Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two ...important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for real-world MINLP problems, we have developed an sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) and used it for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver.
Celotno besedilo
Dostopno za:
BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
•Agricultural water and land resources are optimized simultaneously under complex uncertainties.•Performances of economic, environmental and social dimensions are coordinated and ...assessed.•Uncertainties expressed as fuzzy set associating credibility and hesitations are tackled.•Interrelationships among water and land strategies, GHG emissions, and credibility levels are evaluated.
This study presents an optimization model for the allocation of agricultural water and land resources under uncertainty. The model incorporates intuitionistic fuzzy numbers, fuzzy credibility-constrained programming, mixed-integer non-linear programming, and multi-objective programming into a general framework. The model is capable of (1) balancing the trade-off among economic, environmental, and social considerations in an irrigated agricultural system; (2) optimally allocating limited agricultural water and land resources simultaneously; and (3) dealing with the complexities of non-linearity and fuzzy uncertainties concurrently occurring in both parameters and constraints to objectively reflect practical issues in agricultural water and land resources allocations. The developed model is applied to a real case study in northeast China. The net system benefits, global warming potential, water pollution, resource allocation equity, and agricultural water and land allocation schemes among different subareas in different crop growth periods are obtained under various scenarios. The performance of the model is assessed with alternative schemes. The model can help decision makers realize how much confidence one can have in the optimal solutions and manage agricultural water and land resources in a more efficient and environment-friendly way.
•A multi-objective model is developed for sustainable irrigation allocation.•Complexity of nonlinearity and intuitionistic fuzzy uncertainty can be handled.•Tradeoffs between targets of social, ...economic and resources aspects can be tackled.•Average water allocation is obtained based on joint probabilities of hydrological elements.
Water scarcity causes conflicts among natural resources, society and economy and reinforces the need for optimal allocation of irrigation water resources in a sustainable way. Uncertainties caused by natural conditions and human activities make optimal allocation more complex. An intuitionistic fuzzy multi-objective non-linear programming (IFMONLP) model for irrigation water allocation under the combination of dry and wet conditions is developed to help decision makers mitigate water scarcity. The model is capable of quantitatively solving multiple problems including crop yield increase, blue water saving, and water supply cost reduction to obtain a balanced water allocation scheme using a multi-objective non-linear programming technique. Moreover, it can deal with uncertainty as well as hesitation based on the introduction of intuitionistic fuzzy numbers. Consideration of the combination of dry and wet conditions for water availability and precipitation makes it possible to gain insights into the various irrigation water allocations, and joint probabilities based on copula functions provide decision makers an average standard for irrigation. A case study on optimally allocating both surface water and groundwater to different growth periods of rice in different subareas in Heping irrigation area, Qing’an County, northeast China shows the potential and applicability of the developed model. Results show that the crop yield increase target especially in tillering and elongation stages is a prevailing concern when more water is available, and trading schemes can mitigate water supply cost and save water with an increased grain output. Results also reveal that the water allocation schemes are sensitive to the variation of water availability and precipitation with uncertain characteristics. The IFMONLP model is applicable for most irrigation areas with limited water supplies to determine irrigation water strategies under a fuzzy environment.
Display omitted
•Two-stage control is a feasible solution for P2P energy sharing in low voltage networks.•Two-stage control requires limited measurement and one-way communication.•P2P energy sharing ...reduces energy bills of a community by 30%.•P2P sharing increases annual self-consumption by 10–30%, and self-sufficiency by ∼20%.•With a proper compensation price, P2P sharing ensures every customer be better off.
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.
•DDRO is firstly applied in energy systems optimization under uncertainty.•Deterministic and data-driven robust optimization frameworks are proposed.•The uncertainty set is constructed by SVC based ...on real industrial data.•The DDRO model is formulated as an MINLP problem.•The effect of the regularization parameter on the solution is explored.
In the large-scale industries, optimization of multi-type energy systems to minimize the total energy cost is of great importance and has received worldwide attentions. In the real industrial plants, the deterministic optimization may encounter difficulties because of various uncertainties. In this paper, the deterministic and robust optimization frameworks are proposed for energy systems optimization under uncertainty. A hybrid modeling method is applied to develop building block models based on the mechanism and process historical data. The deterministic optimization model can be further formulated as a mixed-integer non-linear programming problem. Considering enthalpy uncertainties, a generalized intersection kernel support vector clustering is employed to construct the uncertainty set. By introducing the derived uncertainty set in the deterministic optimization model, a robust optimization model is presented. A case study on the energy system of a real ethylene plant is carried out to illustrate the performance of the proposed approach and the effect of regularization parameter κ on the optimization results is studied. The results show that the optimized energy costs are 15148.84 kg/h and 16209.81 kg/h in deterministic and robust optimization methods. Despite higher energy consumption in robust optimization, the proposed method yields a trade-off between energy cost and robustness. The conservatism of the solution can be adjusted by the regularization parameter, and in this system κ=0.02 is recommended.
As the scale of virtual power plants (VPPs) continues to expand, the communication demands between VPPs and the management center are increasing. To maintain the communication of the entire system, ...VPPs operators must pay high costs, and then, how to reduce communication costs as much as possible while ensuring VPPs communication requirements has become an important and difficult issue. However, in the existing literature, there are few scheduling methods for large-scale VPPs communications. To this end, this paper proposes an optimal scheduling method based on software-defined wide area network (SD-WAN) to reduce communication costs. First, the communication network architecture of large-scale VPPs is analyzed in detail, and communication services are categorized according to delay requirements. Second, for the most expensive wide area network layer, a communication network control structure based on SD-WAN is designed, and an optimal scheduling model is established to minimize communication costs while ensuring communication service quality. This model is formulated as a mixed-integer nonlinear programming problem, and then linearized and constraint-relaxed to enable solved by the state-of-the-art solver (i.e., Gurobi). Third, to further overcome the challenge of solving large-scale problems, such as low computation efficiency and memory overflow, a two-stage fast-solving algorithm is proposed, which sorts and categorizes VPPs branch sites and optimizes the problem in two stages, enabling the expedited resolution of the problem. Numerical tests verify the effectiveness of the proposed method. Especially for large-scale VPPs, the proposed algorithm improves computation efficiency by a thousand times without perceivable degradation in performance, compared to the state-of-the-art solver.
•The communication network and service types of large-scale VPPs are established.•The developed model guarantees the stability and economy of VPPs communication.•A two-stage fast-solving algorithm is developed to efficiently solve the problem.
To support artificial intelligence (AI)‐involved tasks offloaded from the mobile devices (MDs), it is necessary to equip the Unmanned Aerial Vehicle (UAV) with custom‐made co‐processor (CP) for ...handling AI workloads in multi‐UAV‐empowered Edge Intelligence. Existing CPU‐oriented task scheduling algorithm cannot apply to the CPU+CP heterogeneous architecture. In this backdrop, this paper first formulates the joint service function placement, collaborative task scheduling, UAV deployment, and MD position determination problem as a Mixed Integer Non‐Linear Programming problem. Then, an alternating optimization‐based algorithm is put forward to derive a sub‐optimal solution of the problem utilizing Differential Evolution and Greedy‐based Hungarian algorithms. A series of experiments are conducted to evaluate the performance of the proposal. Results show that authors' proposal can achieve an overall revenue that is roughly 50% higher than those of existing methods.
To support artificial intelligence (AI)‐involved tasks offloaded from the mobile devices (MDs), it is necessary to equip the Unmanned Aerial Vehicle (UAV) with custom‐made co‐processor (CP) for handling AI workloads in multi‐UAV‐empowered Edge Intelligence. In this backdrop, this paper first formulates the joint service function (SF) placement, collaborative task scheduling, UAV deployment, and MD position determination problem as a Mixed Integer Non‐Linear Programming (MINLP) problem. Then, an alternating optimization‐based algorithm is put forward to derive a sub‐optimal solution of the problem utilizing Differential Evolution (DE) and Greedy‐based Hungarian algorithms.
Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This ...is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the \(1^{st}\) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.
•Proposing an extension of firefly algorithm.•Employment of picewise chaos, for an further enhanced diversity.•Making use of a simple but effective constraint handling method.•Making use of an ...improved local search procedure.
Firefly algorithm (FA) is a newer member of bio-inspired meta-heuristics, which was originally proposed to find solutions to continuous optimization problems. Popularity of FA has increased recently due to its effectiveness in handling various optimization problems. To enhance the performance of the FA even further, an adaptive FA is proposed in this paper to solve mechanical design optimization problems, and the adaptivity is focused on the search mechanism and adaptive parameter settings. Moreover, chaotic maps are also embedded into AFA for performance improvement. It is shown through experimental tests that some of the best known results are improved by the proposed algorithm.
•Exact representation of reactive power demand of the system through standard power flow equations.•Operational constraints are included in the optimization model.•Demand response is modeled through ...a fleet of PHEVs and adjustable loads.•Uncertainty of renewable generation and load is quantified using probability distribution.•Optimization model captures both spatial and temporal variations of critical and non-critical loads.
This paper proposes a method to enhance resiliency of microgrids through survivability. Survivability in this context is to minimize load shed for the duration the microgrid is in islanded mode following a disturbance event. During islanded operation, microgrid loads are prioritized as critical and non-critical loads. The key decision is to ascertain whether to provide energy to non-critical loads after supplying the critical loads or to store excess energy for future dispatches. This task is formulated as a non-linear programming problem. The objective is to minimize the amount of critical load shed while maximizing the amount of non-critical load served for a projected restoration time while adhering to relevant operational and physical constraints. For this extended time-scale problem, uncertainty of renewable generation and load forecast is quantified with probability distribution and confidence levels are used to establish likelihood of forecast error. Distributed generation such as solar and wind farm along with battery energy storage system are modeled. Demand response is implemented through adjustable loads and a fleet of plug in hybrid electric vehicles that can be operated in both grid to vehicle and vehicle to grid mode. Test cases are studied on a modified CIGRE microgrid benchmark test system and results are compared with a temporal decomposition scheme based energy management system.
PDF
