Constraint Generation and Surrogate Relaxation

1988 ◽  
Vol 9 (2) ◽  
pp. 215-218
Author(s):  
Asa Hallefjord ◽  
Kurt Jornsten
Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.


2020 ◽  
Vol 77 (2) ◽  
pp. 539-569
Author(s):  
Nicolas Kämmerling ◽  
Jannis Kurtz

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.


Procedia CIRP ◽  
2019 ◽  
Vol 80 ◽  
pp. 548-553
Author(s):  
Header Alrufaifi ◽  
Bubnish Kumar ◽  
Jeremy L. Rickli

2020 ◽  
Vol 34 (05) ◽  
pp. 7277-7284
Author(s):  
Thayne T. Walker ◽  
Nathan R. Sturtevant ◽  
Ariel Felner

The main idea of conflict-based search (CBS), a popular, state-of-the-art algorithm for multi-agent pathfinding is to resolve conflicts between agents by systematically adding constraints to agents. Recently, CBS has been adapted for new domains and variants, including non-unit costs and continuous time settings. These adaptations require new types of constraints. This paper introduces a new automatic constraint generation technique called bipartite reduction (BR). BR converts the constraint generation step of CBS to a surrogate bipartite graph problem. The properties of BR guarantee completeness and optimality for CBS. Also, BR's properties may be relaxed to obtain suboptimal solutions. Empirical results show that BR yields significant speedups in 2k connected grids over the previous state-of-the-art for both optimal and suboptimal search.


Author(s):  
Dongming Lu ◽  
Shouqian Sun ◽  
Zhijun He

Abstract The IFBMDA is an Information-Flow-Based model for Mechanical Design Automation. This paper first analyzes the mechanical design process from the views of design methodology and cognitive model. Then, two essential assumptions about mechanical design behavior are provided. Based on the analysis and fundamental assumptions, this paper thoroughly describes five submodels which constitute the automation model IFBMDA. They are Information Flow model, Knowledge Processing model, Non-monotonic Expansion Search model, Iterative Constraint Generation and Solution model and Design Process Stage model. Then, this paper also evaluates the model in both practical and theoretical aspects and shows that it is well-developed in both aspects. Finally, the perspective of further mechanical design automation research is outlined.


2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Yang Liu ◽  
Yanli Ye ◽  
Xianbang Chen ◽  
Huaqiang Li ◽  
Yuan Huang

Wind power generation has been widely deployed in the modern power system due to the issues of energy crisis and environment pollution. Meanwhile, the microgrid is gradually regarded as a feasible way to connect and accommodate the distributed wind power generations. Recently, more research studies also focus on incorporating various energy systems, for example, heat and gas into the microgrid in terms of satisfying different types of load demands. However, the uncertainty of wind power significantly impacts the economy of the integrated power-heat-gas microgrid. To deal with this issue, this paper presents a two-stage robust model to achieve the optimal day-ahead economic dispatch strategy considering the worst-case wind power scenarios. The first stage makes the initial day-ahead dispatch decision before the observation of uncertain wind power. The additional adjustment action is made in the second stage once the wind power uncertainty is observed. Based on the duality theory and Big-M approach, the original second-stage problem can be dualized and linearized. Therefore, the column-and-constraint generation algorithm can be further implemented to achieve the optimal day-ahead economic dispatch strategy for the integrated power-heat-gas microgrid. The experimental results indicate the effectiveness of the presented approach for achieving operation cost reduction and promoting wind power utilization. The robustness and the economy of the two-stage robust model can be balanced, of which the performances significantly outperform those of the single-stage robust model and the deterministic model.


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