained optimization problem. When tuning a process, we alternate between these two components, repeatedly selecting compensating times, measuring the resulting dose profile and updating the model until the desired uniformity is achieved. Our proposed method is compared to the conventional non-Bayesian industry method of record, and converges to a desired uniformity in significantly fewer iterations. Finally, the solutions found by our method result in a greater total dose given the same total implantation time and uniformity, increasing the throughput of implantation with no added cost. [ABSTRACT FROM AUTHOR]

This paper investigates the multi-part collaborative task offloading with multiple servers in mobile edge computing (MEC) systems by considering server overload and long-term system performance. Our goal is to achieve the optimal user experience within the range of the network operator’s affordable cost. To this end, we design a two-layer computation offloading framework based on the multi-part offloading mode and the collaborations among small cell base station (SBS) servers. Furthermore, a multi-object constrained optimization problem is formulated, which jointly optimizes user association, channel allocation, and multi-part collaborative task offloading. To solve this problem, we propose a Genetic and Deep Deterministic Policy Gradient (GADDPG)-based computation offloading scheme, where the long-term system performance is considered. Numerical and simulation results demonstrate that the proposed GADDPG-based computation offloading scheme outperforms other methods in effectively solving the server overload and guarantees long-term system performances while ensuring the best user experience. [ABSTRACT FROM AUTHOR]

Featuring the fast response and flexibility in control allocation, an electric vehicle with in-wheel motors is a good platform for implementing advanced vehicle dynamics control. Among many active safety functions of an in-wheel motor driven vehicle (IMDV), lateral stability control is a key technology, which can be realized through torque vectoring. To further advance the lateral stabilization performance of the IMDV, in this article a novel data-driven nonlinear model predictive control (NMPC) is proposed based the recurrent high-order neural network (RHONN) modelling method. First, the new RHONN model is developed to represent vehicle’s nonlinear dynamic behaviors. Different from the conventional physics-based modelling method, the RHONN model forms high-order polynomials by neuron states to feature nonlinear dynamics. Based on the RHONN model, the steady-state responses of vehicle’s yaw rate and sideslip angle are iteratively optimized and set as the control objectives for low-level controller, aiming to improve the system robustness. Besides, a nonlinear model predictive controller is designed based on the RHONN, which is expected to improve the prediction accuracy during the receding horizon control. Further, a constrained optimization problem is formulated to derive the required yaw moment for vehicle lateral dynamics stabilization. Finally, the performance of the developed RHONN-based nonlinear MPC is validated on an IMDV in the CarSim/Simulink simulation environment. The validation results show that the developed approach outperforms the conventional method, and further improves the stable margin of the system. It is able to enhance the lateral stabilization performance of the IMDV under various driving scenarios, demonstrating the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider decentralized large-scale continuous submodular constrained optimization problems over networks, where the goal is to maximize a sum of nonconvex functions with diminishing returns property. However, the computations of the projection step and the whole gradient can become prohibitive in high-dimensional constrained optimization problems. For this reason, a decentralized randomized block-coordinate Frank-Wolfe algorithm is proposed for submoduar maximization over networks by local communication and computation, which adopts the randomized block-coordinate descent and the Frank-Wolfe technique. We also show that the proposed algorithm converges to an approximation fact $(1-e^{-p_{\max }/p_{\min }})$ of the global maximal points at a rate of $\mathcal {O}(1/T)$ by choosing a suitable stepsize, where $T$ is the number of iterations. In addition, we confirm the theoretical results by experiments. [ABSTRACT FROM AUTHOR]

Effective constraint handling techniques (CHTs) are of great significance for evolutionary algorithms (EAs) dealing with constrained optimization problems (COPs). To date, many CHTs, such as penalty function, superiority of feasible solutions, and $\epsilon $ -constraint (EC), have been designed. However, different CHTs are usually suited to different problems, even the most appropriate technique changes along with the stages of the optimization process. Motivated by this phenomenon, we propose a voting-mechanism-based ensemble framework, named voting mechanism for constraint handling (VMCH), to integrate multiple CHTs for solving various COPs. In this framework, each CHT acts as a voter, all voters vote for each pair of solutions, and the solution in each pair with the highest weighted votes is considered better. In addition, an adaptive strategy is developed to adjust the voter weights according to their historical voting performance. To investigate the performance of VMCH in improving existing algorithms, the proposed VMCH is embedded into the three best algorithms in the competition on constrained single objective real-parameter optimization at CEC 2018, namely, MAgES, iLSHADE $\epsilon $ , and IUDE, to form three new algorithm versions, i.e., MAgES-VMCH, iLSHADE $\epsilon $ -VMCH, and IUDE-VMCH. They are compared with seven state-of-the-art peer algorithms. Extensive experiments are conducted on 57 real-world COPs. The ranking results show that the new algorithm version MAgES-VMCH takes first place among the ten comparison algorithms. Moreover, all the new VMCH-enhanced versions of the three best algorithms are superior to their original versions. Therefore, the proposed VMCH framework can achieve competitive performance in solving COPs. [ABSTRACT FROM AUTHOR]

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of variables. Inspired by ensemble clustering that aims to seek a better clustering result from a set of clustering results, we propose self-supervised SNMF (S3NMF), which is capable of boosting clustering performance progressively by taking advantage of the sensitivity to initialization characteristic of SNMF, without relying on any additional information. Specifically, we first perform SNMF repeatedly with a random positive matrix for initialization each time, leading to multiple decomposed matrices. Then, we rank the quality of the resulting matrices with adaptively learned weights, from which a new similarity matrix that is expected to be more discriminative is reconstructed for SNMF again. These two steps are iterated until the stopping criterion/maximum number of iterations is achieved. We mathematically formulate S3NMF as a constrained optimization problem, and provide an alternative optimization algorithm to solve it with the theoretical convergence guaranteed. Extensive experimental results on 10 commonly used benchmark datasets demonstrate the significant advantage of our S3NMF over 14 state-of-the-art methods in terms of 5 quantitative metrics. The source code is publicly available at https://github.com/jyh-learning/SSSNMF. [ABSTRACT FROM AUTHOR]

Distribution systems are becoming more active and provide more power support for transmission systems via their connection points at the transmission-distribution (T-D) interfaces. This paper proposes a chance constrained optimization model to estimate the flexibility area at a T-D interface. In this model, network flexibility is for the first time involved and facilitated by introducing power flow routers (PFRs) into the distribution system. The chance-constrained flexibility area (CCFA) given by the proposed model provides a description of the aggregated power dispatchability of distribution system with the guarantee of low risks of voltage violations under renewable uncertainties. We exploit the mechanism of network flexibility and reveal that it significantly reduces the voltage standard deviations, which cannot be achieved by node power flexibility. To evaluate the CCFA, an efficient two-layer iteration algorithm is designed. The inner layer finds the boundary point of CCFA along a given direction for active and reactive power. The outer layer determines those key directions to be included in the estimation as the corresponding points capture the features of the CCFA boundary. Case studies show that PFRs significantly enlarge the CCFA, which reveals that network flexibility is an important supplement to node power flexibility in T-D interaction. [ABSTRACT FROM AUTHOR]

The success of fog radio access networks (F-RANs) is critically dependent on the potential quality of service (QoS) that they can offer to users in the face of capacity-constrained fronthaul links and limited caches at their remote radio heads (RRHs). In this context, the collaborative beamforming design is very challenging, since it constitutes a large-dimensional nonlinearly constrained optimization problem. The paper develops a new technique for tackling these critical challenges in fog computing. We show that all the associated constraints can be efficiently dealt with maximizing the geometric mean (GM) of the user throughputs (GM-throughput) subject to the affordable total transmit power constraints. To elaborate, the GM-throughput maximization judiciously exploits the fronthaul links and the RRHs’ caches by relying on our novel algorithm, which evaluates low-complexity closed-form expressions in each of its iterations. The problem of F-RAN energy-efficiency is also addressed while maintaining the target throughput. Numerical examples are provided for quantifying the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Growth hormone (GH) is secreted by cells in the anterior pituitary on two time scales: discrete pulses over minutes that occur within a 24-hr pattern. Secretion reflects the balance of stimulatory and inhibitory inputs from the hypothalamus and is influenced by gonadal steroids, stress, nutrition, and sleep/wake states. We propose a novel approach for the analysis of GH data and use this approach to quantify (i) the timing, amplitude and the number of GH pulses and (ii) GH infusion, clearance and basal secretion (i.e., time invariant) rates, using serum GH sampled every 10 minutes during an 8-hour sleep study in 18 adolescents. In our method, we approximate hormonal secretory events by deconvolving GH data via a two-step coordinate descent approach. The first step utilizes a sparse-recovery approach to estimate the timing and amplitude of GH secretory events. The second step estimates physiological parameters. Our method identifies the timing and amplitude of GH pulses and system parameters from experimental and simulated data, with a median ${R^2}$ R 2 of 0.93, among experimental data. Recovering GH pulses and model parameters using this approach may improve the quantification of GH parameters under different physiological and pathological conditions and the design and monitoring of interventions. [ABSTRACT FROM AUTHOR]

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data. [ABSTRACT FROM AUTHOR]

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic constraints that admit efficient projection. Problems of this form arise frequently in the context of semidefinite programming as well as when various NP-hard problems are solved approximately via semidefinite relaxation. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms, such as the stochastic Frank-Wolfe (FW) algorithm. On the other hand, the second set of constraints cannot be handled in the same way, and must be incorporated as an indicator function within the objective function, thereby complicating the application of FW methods. Similar problems have been studied before; however, they suffer from slow convergence rates. This work, equipped with momentum based gradient tracking technique, guarantees fast convergence rates on par with the best-known rates for problems without the second set of constraints. Zeroth-order variants of the proposed algorithms are also developed and again improve upon the state-of-the-art rate results. We further propose the novel trimmed FW variants that enjoy the same convergence rates as their classical counterparts, but are empirically shown to require significantly fewer calls to the linear minimization oracle speeding up the overall algorithm. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem. [ABSTRACT FROM AUTHOR]

Differential dynamic programming (DDP) is a well-recognized method for trajectory optimization due to its fast convergence characteristics. However, the original DDP requires a predefined final time and cannot handle nonlinear constraints in optimization. This prohibits the application of DDP for autonomous vehicles due to the heuristic nature of setting a final time beforehand and the existence of inherent physical limits. This article revisits DDP by dynamically optimizing the final time via the first-order optimality condition of the value function and using augmented Lagrangian method to tackle the issue of nonlinear constraints. The resultant algorithm is termed as flexible final time constrained differential dynamic programming (FFT-CDDP). Extensive numerical simulations for a three-dimensional guidance problem are used to demonstrate the working of FFT-CDDP. The results indicate that the proposed FFT-CDDP provides much higher computational efficiency and stronger robustness against the initial solution guess, compared with the off-the-shelf general purpose optimal control software (GPOPS) algorithm. [ABSTRACT FROM AUTHOR]