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Combinatorial Integral Approximation Decompositions for mixed-integer Optimal Control

ALGORITHMS 2022年第4期15卷 121-121页

作者： Zeile, Clemens Weber, Tobias Sager, Sebastian Otto von Guericke Univ Dept Math D-39106 Magdeburg Germany

Solving mixed-integer nonlinear programs (MINLPs) is hard from both a theoretical and practical perspective. Decomposing the nonlinear and the integer part is promising from a computational point of view. In general, however, no bounds on the objective value gap can be established and iterative procedures with potentially many subproblems are necessary. The situation is different for mixed-integer optimal control problems with binary variables that switch over time. Here, a priori bounds were derived for a decomposition into one continuous nonlinear control problem and one mixed-integer linear program, the combinatorial integral approximation (CIA) problem. In this article, we generalize and extend the decomposition idea. First, we derive different decompositions and analyze the implied a priori bounds. Second, we propose several strategies to recombine promising candidate solutions for the binary control functions in the original problem. We present the extensions for ordinary differential equations-constrained problems. These extensions are transferable in a straightforward way, though, to recently suggested variants for certain partial differential equations, for algebraic equations, for additional combinatorial constraints, and for discrete time problems. We implemented all algorithms and subproblems in AMPL for a proof-of-concept study. Numerical results show the improvement compared to the standard CIA decomposition with respect to objective function value and compared to general-purpose MINLP solvers with respect to runtime.

关键词： optimal control switched dynamic systems mixed-integer nonlinear programming mixed-integer linear programming ordinary differential equations approximation methods

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A novel bidding method for combined heat and power units in district heating systems

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2020年第4期11卷 1137-1156页

作者： Blanco, Ignacio Andersen, Anders N. Guericke, Daniela Madsen, Henrik Tech Univ Denmark Dept Appl Math & Comp Sci DK-2800 Lyngby Denmark EMD Int AS Niels Jernesvej 10 DK-9220 Aalborg Denmark

We propose a bidding method for the participation of combined heat and power (CHP) units in the day-ahead electricity market. More specifically, we consider a district heating system where heat can be produced by CHP units or heat-only units, e.g., gas or wood chip boilers. We use a mixed-integer linear program to determine the optimal operation of the portfolio of production units and storages on a daily basis. Based on the optimal production of subsets of units, we can derive the bidding prices and amounts of electricity offered by the CHP units for the day-ahead market. The novelty about our approach is that the prices are derived by iteratively replacing the production of heat-only units through CHP production. This results in an algorithm with a robust bidding strategy that does not increase the system costs even if the bids are not won. We analyze our method on a small realistic test case to illustrate our method and compare it with other bidding strategies from literature, which consider CHP units individually. The analysis shows that considering a portfolio of units in a district heating system and determining bids based on replacement of heat production of other units leads to better results.

关键词： Day-ahead electricity market Combined heat and power units District heating Bidding method mixed-integer linear programming Operational planning

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Stochastic home energy management system via approximate dynamic programmingInspec keywordsOther keywords

IET ENERGY SYSTEMS INTEGRATION

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IET ENERGY SYSTEMS INTEGRATION 2020年第4期2卷 382-392页

作者： Liu, Xuebo Wu, Hongyu Wang, Li Faqiry, M. Nazif Kansas State Univ Mike Wiegers Dept Elect & Comp Engn Manhattan KS 66506 USA

This study proposes an approximate dynamic programming (ADP) method for a stochastic home energy management system (HEMS) that aims to minimise the electricity cost and discomfort of a household under uncertainties. The study focuses on a HEMS that optimally schedules heating, ventilation, and air conditioning, water heater, and electric vehicle, while accounting for uncertainties in outside temperature, hot water usage, and non-controllable net load. The authors approach the ADP-based HEMS via an effective combination of Sobol sampling backward induction and a K-D tree nearest neighbour techniques for the value function approximation. A subset of possible states is sampled and used to create an approximation of the value of being in aggregated states. They compare the ADP approach with other prevailing HEMS methods, including dynamic programming (DP) and mixed-integer linear programming (MILP), in a model predictive control framework. Simulation results show that the proposed ADP approach can yield near-optimal appliance schedules under uncertainties when finely discretised. Merits and drawbacks of the proposed ADP method in comparison with DP and MILP are also revealed.

关键词： linear programming demand side management integer programming predictive control function approximation dynamic programming energy management systems domestic appliances nearest neighbour methods trees (mathematics) HVAC electric vehicles mixed-integer linear programming ADP approach near-optimal appliance schedules ADP method stochastic home energy management system approximate dynamic programming method electricity cost optimal scheduling water heater electric vehicle hot water usage noncontrollable net load ADP-based HEMS K-D tree nearest neighbour techniques value function approximation HEMS methods heating-ventilation-air conditioning outside temperature Sobol sampling backward induction model predictive control framework

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An exact method with decomposition techniques and combinatorial Benders' cuts for the type-2 multi-manned assembly line balancing problem

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OPERATIONS RESEARCH PERSPECTIVES 2020年 7卷

作者： Michels, Adalberto Sato Lopes, Thiago Cantos Magatao, Leandro Univ Tecnol Fed Parana UTFPR Programa Posgrad Engn Eletr & Informat Ind CPGEI Curitiba Parana Brazil

Multi-manned assembly lines are widely applied to manufacturing industries that produce large-size products and are concerned with high levels of productivity. Such lines are commonly found in automotive industries, where different tasks are simultaneously performed by more than one worker on the same product in multi operated stations, giving rise to a class of balancing problem that aims to minimize the line's cycle time. This clear practical application had made the type-2 multi-manned assembly line balancing problem to be explored in the past. However, only few small-size instances could be solved by preceding exact solution approaches, whereas large and real-life cases still lack optimality proofs since they were tackled by heuristics. In this work, a new mixed-integer linear programming model is presented and its modeling decisions discussed. Moreover, an innovative exact solution procedure employing a combination of decomposition techniques and combinatorial Benders' cuts is presented to solve large and real-life instances optimally. Tests on an extended literature dataset and a real-life assembly plant case study have demonstrated that the proposed algorithm outperforms previously developed methods in terms of solution quality by an ample margin in efficiency gains. Synergies between the algorithm's components are also revealed. Finally, the proposed exact method has been able to yield 60 optimal results out of a 108-instance dataset, with the remaining 48 solutions presenting a small integer gap (less than 2%).

关键词： Multi-manned assembly line balancing Cycle time minimization Combinatorial Benders' cuts mixed-integer linear programming

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Big-M based MILP method for SCUC considering allowable wind power output interval and its adjustable conservativeness

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Global Energy Interconnection 2021年第2期4卷 193-203页

作者： Liudong Zhang Qibing Zhang Haifeng Fan Haiwei Wu Chunlei Xu State Grid Jiangsu Electric Power Company LTD.Nanjing 210024P.R.China

In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable *** wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power ***,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is ***,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust *** can establish a trade-off between economy and *** develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable *** studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.

关键词： Big-M method Security-constrained unit commitment Robust optimization mixed-integer linear programming Allowable wind power output interval Adjustable conservativeness

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Energy management platform for integrated battery-based energy storage - solar PV system: a case studyInspec keywordsOther keywords

IET ENERGY SYSTEMS INTEGRATION

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IET ENERGY SYSTEMS INTEGRATION 2020年第4期2卷 373-381页

作者： Suthar, Sachinkumar Pindoriya, Naran M. Indian Inst Technol Gandhinagar Elect Engn Palaj Gujarat India

This study develops an energy management platform for battery-based energy storage (BES) and solar photovoltaic (PV) generation connected at the low-voltage distribution network. The sewage treatment plant of Gujarat International Finance Tec-City located in the Gujarat state is considered as a testbed. The contribution of this case study is twofold: (i) Formulation and lab-scale implementation of an optimal scheduling algorithm to charge/discharge BES while minimising the net energy purchase cost. (ii) Development of a fuzzy logic-based speed control strategy for aeration blower to enhance the process efficiency. A stochastic optimisation problem was formulated as mixed-integer linear programming to achieve the charging and discharging schedules of BES. The simulation study on speed control of aeration blower was carried out to demonstrate the air injection control for optimal dissolved oxygen level in the aeration basin at the testbed. Simulation results of the case study and lab-scale hardware realisation (through real-time digital simulator interfaced with modular hardware) were presented to validate the demand- and supply-side energy management platform.

关键词： photovoltaic power systems energy management systems distribution networks fuzzy logic energy storage optimisation fuzzy control battery storage plants velocity control energy management platform integrated battery-based energy storage solar PV system low-voltage distribution network Gujarat International Finance Tec-City lab-scale implementation net energy purchase cost fuzzy logic-based speed control strategy aeration blower solar photovoltaic generation Gujarat state optimal scheduling algorithm charge-discharge BES stochastic optimisation problem mixed-integer linear programming speed control air injection control optimal dissolved oxygen level aeration basin real-time digital simulator modular hardware demand-side energy management platform supply-side energy management platform

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Simulated Annealing Algorithm for Multi Depot Two-Echelon Capacitated Vehicle Routing Problem

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EUROPEAN TRANSPORT-TRASPORTI EUROPEI 2020年第78期

作者： Kancharla, Surendra Reddy Ramadurai, Gitakrishnan Indian Inst Technol Madras Dept Civil Engn Chennai 600036 Tamil Nadu India

Although urban freight transport is a significant contributor to the development of a country, it has adverse effects on the environment and the quality of life in urban areas. To reduce these adverse effects, we can deploy sustainable city logistic strategies. Scheduling and routing of vehicles is a crucial decision in city logistic strategies. Hence, in this paper, we solve the Multi-Depot Two Echelon Capacitated Vehicle Routing Problem (MD2E-CVRP), which is a variant of Vehicle Routing Problem (VRP) with heterogeneous fleets at both levels. Since VRP is NP-hard, we have proposed a Simulated Annealing (SA) based heuristic solution algorithm and have tested it on the standard 2E- CVRP and MD2E-CVRP instances. The results obtained from SA have a good solution quality at just one-fiftieth of computational time using CPLEX and was found to be faster than Adaptive Large Neighborhood Search (ALNS) with only a marginal drop in solution quality.

关键词： Two-Echelon Capacitated Vehicle Routing Problem Simulated Annealing mixed-integer linear programming

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Convex mixed-integer optimization with Frank-Wolfe methods

arXiv

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arXiv 2022年

作者： Hendrych, Deborah Troppens, Hannah Besançon, Mathieu Pokutta, Sebastian Freie Universität Berlin Germany Zuse Institute Berlin Germany Technische Universität Berlin Germany

mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank-Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear minimization oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems. © 2022, CC BY.

关键词： mixed-integer linear programming

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Two-row and two-column mixed-integer presolve using hashing-based pairing methods

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2020年第3-4期8卷 205-240页

作者： Gemander, Patrick Chen, Wei-Kun Weninger, Dieter Gottwald, Leona Gleixner, Ambros Martin, Alexander Friedrich Alexander Univ Erlangen Nurnberg Dept Math Cauerstr 11 D-91058 Erlangen Germany Beijing Inst Technol Sch Math & Stat Beijing 100081 Peoples R China Zuse Inst Berlin Dept Math Optimizat Takustr 7 D-14195 Berlin Germany

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.

关键词： linear programming mixed-integer linear programming Optimization solver Presolve

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Modelo para planejamento da expansão de sistemas de distribuição considerando confiabilidade

Modelo para planejamento da expansão de sistemas de distrib...

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作者： Cruz, Gederson Alvaro da

This work presents an optimization model for the expansion planning problem of distribution systems considering reliability. The addition of new branches and the reconductoring of existing branches are the investment alternatives in the expansion plan. In addition, the optimization model evaluates energy losses of the feeders, nodal voltage limit violations and reliability to find the best expansion plan of the distribution system. Reliability is obtained by means of the main indexes, i.e. energy not supplied (ENS), system average interruption frequency index (SAIFI), and system average interruption duration index (SAIDI). The objective function of the optimization model is composed of three components: investment costs, operating costs, and reliability costs. In this work, the steady state operating point of the distribution systems are calculated using a linearized model. In addition, the proposed optimization model uses a linear objective function, linear constraints, and continuous and integer variables, and it is represented as a mixedinteger linear programming (MILP) problem. The optimization model is described in the OPL programming language and solved using the CPLEX solver. In order to demonstrate the applicability of the optimization model, four cases contemplating different objective functions were implemented in two distribution systems: a 10-node system and a 54- node system. The numerical results demonstrate the relevance of considering reliability in expansion planning of distribution systems. ...

关键词： Optimization model Planejamento da expansão do sistema elétrico Expansion planning problem of distribution systems Energia elétrica : Distribuição Análise de confiabilidade Reliability mixed-integer linear programming Dissertação

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