Hydro Unit Commitment via Mixed Integer Linear Programming: A Case Study of the Three Gorges Project, China

One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.

Optimal operation of water-energy microgrids; a mixed integer linear programming formulation

The Three Gorges Project (TGP) is a landmark Chinese hydroelectric project with the goal of harnessing the Yangtze River and developing its water resources. Because of its enormous size and far-reaching influence, the project's impact on the Yangtze River's original ecological environ- ment has been a concern to many people. This article exam- ines the environmental effects of TGP with regard to reser- voir-induced seismicity and bank stability, climate changes, sedimentation and bank erosion, the protection of aquatic species and water quality, and resettlement. Based on the op- eration monitoring data of TGP in 10 years (2003—2012), this article analyzes the tendency of reservoir-induced seis- micity and bank stability, developing trend of sedimentation and bank erosion, the interplay between climate change and TGP, the distribution and cause of water contamination, the situation of aquatic species' protection and living situation of resettled residents. At the same time, this article lists the comprehensive benefits of TGP in flood control, power gen - eration, shipping, water supply, energy conservation and emission reduction. In the end, the authors deem that there is a dynamic and harmonious relationship between humankind and nature. The cognition about TGP will be progressed in practice, and harmonious relationship between the environ- ment and TGP will be achieved through more practice.

The redundancy allocation problem (RAP) aims to find an allocation of redundant components that maximizes system reliability under resource constraints. In this paper, we consider the RAP for complex systems with heterogeneous components, which may have bridges or interconnecting subsystems and are generally more complicated in structure than commonly studied series-parallel systems. A major challenge of the RAP is that the reliability function is nonlinear. To tackle this, we develop six exact mixed integer linear programming (MILP) formulations, which, to our knowledge, are the first of such formulations for the problem. The key idea is to use binary variables and big-M constraints to successively linearize each product term in the reliability function. In addition, we propose a novel tree representation of the reliability function to establish the interconnections between different product terms, which is then used to reduce the number of decision variables and constraints needed in the linearization. We also propose an alternative form of the reliability function that only involves the failure probabilities of subsystems, and leverage this to derive better variable bounds, smaller big-M constants, and simpler formulations. We compare the six MILP formulations by solving them directly using an MILP solver based on three sets of test instances of varying complexity. Results indicate that all formulations achieve optimal solutions quickly for the first set and within reasonable computation times for the second set. For the third set, two formulations can always be solved within a given time limit. Overall, the MILP formulation derived based on the alternative form of the reliability function and a specific type of tree representation scheme performs the best. We also demonstrate that our approach is more robust and scalable than a benchmark branch-and-bound method. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by National Natural Science Foundation of China [Grants 72310107003, 72471189, 71901176]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0842 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0842 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In the literature, e.g. [10], one can find the so-called basic UAV mission target assignment in which m UAVs each with a capacity limit q visit n targets in a cooperative manner (and return to their departure points) such that the cost incurred by each UAV’s travel is minimized. In [10], we proposed a mixed integer linear program (MILP) formulation which exactly solves the problem, as well as four alternative MILP formulations which are computationally less intensive (and therefore suited for real-time purposes) yet yield a theoretically guaranteed sub-optimal solution. In this chapter, we further consider timing constraints imposed on some p of the targets, so-called prime targets. This consideration is often required for scenarios in which prime targets must be visited in a pre-defined time interval, and mathematically results in the addition of several integer linear constraints to the previous MILP formulation making the problem computationally intractable. We propose a novel procedure of adding these cumbersome timing constraints to the previous MILP formulation, in order to avoid increasing too much computational cost under practically valid assumptions. We first show that the proposed procedure still guarantees the previously claimed theoretical solution quality associated with the basic mission. We then show through extensive numerical simulations that under certain conditions, our algorithms return solutions which are still computationally manageable.

The Yangtze River and its tributaries located in Three Gorges Project (TGP) reservoir was influenced by the operation of TGP reservoir, and the water quality problems were becoming serious these years. Mass transportation in the tributaries was interacted with the hydrodynamic field. Then, a parallelized three dimensional unstructured mesh water quality model was applied to Xiangxi River - one of tributaries of Yangtze River - to simulate the changing processes of flowing and nutrients including TP and TN. The results show that the parallelization model can enhance the simulation efficiency, especially when the computational scale is large. The parallelized model was executed in Windows operation system could make sufficient use of the resources of low-end multi-core personal computer. The parallelized model could provide a new tool for river water quality research and the information for management of TGP reservoir.

An MILP formulation for optimizing detailed schedules of a multiproduct pipeline network

Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

This article focuses on the situation of women migrants displaced by the Three Gorges Project (TGP) in China. It examines the participation and types of work undertaken by women migrants in the resettlement process, the strategies of the government and women migrants in coping with risks (especially impoverishment) that migrant families face after physical displacement, and some gender-related issues relevant to planning in the TGP. Data show that women migrants have limited opportunities to participate in the decision-making process of displacement. Following resettlement, women migrants face difficulties in finding employment in the non-agricultural sector while those who remain in the agricultural sector encounter extreme difficulties in attempting to engage in new agricultural practices in their new environments. The study found that a gendered perspective in planning for livelihood reconstruction and skills training is generally inadequate or absent.

The owner-responsibility system is conducted for implementation of the Three Gorges Project (TGP). For the construction management of the project, the contracting system, the contract administration system, and the construction supervision system are executed for the project management. Contractors for civil projects are determined through bidding and contracting. The permanent equipment and construction materials are purchased through bidding. Some of large-sized construction machines and mechanical and electrical equipment are procured by the international competitive bids. Qualified engineers from qualified engineering bodies, scientific research organizations, and construction companies are selected for the construction supervision. This paper covers the construction of the TGP in some detail, particularly the main dam structure, diversion work, the construction program, and management, project cost, and financing.

Joint scheduling and power control schemes have previously been proposed to reduce power dissipation in wireless ad hoc networks. However, instead of power consumption, throughput is a more important performance concern for some emerging multihop wireless networks, such as wireless mesh networks. This paper examines joint link scheduling and power control with the objective of throughput improvement. The MAximum THroughput link Scheduling with Power Control (MATH-SPC) problem is first formulated and then a mixed integer linear programming (MILP) formulation is presented to provide optimal solutions. However, simply maximizing the throughput may lead to a severe bias on bandwidth allocation among links. To achieve a good tradeoff between throughput and fairness, a new parameter called the demand satisfaction factor (DSF) to characterize the fairness of bandwidth allocation and formulate the MAximum Throughput fAir link Scheduling with Power Control (MATA-SPC) problem is defined. An MILP formulation and an effective polynomial-time heuristic algorithm, namely, the serial linear programming rounding (SLPR) heuristic, to solve the MATA-SPC problem are also presented. Numerical results show that bandwidth can be fairly allocated among all links/flows by solving the MILP formulation or by using the heuristic algorithm at the cost of a minor reduction of network throughput. In addition, extensions to end-to-end throughput and fairness and multiradio wireless multihop networks are discussed.

In this paper, we seek to jointly minimize the network power consumption and the user transmission delays in green wireless access networks. We recently studied the case of a WLAN, where we evaluated the tradeoffs between these two minimization objectives using a Mixed Integer Linear Programming (MILP) formulation. However, the MILP formulation could not deliver solutions in a reasonable amount of time due to computational complexity issues. As a result, we propose here a heuristic algorithm for the power-delay minimization problem. The proposed heuristic aims to compute the transmit power level of the Access Points (APs) deployed in the network and associate users with these APs in a way that jointly minimizes the total network power and the total network delay. The simulation results show that the proposed algorithm has a low computational complexity, which makes it advantageous compared with the optimal scheme, particularly in dense networks. Moreover, the heuristic algorithm performs close to optimally and provides power savings of up to 45% compared with legacy networks.

Autonomous vehicles have emerged as transformative technologies with vast implications across various domains, including surveillance. However, they are constrained by battery limitations, which can hinder their usability and efficiency. Designing algorithms to efficiently utilize them optimizing their battery usage, is crucial to unlocking their full potential. This paper addresses this challenge by studying an extension of the rural postman problem with multiple depots and rechargeable and reusable vehicles that can make multiple trips but have limited battery capacity. It presents a new Mixed Integer Linear Programming (MILP) formulation to find optimal solutions to the problem and proposes a new heuristic called the multi-trip (MT) algorithm. The paper describes the results of a study that tested the MT algorithm, other heuristics, and the MILP formulation on both benchmark instances and larger, real-world instances generated from road maps. Our results show that the MT algorithm found feasible solutions for every instance and produced better solutions than heuristics from the literature on 38 of the 39 instances that were tested. Due to its requirements for memory and computing time, the Gurobi optimizer used for solving the MILP formulation could not find optimal solutions for the largest instances that we tested. This research contributes to enhancing the efficiency and effectiveness of battery-operated unmanned by developing new heuristics to address the challenge of battery limitations.

The impoundment of the Three Gorges Project (TGP) may influence the natural reproduction of the Chinese sturgeon. From 2009 to 2011, a five-method investigation was conducted to analyse this influence. The Chinese sturgeon reproduced in late November 2009 to 2011, which was about two weeks later than in 2003 to 2006. The water discharge and water temperature did not exhibit any evident difference from 2003 to 2011. The investigation showed that the spawning sites transferred near the Gezhouba dam in 2010 and 2011. The estimated parent Chinese sturgeon greatly increased in 2011, which suggested that stopping the catching of parent fish increased the natural spawning number. The integral survival rate before the fish enters into the sea should be assessed, however. All the monitoring dates from 1997 to 2011 showed that the Chinese sturgeon could finish natural reproduction, while the Three Gorges Dam operated during the 175 m trial impoundment. Yet, spawning time was delayed and water temperature during spawning was slightly higher than before. The increase of spawning size in 2011 showed the number of parent fish has more influence in the reproduction number than the operation of TGP. Earlier impoundment to avoid the spawning time of Chinese sturgeon may be the key to reducing the effect on the natural reproduction of Chinese sturgeon.

Natural occurrence of C4 species, life form, altitude pattern, and infection by the Three Gorges Project (TGP) were studied in the TGP region. 76 species (about 2.5 % of the total 2 685 vascular plant species in the region), in 6 families and 42 genera, were identified with C4 photosynthesis. 91 % of these C4 species belong to Monocotyledoneae, e.g. Cyperaceae (14 species), Gramineae (54 species), and Commelinaceae (1 species). Of these C4 species, Gramineae was the leading C4 family: 54 C4 grass species (71 % of the total C4 species), about 36 % of the total grasses, were identified in the TGP region. 98 % C4 species was found in therophyte (55 %) and hemicryptophyte (43 %). This is consistent with high grass and sedge compositions in the region. Most habitats of more than a half of these C4 species (65 %) will be submerged permanently, but no species will be endangered or extinct, because 95 % C4 species can be found from 500 to 800 m above sea level. The abundance of some C4 species will be dropped due to the reduction of distribution scope. It will take a long-term to explore the effects of the TGP on plants, vegetation, and environment.