Showing papers on "Nonlinear programming published in 2019"

Adaptive Distributionally Robust Optimization

Abstract: We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of pro...

Multi-objective optimization for energy-efficient flexible job shop scheduling problem with transportation constraints

Abstract: Manufacturing enterprises nowadays face huge environmental challenges because of energy consumption and associated environmental impacts. One of the effective strategies to reduce energy consumption is by employing intelligent scheduling techniques. Production scheduling can have significant impact on energy saving in manufacturing system from the operation management point of view. Resource flexibility and complex constraints in flexible manufacturing system make production scheduling a complicated nonlinear programming problem. To this end, a multi-objective optimization model with the objective of minimizing energy consumption and makespan is formulated for a flexible job shop scheduling problem with transportation constraints. Then, an enhanced genetic algorithm is developed to solve the problem. Finally, comprehensive experiments are carried out to evaluate the performance of the proposed model and algorithm. The experimental results revealed that the proposed model and algorithm can solve the problem effectively and efficiently. This may provide a basis for the decision makers to consider energy-efficient scheduling in flexible manufacturing system.

A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems

Abstract: Separable nonlinear least-squares (SNLLS) problems arise frequently in many research fields, such as system identification and machine learning. The variable projection (VP) method is a very powerful tool for solving such problems. In this paper, we consider the regularization of ill-conditioned SNLLS problems based on the VP method. Selecting an appropriate regularization parameter is difficult because of the nonlinear optimization procedure. We propose to determine the regularization parameter using the weighted generalized cross-validation method at every iteration. This makes the original objective function changing during the optimization procedure. To circumvent this problem, we use an inequation to produce a consistent demand of decreasing at successive iterations. The approximation of the Jacobian of the regularized problem is also discussed. The proposed regularized VP algorithm is tested by the parameter estimation problem of several statistical models. Numerical results demonstrate the effectiveness of the proposed algorithm.

ALTRO: A Fast Solver for Constrained Trajectory Optimization

Abstract: Trajectory optimization is a widely used tool for robot motion planning and control. Existing solvers for these problems either rely on off-the-shelf nonlinear programming solvers that are numerically robust and capable of handling arbitrary constraints, but tend to be slow because they are general purpose; or they use custom numerical methods that take advantage of the problem structure to be fast, but often lack robustness and have limited or no ability to reason about constraints. This paper presents ALTRO (Augmented Lagrangian TRajectory optimizer), a solver for constrained trajectory optimization problems that handles general nonlinear state and input constraints and offers fast convergence and numerical robustness thanks to careful exploitation of problem structure. We demonstrate its performance on a set of benchmark motion-planning problems and offer comparisons to the standard direct collocation method with large-scale sequential quadratic programming and interior-point solvers.

A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm

Abstract: The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental-related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time.

Performance of hybrid quantum-classical variational heuristics for combinatorial optimization.

Abstract: The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum-classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.

Optimal Real-Time Operation Strategy for Microgrid: An ADP-Based Stochastic Nonlinear Optimization Approach

Abstract: This paper proposes an approximate dynamic programming (ADP) based algorithm for the real-time operation of the microgrid under uncertainties. First, the optimal operation of the microgrid is formulated as a stochastic mixed-integer nonlinear programming (MINLP) problem, combining the ac power flow and the detailed operational character of the battery. For this NP-hard problem, the proposed ADP based energy management algorithm decomposes the original multitime periods MINLP problem into single-time period nonlinear programming problems. Thus, the sequential decisions can be made by solving Bellman's equation. Historical data is utilized offline to improve the optimality of the real-time decision, and the dependency on the forecast information is reduced. Comparative numerical simulations with several existing methods demonstrate the effectiveness and efficiency of the proposed algorithm.

A Kind of Novel Method of Power Allocation With Limited Cross-Tier Interference for CRN

Abstract: A kind of novel method of power allocation with limited cross-tier interference for cognitive radio network (CRN) is proposed in this paper. In this method, an interference-limited power allocation algorithm based on filter bank multi-carrier-offset quadrature amplitude modulation (FBMC-OQAM) is put forward. In order to improve the energy efficiency of the entire network and protect secondary users (SUs) in the network from too much interference, cross-tier interference limit is adopted, at the same time, virtual queue is designed to transform the extra packet delay caused by the contention for the channel of multi-user into the queuing delay. Taking the energy efficiency as the objective function, a nonlinear programming approach with nonlinear constraints is innovatively proposed under the constraints of time delay and transmission power. An iterative algorithm in order to solve the problem is also put forward. In the new algorithm, the fractional objective function is transformed into polynomial form, and the global optimal solution is obtained by iteration after reducing the computational complexity. In addition, a sub-optimal algorithm is proposed to reduce computational complexity. The experimental results show that the optimal algorithm has higher performance while the sub-optimal algorithm has a lower computational complexity. The presented method has very good practical importance for the CRN.

Micro Water–Energy Nexus: Optimal Demand-Side Management and Quasi-Convex Hull Relaxation

Abstract: In some countries and regions, water distribution and treatment consume a considerable amount of electric energy. This paper investigates the water network's potential ability to provide demand response services to the power grid for the management of renewable resources under the framework of a distribution-level water–energy nexus (micro WEN). In particular, the hidden controllable water loads, such as irrigation systems, were closely studied as virtual energy storage to improve the flexibility of electrical grids. An optimization model is developed for the demand-side management (DSM) of micro WEN, and the simulation results assert that grid flexibility indeed benefits from taking controllable water loads into account. Although the proposed optimal DSM model is a computationally intractable mixed-integer nonlinear programming (MINLP) problem, quasi-convex hull techniques were developed to relax the MINLP into a mixed-integer convex programming (MICP) problem. The numerical study shows that the quasi-convex hull relaxation is tight and that the resulting MICP problem is computationally efficient.

Flexible, reliable, and renewable power system resource expansion planning considering energy storage systems and demand response programs

Abstract: This study presents a flexible, reliable, and renewable power system resource planning approach to coordinate generation, transmission, and energy storage (ES) expansion planning in the presence of demand response (DR). The flexibility and reliability of the optimal resource expansion planning are ensured by means of appropriate constraints incorporated into the proposed planning tool where thermal generation units, ES systems, and DR programs are considered as flexibility resources. The proposed planning tool is a mixed-integer non-linear programming (MINLP) problem due to the non-linear and non-convex constraints of AC power flow equations. Accordingly, to linearise the proposed MINLP problem, the AC nodal power balance constraints are linearised by means of the first-order expansion of Taylor's series and the line flow equations are linearised by means of a polygon. Additionally, the stochastic programming is used to characterise the uncertainty of loads, a maximum available power of wind farms, forecasted energy price, and availability/unavailability of generation units and transmission lines by means of a sufficient number of scenarios. The proposed planning tool is implemented on the IEEE 6-bus and the IEEE 30-bus test systems under different conditions. Case studies illustrate the effectiveness of the proposed approach based on both flexibility and reliability criteria.

Generalized hp Pseudospectral-Convex Programming for Powered Descent and Landing

Abstract: In this paper a generalized hp method is combined with pseudospectral methods and convex optimization to provide a high-accuracy, real-time capable method able to compute optimal trajectories for planetary powered descent and landing phases of a spacecraft. The benefits of the method are demonstrated for the Mars Science Laboratory study case. Numerical simulations show that the method provides a suitable alternative to the standard convex approaches, and represents a good trade-off between accuracy and computational speed.

Derivative-Free Optimization of Noisy Functions via Quasi-Newton Methods

Abstract: This paper presents a finite-difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptiv...

Dual-Setting Directional Overcurrent Relays for Protecting Automated Distribution Networks

Abstract: This paper elaborates a new protection scheme based on dual-setting DOCRs for automated distribution networks. In this course, the reduction in relays operation time saturates as the number of these relays increases. Thus, optimal deployment of dual-setting DOCRs should be specified in an efficient manner. To do so, a multiobjective optimization approach is established, which compromises the reduction of total operation time and the number of dual-setting DOCRs. Coordination constraints are accommodated and nonstandard inverse-time characteristics are established to intensify flexibility of the proposed strategy. The proposed model lies within a nonlinear programming fashion, which is tackled by particle swarm optimization. Moreover, the augmented $\varepsilon $ -constraint approach is utilized to reach the Pareto-optimal solutions following which the fuzzy decision making process determines the best compromised solution. Detailed simulation studies are carried out to interrogate performance of the proposed approach.

Trajectory Optimization for Wheeled-Legged Quadrupedal Robots Using Linearized ZMP Constraints

Abstract: We present a trajectory optimizer for quadrupedal robots with actuated wheels. By solving for angular, vertical, and planar components of the base and feet trajectories in a cascaded fashion and by introducing a novel linear formulation of the zero-moment point balance criterion, we rely on quadratic programming only, thereby eliminating the need for nonlinear optimization routines. Yet, even for gaits containing full flight phases, we are able to generate trajectories for executing complex motions that involve simultaneous driving, walking, and turning. We verified our approach in simulations of the quadrupedal robot ANYmal equipped with wheels, where we are able to run the proposed trajectory optimizer at 50 Hz. To the best of our knowledge, this is the first time that such dynamic motions are demonstrated for wheeled-legged quadrupedal robots using an online motion planner.

Joint Spectrum and Power Allocation for NOMA Enhanced Relaying Networks

Abstract: In this paper, we investigate the joint resource allocation for the non-orthogonal multiple access (NOMA)-enhanced relaying networks involving the subcarrier pair, subcarrier-user assignment, as well as power allocation. In the NOMA-enhanced relaying networks, the relay is capable of communicating with multiple users on one subcarrier using the NOMA technology. To maximize the system throughput, the joint resource allocation problem is formulated as a mixed-integer nonlinear programming problem, which is difficult to tackle in general. Furthermore, there is strong coupling between the subcarrier-user assignment and the power allocation due to the multi-user interference in the NOMA system. To reduce the complexity, we separate the joint resource allocation problem as two subproblems in terms of the subcarrier assignment (subcarrier pair and subcarrier-user assignment) and power allocation, respectively. In particular, we propose a subcarrier assignment scheme based on the simulated annealing algorithm to optimize the subcarrier pair and subcarrier-user assignment with the fixed power allocation. Then, the power allocation problem is transformed as a difference of convex functions programming problem, and the sequence convex programming method is adopted to solve it. The simulation results illustrate that the proposed algorithm can effectively improve the system throughput.

Optimal Operation of Unbalanced Three-Phase Islanded Droop-Based Microgrids

Abstract: This paper presents a new mixed-integer nonlinear programming (MINLP) model for the optimal operation of unbalanced three-phase droop-based microgrids. The proposed MINLP model can be seen as an extension of an optimal power flow for microgrids operating in islanded mode, that aims to minimize the total amount of unsupplied demand and the total distributed generator (DG) generation cost. Since the slack bus concept is not longer valid, the proposed model considers the frequency and voltage magnitude reference as variables. In this case, DGs units operate with droop control to balance the system and provide a frequency and voltage magnitude reference. Additionally, a set of efficient linearizations are introduced in order to approximate the original MINLP problem into a mixed-integer linear programming (MILP) model that can be solved using commercial solvers. The proposed model has been tested in a 25-bus unbalanced three-phase microgrid and a large 124-node grid, considering different operational and time-coupling constraints for the DGs and the battery systems (BSs). Load curtailment and different modes of operation for the wind turbines have also been tested. Finally, an error assessment between the original MINLP and the approximated MILP model has been conducted.

Tensor Complementarity Problems—Part II: Solution Methods

Abstract: This work, with its three parts, reviews the state-of-the-art of studies for the tensor complementarity problem and some related models. In the first part of this paper, we have reviewed the theoretical developments of the tensor complementarity problem and related models. In this second part, we review the developments of solution methods for the tensor complementarity problem. It has been shown that the tensor complementarity problem is equivalent to some known optimization problems, or related problems such as systems of tensor equations, systems of nonlinear equations, and nonlinear programming problems, under suitable assumptions. By solving these reformulated problems with the help of structures of the involved tensors, several numerical methods have been proposed so that a solution of the tensor complementarity problem can be found. Moreover, based on a polynomial optimization model, a semidefinite relaxation method is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite. Further applications of the tensor complementarity problem will be given and discussed in the third part of this paper.

Predictive Maneuver Planning for an Autonomous Vehicle in Public Highway Traffic

Abstract: This paper outlines a predictive maneuver-planning method for autonomous vehicle navigating public highway traffic. The method integrates discrete maneuvering decisions, i.e., lane and reference speed selection automata, with a model predictive control-based motion trajectory-planning scheme. A key notion is to apply a predictive reference speed pre-planning for each lane at each time step of a selected prediction horizon. This is done based on the predicted likely motion of the autonomous vehicle and other object vehicles subject to sensor noise and environmental disturbances. Then, an optimization problem is configured that computes safe, sub-optimal plans for the trajectories of both the motion states (and inputs) and maneuver references for the prediction horizon to accomplish maneuvers like lane keeping, lane change, or obstacle avoidance. While a first formulation of the problem results in a mixed-integer nonlinear programming problem, it is shown that a relaxation can be adopted that reduces the computational complexity to a low-order polynomial time nonlinear program that can be solved more efficiently. Through simulation of a series of multi-lane highway scenarios and comparison with one-maneuver planning approach and an adaptive cruise control approach, the proposed predictive maneuver planning is illustrated to better accommodate the traffic environment with feasible execution time. Also, the reference speed pre-planning improves the optimality and the robustness of the maneuver decision in trajectory planning without adding computational complexity to the optimization problem.

When Edge Computing Meets Microgrid: A Deep Reinforcement Learning Approach

Abstract: The computational tasks at multiaccess edge computing (MEC) are unpredictable in nature, which raises uneven energy demand for MEC networks. Thus, to handle this problem, microgrid has the potentiality to provides seamless energy supply from its energy sources (i.e., renewable, nonrenewable, and storage). However, supplying energy from the microgrid faces challenges due to the high uncertainty and irregularity of the renewable energy generation over the time horizon. Therefore, in this paper, we study about the microgrid-enabled MEC networks’ energy supply plan, where we first formulate an optimization problem and the objective is to minimize the energy consumption of microgrid-enabled MEC networks. The problem is a mixed integer nonlinear optimization with computational and latency constraints for tasks fulfillment, and also coupled with the dependencies of uncertainty for both energy consumption and generation. Therefore, we show that the problem is an NP-hard problem. As a result, second, we decompose our formulated problem into two subproblems: 1) energy-efficient tasks assignment problem for MEC into community discovery problem and 2) energy supply plan problem into Markov decision process. Third, we apply a low complexity density-based spatial clustering of applications with noise to solve the first subproblem for each base station distributedly. Sequentially, we use the output of the first subproblem as a input for solving the second subproblem, where we apply a model-based deep reinforcement learning. Finally, the simulation results demonstrate the significant performance gain of the proposed model with a high accuracy energy supply plan.

Implementing Regularized Predictive Control for Simultaneous Real-Time Footstep and Ground Reaction Force Optimization

Abstract: This work presents a successful implementation of a nonlinear optimization-based Regularized Predictive Control (RPC) for legged locomotion on the MIT Cheetah 3 robot platform. Footstep placements and ground reaction forces at the contact feet are simultaneously solved for over a prediction horizon in real-time. Often in academic literature not enough attention is given to the implementation details that make the theory work in practice and many times it is precisely these details that end up being critical to the success or failure of the theory in real world applications. Nonlinear optimization for real-time legged locomotion control in particular is one of the techniques that has shown promise, but falls short when implemented on hardware systems subjected to computation limits and undesirable local minima. We discuss various algorithms and techniques developed to overcome some of the challenges faced when implementing nonlinear optimization-based controllers for dynamic legged locomotion.