Constrained Nonlinear Programming Research Articles

Control-Barrier-Function-Based Design of Gradient Flows for Constrained Nonlinear Programming

Control-Barrier-Function-Based Design of Gradient Flows for Constrained Nonlinear Programming

Game Theory Based Dynamic Event-Driven Service Scheduling in Cloud Manufacturing

Due to the individualized consumer needs, cloud manufacturing (CMfg) has been widely used in the optimization of available manufacturing resource allocation to enhance resource utilization and reduce energy consumption. However, efficient scheduling of tasks and subtasks under dynamic CMfg environments to these re-sources are challenging problems. This paper proposes a game theory based on task scheduling and model selection for effectively exploiting distributed manufacturing resources in CMfg, and the Nash equilibrium (NE) in this game theory is implemented by a double ant colony optimization (DACO) algorithm. Through this model, services provided by different providers can handle a batch of tasks in real-time. Besides, to satisfy different service providers and demanders, the proposed approach considers multiple task attributes simultaneously, including completion time, cost, service quality, service composition capability, service availability, energy consumption, service sustainability, service maintainability, and service trust. Simulation results demonstrate that the proposed method is not only effective for the relevant optimization objective but also can achieve great performance under real-time CMfg environments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To provide the best production guides, the efficiency of configuration optimization of manufacturing resources is critical to the control and management of smart manufacturing systems. This paper investigates the dynamic scheduling problem for manufacturing services in CMfg. Previous task scheduling approaches fail to evaluate multiple factors together, like completion time, cost, and energy consumption. Also, the traditional scheduling method cannot respond to requests caused by service state changes in an efficient way. Therefore, in this paper, a game theory model that consists of a static scheduling sub-game and a dynamic selection sub-game is presented. This model is achieved by adopting a proposed double ant colony optimization algorithm that solves constrained non-linear programming. Simulation experiments shown in this paper prove that the proposed method outperforms existing scheduling methods in multiple aspects, including completion time and energy consumption. Also, this method can be readily implemented and incorporated into real production environments. Future work can improve the proposed method by analyzing the uncertainty during scheduling tasks and sharing the logistics resources on the same routes.

Continuous Low-Thrust Maneuver Planning for Space Gravitational Wave Formation Reconfiguration Based on Improved Particle Swarm Optimization Algorithm

This study proposes a three-spacecraft formation reconfiguration strategy of minimum fuel for space gravitational wave detection missions in the high Earth orbit (105 km). For solving the limitations of measurement and communication in long baseline formations, a control strategy of a virtual formation is applied. The virtual reference spacecraft provides a desired relative state between the satellites, which is then used to control the motion of the physical spacecraft to maintain the desired formation. A linear dynamics model based on relative orbit elements' parameterization is used to describe the relative motion in the virtual formation, which facilitates the inclusion of J2, SRP, and lunisolar third-body gravity effects and provides a direct insight into the relative motion geometry. Considering the actual flight scenarios of gravitational wave formations, a formation reconfiguration strategy based on continuous low thrust is investigated to achieve the desired state at a given time while minimizing interference to the satellite platform. The reconfiguration problem is considered a constrained nonlinear programming problem, and an improved particle swarm algorithm is developed to solve this problem. Finally, the simulation results demonstrate the performance of the proposed method in improving the maneuver sequence distribution and optimizing maneuver consumption.

Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Optimization of a two-echelon supply chain with random demand and random defect rate under strict carbon cap policy

PurposeThe yield of defective items and emissions of greenhouse gases in supply chains are areas of concern. Organizations try to reduce the yield defective items and emissions. In this paper, a constrained optimization model is developed with consideration of the yield of defective items and strict carbon cap policy simultaneously and then optimized. Further, sensitivity analyses have been carried out to draw different managerial insights. Precisely, we have tried to address the following research questions: (1) how to optimize the cost for a two-echelon supply chain considering yield of defective items and strict carbon cap policy, (2) how the total expected cost and total expected emissions act with changing parameters.Design/methodology/approachThe mathematical modeling approach has been adopted to develop a model and further optimized it with optimization software. Costs and emissions from different areas of a supply chain have been derived and then the total cost and total emissions have been formulated mathematically. One constrained mixed-integer nonlinear programming (MINLP) problem has been formulated and solved considering emissions-related, velocity and production related-constraints. Further, different sensitivity analyses have been derived to draw some managerial insights.FindingsIn this paper, many decision variables have been calculated with a set of basic values of other parameters. It has been found that both cost and emissions can be controlled by controlling different parameters. It has been also found that some parameters have very little or no influence either on cost or emissions. In most cases, originations may exhaust the given limit of carbon cap to optimize their costs.Originality/valueIn spite of my sincere efforts, no paper has been found that has considered the yield of defective items and strict carbon cap policy simultaneously. In this paper, it is assumed that both demand and defect rates are random in nature. The model, presented in this paper may give insights to develop different supply chain models with consideration of both defective items and strict carbon cap policy. Sensitivity analyses, drawn in this paper may give deep insights to managers and carbon regulatory bodies.

HNN-based generalized predictive control for turbofan engine direct performance optimization

The aero-engine performance optimization control is to find the appropriate control variables to maximize or minimize the comprehensive index of one or more performance parameters while ensuring its safe operation. Traditional performance seeking control is mainly based on indirect control, with complex structure and large error. This paper develops an HNN (Hopfield Neural Network)-based generalized predictive control strategy for turbofan engine direct performance optimization. With a Hopfield network as the optimization algorithm and a CARIMA model based on generalized prediction criterion as the optimization model, an optimal controller is designed. Together with the identification module and the self-adaptive module, an integrated performance optimization control system is formed. Namely, the adaptive model calculates the unmeasurable performance parameters of the engine for the CARIMA model identification. Then HNN performs the iterative operation to obtain the optimal control variables for a given objective. The main contribution of this paper is to propose a direct performance control structure to avoid the nonlinear conversion of control reference; meanwhile, the linear CARIMA model is combined with HNN algorithm to build a neural network for solving constrained nonlinear programming problems, and mutation operation is introduced to improve its global search capability, which is evident in the minimum turbine temperature optimization mode. The method is evaluated on a turbofan model from the aspects of model verification, performance optimization control simulation at multiple operating points and under degeneration conditions. The results confirm the satisfactory performance of the proposed strategy at the selected points and conditions. And compared with the traditional algorithms, the computer calculation time is greatly shortened.

Hexagonal fuzzy approximation of fuzzy numbers and its applications in MCDM

Numerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In fuzzy multi-criteria decision-making (fuzzy MCDM) methods, intelligent information system and fuzzy control-theoretic models, complex qualitative information are extracted from expert’s knowledge as linguistic variables and are modeled by linear/non-linear fuzzy numbers. In numerical computations and experiments, the information/data are fitted by nonlinear functions for better accuracy which may be little hard for further processing to apply in real-life problems. Hence, the study of non-linear fuzzy numbers through triangular and trapezoidal fuzzy numbers is very natural and various researchers have attempted to transform non-linear fuzzy numbers into piecewise linear functions of interval/triangular/trapezoidal in nature by different methods in the past years. But it is noted that the triangular/trapezoidal approximation of nonlinear fuzzy numbers has more loss of information. Therefore, there is a natural need for a better piecewise linear approximation of a given nonlinear fuzzy number without losing much information for better intelligent information modeling. On coincidence, a new notion of Generalized Hexagonal Fuzzy Number has been introduced and its applications on Multi-Criteria Decision-Making problem (MCDM) and Generalized Hexagonal Fully Fuzzy Linear System (GHXFFLS) of equations have been studied by Lakshmana et al. in 2020. Therefore, in this paper, approximation of nonlinear fuzzy numbers into the hexagonal fuzzy numbers which includes trapezoidal, triangular and interval fuzzy numbers as special cases of Hexagonal fuzzy numbers with less loss/gain of information than other existing methods is attempted. Since any fuzzy information is satisfied fully by its modal value/core of that concept, any approximation of that concept is expected to be preserved with same modal value/core. Therefore, in this paper, a stepwise procedure for approximating a non-linear fuzzy number into a new Hexagonal Fuzzy Number that preserves the core of the given fuzzy number is proposed using constrained nonlinear programming model and is illustrated numerically by considering a parabolic fuzzy number. Furthermore, the proposed method is compared for its efficiency on accuracy in terms of loss of information. Finally, some properties of the new hexagonal fuzzy approximation are studied and the applicability of the proposed method is illustrated through the Group MCDM problem using an index matrix (IM).

A Comparison of Normal Cone Conditions for Homotopy Methods for Solving Inequality Constrained Nonlinear Programming Problems

Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

Analysis and Optimization of Energy Consumption in Two-Machine Bernoulli Lines With General Bounds on Machine Efficiency

In energy-intensive production systems, machines consume a huge amount of energy during the production process. Since the high energy consumption is prominent in production systems, reducing the energy consumption and improving the energy efficiency are of great significance. In this article, the problem of minimizing the total energy consumption in the two-machine Bernoulli line with general lower and upper bounds of machine efficiencies is investigated. Specifically, first, it is formulated as a nonlinear constrained programming. Then, the structure of its feasible region and properties of its objective function are analyzed. Based on these explorations, its optimal solution is constructed from the solution of a relaxation problem (i.e., the problem without general bounds on machine efficiencies), which has been analyzed and solved in the literature. Finally, the results obtained are extended to the problem of minimizing the energy consumption per job to improve the energy efficiency of the two-machine Bernoulli line. The sensitivity analysis of the optimal objective value with respect to the required production rate is carried out for both the total energy consumption and the energy consumption per job optimization models. Note to Practitioners —As is well known, reducing the energy consumption and improving the energy efficiency in energy-intensive production systems are of great significance. In practical production systems, due to physical limitations, machine efficiencies are usually confined to a subset of (0, 1]. Although for the case without machine-efficiency restrictions (i.e., the efficiencies can be selected in (0, 1]), the problems of reducing the energy consumption and improving the energy efficiency have been investigated for some production systems, the machine-efficiency-constrained problems, which are more practical and challenging, have not been examined yet. In this article, two problems, which minimize the total energy consumption and the energy consumption per job in the two-machine Bernoulli line, respectively, are formulated and solved. In the future, this research will be extended to long Bernoulli lines and systems with geometric, exponential, and nonexponential machine reliability models, and the results obtained will be implemented in practical production systems.

A Prediction Model of Vitrinite Reflectance for Suppression of Organic-Matter Maturation by Overpressure

Vitrinite reflectance is the most commonly used index in the study of source rock evaluation, diagenetic stage division, basin simulation, and diagenesis. Because data on vitrinite reflectance are limited, many prediction models have been proposed to address this problem. However, these models may fail to predict vitrinite reflectance effectively in overpressured basins because overpressure can suppress organic-matter maturation. Overpressure appears to reduce the degree of disorder in the hydrocarbon generation reaction system and to increase the mechanical work against the force of pore fluid that occurs as the volume of the activated complex increases, thereby reducing the preexponential factor and increasing the activation energy of the hydrocarbon generation reaction; therefore, organic-matter maturation is slowed. In this article, the reasons for the abnormally low vitrinite reflectance in the overpressured system were analyzed, which revealed that overpressure is interpreted as significantly suppressing organic-matter maturation. A new prediction model for vitrinite reflectance, A-Ea-Ro, is proposed that accounts for the suppression of overpressure in organic-matter maturation based on data from wells in the Fukang Sag in the Junggar Basin, northwestern China. The overpressure is modeled by introducing a preexponential factor and activation energy in this model. Based on measured drilling and geochemical data and simulated data, the overpressure controlling factors were optimized by a nonlinear constrained programming method and assigned 151.23 MPa and 30.65 kJ·mol−1·MPa−1, respectively. Prediction models including A-Ea-Ro were applied to wells Fu10 and Mu7 of Fukang Sag. The reflectance values predicted by the model A-Ea-Ro, applied to wells Fu10 and Mu7, were in good agreement with the measured values. This model provides a closer match between predicted and observed vitrinite reflectance values for this study area.

An Optimal Multivariable Constrained Nonlinear (MVCNL) Stochastic Microgrid Planning and Operation Problem With Renewable Penetration

Microgrids (MGs) are promising archetypes for the penetration of renewable energy sources (RES) into the system for reducing carbon footprints. This article presents a cost-based optimization model using a stochastic programming to obtain the optimal size of distributed energy resources including RES. Uncertainties in the solar output and the load demand data are considered using multiple scenarios with random variations, which are based on beta distribution. The objective function is formulated as a cost-based multivariable constrained nonlinear convex programming problem. Other than planning costs, the objective function also includes per day running or operational costs such as unit commitment costs as well as the switching costs associated with the dispatchable units. The overall problem is simulated under MATLAB environment. Quantitative results indicate the impact of operational paradigm along with the planning of an MG in the form of cost analysis with different reliability conditions. An assessment of results in tabular form is presented, which incorporates the optimal sizing of MG under the different system reliability conditions and constraints. Some additional cases pertain to the generation and the load demand scenarios have also been included in the article.

A distributed charging strategy based on day ahead price model for PV-powered electric vehicle charging station

This paper studies a distributed charging model based on day-ahead optimal internal price for PV-powered Electric Vehicle (EV) Charging Station (PVCS). Considering the feed-in-tariff of PV energy, the price of utility grid and the forecast model of PV based on back-propagation neural network (BPNN), a system operation model of PVCS is introduced, which consists of the profit model of PVCS operator (PO) and the cost model of EV users. The model proposed in this paper can be designed as a Stackelberg game model, where the PO acts as the leader and all EV users participated are regarded as the followers. An optimization strategy based on heuristic algorithm and nonlinear constrained programming are adopted by the PO and each EV user, respectively. Moreover, a real-time billing strategy is proposed to deal with the errors from the forecasted PV energy and the expected charging arrangements. Finally, through a practical case, the validity of the model is verified in terms of increasing operation profit and reducing charging cost.

Peer-to-peer energy sharing through a two-stage aggregated battery control in a community Microgrid

Peer-to-peer (P2P) energy sharing allows the surplus energy from distributed energy resources (DERs) to trade between prosumers in a community Microgrid. P2P energy sharing is being becoming more attractive than the conventional peer-to-grid (P2G) trading. However, intensive sensing and communication infrastructures are required either for information flows in a local market or for building a central control system. Moreover, the existing pricing mechanisms for P2P energy sharing could not ensure all the P2P participants gain economic benefits. This work proposed a two-stage aggregated control to realize P2P energy sharing in community Microgrids, where only the measurement at the point of common coupling (PCC) and one-way communication are required. This method allows individual prosumers to control their DERs via a third party entity, so called energy sharing coordinator (ESC). In the first stage, a constrained non-linear programming (CNLP) optimization with a rolling horizon was used to minimize the energy costs of the community. In the second stage, a rule based control was carried out updating the control set-points according to the real-time measurement. The benefits of P2P energy sharing were assessed from the community’s as well as individual customers’ perspective. The proposed method was applied to residential community Microgrids with photovoltaic (PV) battery systems. It was revealed that P2P energy sharing is able to reduce the energy cost of the community by 30% compared to the conventional P2G energy trading. The modified supply demand ratio based pricing mechanism ensures every individual customer be better off, and can be used as a benchmark for any P2P energy sharing model. For consumers, the electricity bill is reduced by ∼12.4%, and for prosumers, the annual income is increased by ∼£57 per premises.

Optimal Coordination of Directional Overcurrent Relays in Microgrids by Using Cuckoo-Linear Optimization Algorithm and Fault Current Limiter

Nowadays, distributed generations (DGs) and microgrids play a significant role in development of power systems, but DGs produce several protection problems especially in optimal coordination of directional overcurrent relays (DORs). Optimal coordination of DORs is a highly constrained nonlinear programming problem, which has attracted attention of many research studies in recent years. Cuckoo optimization algorithm (COA) is introduced as an optimization tool based on behavior patterns of Cuckoos. In this paper, COA and linear programming (LP) are combined as a new hybrid COA-LP optimization algorithm in order to optimize the coordination protection of DORs in microgrids and find the optimum value of fault current limiter at the point of common coupling. The optimum settings of DORs are obtained for both modes of operation: 1) grid-connected and 2) island mode. The proposed algorithm is applied to Canadian distribution benchmark and a modified IEEE 14 bus networks and compared with particle swarm optimization (PSO) and genetic algorithm (GA). The obtained results show that the computational efficiency of the proposed COA-LP is better than PSO and GA in terms of speed and total operating time of DORs.

SCWOA: an efficient hybrid algorithm for parameter optimization of multi-pass milling process

In order to minimize total production time in multi-pass milling process, selecting optimal values of the process parameters is of great importance. The parameter optimization model of multi-pass milling process is a Constrained Non-Linear Programming formulation. Due to nonlinearity and complexity of the mathematical model, developing new solution methodologies, which can provide efficient solutions, is essential. For this purpose, in this paper a novel hybrid algorithm called Sine–Cosine Whale Optimization Algorithm is proposed for parameter optimization problem of multi-pass milling process in order to minimize total production time. The SCWOA uses exploration and exploitation abilities of the two basic algorithms to achieve better solutions. To show efficiency of the proposed algorithm, an experimental study is carried out and the result of the proposed algorithm is compared to the ones in the literature. The findings revealed that SCWOA provides promising solutions which result in significantly lower production time.

Protection Coordination for Microgrids With Grid-Connected and Islanded Capabilities Using Communication Assisted Dual Setting Directional Overcurrent Relays

This paper proposes a communication assisted dual setting relay protection scheme for micro-grids with grid connected and islanded capability. Previous work on dual setting relays has been applied to grid connected distributed generation systems only, but one major shortcoming is the failure of the backup scheme to operate in a coordinated manner. The proposed scheme relies on the use of dual setting directional overcurrent relays that are capable of operating in both forward and reverse directions, with different settings, and with a low bandwidth communication to maintain proper protection coordination. The problem is formulated as a non-linear constrained programming problem where the relay settings are optimally determined to minimize the overall relay operating time for primary and backup operation. The scheme is tested on a modified version of the IEEE 30 bus test system equipped with distributed generation and with capability of operating in an islanded mode. The proposed scheme is compared against the conventional scheme and the results show that it is capable of overcoming the problem of infeasibility, experienced by the conventional method, without the need of installing fault current limiters. Furthermore, it achieves remarkable reduction in both the primary and backup relay operating times, which was reflected in a reduction in the total relay operating time.

Parallel Secure Outsourcing of Large-scale Nonlinearly Constrained Nonlinear Programming Problems

Nonlinearly constrained nonlinear programming (NLC-NLP) problems arise in various optimal decision-making fields, such as financial engineering, urban planning, supply chain management, and power system control. These real-world NLC-NLP problems are usually large-scale because they need to take into account massive variables and constraints. Solving NLC-NLP problems with common algorithms, e.g., the gradient projection method (GPM), generally incurs very high time complexity. This results in the inevitable inability of solving large-scale NLC-NLP problems by using general-purpose computers within a feasible time. To address this challenge, a cost-effective solution is to adopt cloud computing, but this raises security concerns since real-world NLC-NLP problems always carry sensitive information. Previous secure outsourcing algorithms try to protect sensitive information, but still let cloud service tenants bear heavy computation workload. To fill the gap, we develop a practical secure outsourcing algorithm for solving large-scale NLC-NLP problems with the GPM. To be more prominent, we also parallelize the secure outsourcing algorithm for accelerating computations and avoiding possible memory overflowing. We implement the proposed algorithm on the Amazon Elastic Compute Cloud (EC2) and a laptop, and notice that it can significantly reduce the tenant's computing time even for large-scale NLC-NLP problems.

Optimizing sheddable and shiftable residential electricity consumption by incentivized peak and off-peak credit function approach

Many current studies on smart grid in electricity market are indicative of the key role it plays in electricity generation, distribution, retailing and end-user management. Demand response programs (DRPs) can be used to lower high energy prices in wholesale electricity markets, and ensure the security of power systems when at risk. The concern of most researchers in this field is to further unearth the potential of smart grid in the direction of demand response (DR) through enhanced demand side management (DSM) centering on the behavior of the end-user. Our model proposes a more effective way in using incentive based demand response program to help residential customers derive more benefits from smart grid. The constrained non-linear programming (CNLP) model optimizes residential consumption of electricity by shaving of load at peak and increasing of load at off-peak to help generators reduce production cost at peak times and increase revenue at of off-peaks. The model uses a credit function to regulate consumption and reward end-users for load shedding and load shifting at peaks and also at off-peaks reward end-users for increasing load. The simulated results show that, high consumption appliances are best used at dawn, midday, and at night, if consumers want to cut down cost. The corresponding effect is that, generating and distribution companies derive the right revenue from their investments by not producing beyond their capacity during peaks at high cost and maintain constant power supply in and environmentally friendly manner.

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

ABSTRACTAn efficient primal-dual interior-point algorithm using a new non-monotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented.