This paper tackles key industry needs in the scope of the AC Security-Constrained Optimal Power Flow (SCOPF) framework, specifically two major challenging requirements regarding generators' post-contingency behavi...
详细信息
This paper tackles key industry needs in the scope of the AC Security-Constrained Optimal Power Flow (SCOPF) framework, specifically two major challenging requirements regarding generators' post-contingency behavior: the (droop-based) frequency response and the voltage control mechanism (including PV/PQ switching). To this end, and to obtain a sufficiently accurate solution with a reasonable computational burden, we propose an approximation approach to SCOPF which extends significantly an existing algorithm with novel modelling elements: a continuous formulation to model generators' post-contingency responses based on successive approximations, a technique to evaluate the viability of contingencies with respect to the base case set-points, and the complexity reduction of all post-contingency states through network compression and power flow piecewise linearization. All new features are validated both separately and in unison, to monitor the improvement of the solution time and the potential degradation of the solution's quality. The proposed approach is successfully applied to three power system network models, the largest of which consists of 2,000 buses and more than 3,000 contingencies. Finally, the trade-off between the limitations in terms of solution quality and the benefits in terms of computational effort are assessed for all proposed approximations.
We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formu...
详细信息
We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integernonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying simple rounding heuristics to solutions of the relaxed problem can fail to identify the correct number and location of the sources. We develop two new rounding heuristics that exploit the value and a physical interpretation of the continuous relaxation solution, and we apply a steepest-descent improvement heuristic to obtain satisfactory solutions to both two- and three-dimensional inverse problems. We also provide the code used in our numerical experiments in open-source format.
Solving mixed-integernonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible ...
详细信息
Solving mixed-integernonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integernonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.
Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essent...
详细信息
Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essential in such systems, but existing JSP literature often overlooks workplace fatigue, which harms employees’ well-being and costs U.S. employers up to €127 billion annually. In this work, we propose fatigue consideration in the job-shop scheduling problem in a cobotic order picking system to mitigate its negative effects. We present a new bi-objective mixedintegernonlinearprogramming problem formulation that considers worker fatigue and productivity during schedule optimisation. To put the results of simulated optimisation in perspective, we experimentally validate the fatigue model and scheduling results in a real operation. The mathematical model finds solutions that conventional single-objective optimisation cannot, allowing fractional fatigue distribution improvements more than 4x larger than the decrease in productivity they require in 53% of the considered virtual cases. The experiments show that our predictive fatigue model has an average RMSE of 2.20 kcal/min in estimating energy expenditure rates compared to heart rate measurements. It also shows a low correlation, meaning it is unfit for application. On the other hand, fatigue-conscious schedules show no clear benefit regarding measured and perceived fatigue. However, the scheduling model could also use heart rate measurements that do not show these inaccuracies. Our study highlights the need to further develop and validate the mathematical formulation and fatigue model and extend to other human factors and indirect fatigue effects.
We describe a computationally effective method for generating lift-andproject cuts for convex mixed-integernonlinear programs (MINLPs). The method relies on solving a sequence of cut-generating linear programs and in...
详细信息
We describe a computationally effective method for generating lift-andproject cuts for convex mixed-integernonlinear programs (MINLPs). The method relies on solving a sequence of cut-generating linear programs and in the limit generates an inequality as strong as the lift-and-project cut that can be obtained from solving a cut-generating nonlinear program. Using this procedure, we are able to approximately optimize over the rank one lift-and-project closure for a variety of convex MINLP instances. The results indicate that lift-and-project cuts have the potential to close a significant portion of the integrality gap for convex MINLPs. In addition, we find that using this procedure within a branch-and-cut solver for convex MINLPs significantly reduces the total solution time for many instances. We also demonstrate that combining lift-and-project cuts with an extended formulation that exploits separability of convex functions yields significant improvements in both relaxation bounds and the time to calculate the relaxation. Overall, these results suggest that with an effective separation routine, like the one proposed here, lift-and-project cuts may be as effective for solving convex MINLPs as they have been for solving mixed-integer linear programs.
Car-sharing, electrification, and autonomous driving are greatly revolutionizing the future of the transportation system. This study proposes a location routing problem for the car-sharing system with autonomous elect...
详细信息
Car-sharing, electrification, and autonomous driving are greatly revolutionizing the future of the transportation system. This study proposes a location routing problem for the car-sharing system with autonomous electric vehicles to determine optimal station location and vehicle routing, where each station is both a depot and a charging station. A mathematical model is formulated and then extended to three variants, while simultaneously considering different recharging and service options. The proposed mixed-integernonlinear models are separately solved by general algebraic modeling system (GAMS) and genetic algorithm (GA), and the efficiency of the GA is demonstrated. The comparative experimental results of instances are presented, and the benefits of allowing partial recharge are obtained. More significant savings in cost can be achieved if partial service is simultaneously allowed. Furthermore, the trade-off between the operator's interests and the interests of users, as well as the operator's immediate profits and future profits, are explored through sensitivity analysis.
Underwater radiated noise (URN) emanating from ships can adversely impact the life functions of certain marine mammals that rely on sound to navigate, communicate, and locate prey. This paper formulates an optimal voy...
详细信息
Underwater radiated noise (URN) emanating from ships can adversely impact the life functions of certain marine mammals that rely on sound to navigate, communicate, and locate prey. This paper formulates an optimal voyage scheduling problem to mitigate the impact of URN on sensitive marine species by choosing amongst different possible paths and specifying the cruising speed along the selected path. We focus on all-electric ships (AESs) owing to their greater flexibility for speed regulation by coordinating an integrated power system. The proposed optimization model schedules generators and energy storage devices toward minimizing the operation cost while satisfying constraints pertinent to URN levels and atmospheric greenhouse gas (GHG) emissions, the electric power network and operational limits, and expected voyage timelines, culminating in a mixed-integer nonlinear programming problem. To promote com-putational tractability, we approximate the nonlinear relationships for URN, propulsion load, and fuel consumption with piecewise linear functions. This leads to a mixed-integer second -order cone programming problem, which enables convergence to the global optimum and computationally efficient solutions. We illustrate the effectiveness of the proposed model in curbing URN levels and GHG emissions with numerical case studies involving an 18-node ship test system.
We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficienc...
详细信息
We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications.
The EU's climate targets are increasingly affecting the building sector. Energy-efficient buildings should therefore be built as airtight as possible in order to meet these targets - ventilation systems are necess...
详细信息
The EU's climate targets are increasingly affecting the building sector. Energy-efficient buildings should therefore be built as airtight as possible in order to meet these targets - ventilation systems are necessary to ensure a comfortable indoor climate. In the planning of ventilation systems, the placement, wiring and operation of the fans, among other things, must be considered. If, instead of the conventional planning for the maximum load case, the partial load scenarios are included, oversizing is reduced and energy efficiency is increased. In addition, there are new ventilation approaches that include distributed components in the central duct network and thus offer further opportunities to increase the energy efficiency of the systems. If one now considers multiple load cases and allows distributed components in the design, the number of combinations exceeds any human manageable amount and the human made design decision becomes far from optimal as a result. Therefore, in this paper a method is presented that uses mathematical optimisation techniques to control the complexity and support the design. The planning task is modeled techno-economically as a minimisation problem with respect to life-cycle costs (mixed-integernonlinear Program) and solved with discrete optimisation methods. The approach is then tested on a case study, with which savings of 22% in life-cycle costs are achieved while reducing energy consumption by 28%. Furthermore, the embedding in the real planning process is considered and shown that the division into several planning phases has a negative impact on the efficiency of the ventilation system. These results show that increasing the complexity of the planning task and modelling and solving it using discrete optimisation methods allows for a huge increase in the efficiency of the ventilation system.
The power transmission systems are mainly protected by distance relays (DisRs) as a primary protection and directional overcurrent relays (DOCRs) as a backup protection. These two types of relays have a different oper...
详细信息
The power transmission systems are mainly protected by distance relays (DisRs) as a primary protection and directional overcurrent relays (DOCRs) as a backup protection. These two types of relays have a different operation principle that, sometimes, leads to miscoordination problems. In this paper, a new approach for DOCRs and DisRs coordination considering the DOCRs time-voltage-current characteristic (TVC-C) is proposed to fully eliminate the miscoordination problems found in the already published works. The coordination problem is formulated as a mixed-integer nonlinear programming (MINLP) considering a new proposed objective function. Furthermore, two new decision variables related to TVC-Cs are proposed namely: the type and the voltage control variable. An enhanced version of the hybrid GSA-SQP method is proposed to solve the developed opti-mization problem. In order to check the applicability of the proposed relays coordination method on small and large and more complex systems, the IEEE 9-bus and IEEE 39-bus are used for this task. The obtained results are compared with the published works which show the superiority of the proposed method in terms of satisfaction of all coordination constraints.
暂无评论