scholarly journals Robust Maximum Coverage Facility Location Problem with Drones Considering Uncertainties in Battery Availability and Consumption

2020 ◽  
pp. 036119812096809
Author(s):  
Darshan R. Chauhan ◽  
Avinash Unnikrishnan ◽  
Miguel Figliozzi ◽  
Stephen D. Boyles
Keyword(s):  
Robust Optimization ◽  
Facility Location Problem ◽  
Computational Time ◽  
Facility Locations ◽  
Maximum Coverage ◽  
Robust Model ◽  
Average Maximum ◽  
Deterministic Solution ◽  
Battery Consumption ◽  
Battery Energy

Given a set of a spatially distributed demand for a specific commodity, potential facility locations, and drones, an agency is tasked with locating a pre-specified number of facilities and assigning drones to them to serve the demand while respecting drone range constraints. The agency seeks to maximize the demand served while considering uncertainties in initial battery availability and battery consumption. The facilities have a limited supply of the commodity being distributed and also act as a launching site for drones. Drones undertake one-to-one trips (from located facility to demand location and back) until their available battery energy is exhausted. This paper extends the work done by Chauhan et al. and presents an integer linear programming formulation to maximize coverage using a robust optimization framework. The uncertainty in initial battery availability and battery consumption is modeled using a penalty-based approach and gamma robustness, respectively. A novel robust three-stage heuristic (R3SH) is developed which provides objective values which are within 7% of the average solution reported by MIP solver with a median reduction in computational time of 97% on average. Monte Carlo simulation based testing is performed to assess the value of adding robustness to the deterministic problem. The robust model provides higher and more reliable estimates of actual coverage under uncertainty. The average maximum coverage difference between the robust optimization solution and the deterministic solution is 8.1% across all scenarios.

scholarly journals Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Ke Shang ◽  
Felix T. S. Chan ◽  
Stephen Karungaru ◽  
Kenji Terada ◽  
Zuren Feng ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Robust Optimization ◽  
Comparative Studies ◽  
Complex Model ◽  
Orienteering Problem ◽  
Two Stage ◽  
Second Stage ◽  
Robust Model ◽  
Uncertainty Set

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights.

Advanced Robust Optimization Approach for Design Optimization With Interval Uncertainty Using Sequential Quadratic Programming

2013 ◽  
Author(s):  
Jianhua Zhou ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Linear Equations ◽  
Variable Parameter ◽  
Optimal Solution ◽  
Interval Uncertainty ◽  
Computational Time ◽  
Optimization Approach ◽  
Engineering Optimization ◽  
Loop Optimization ◽  
New Approach

Uncertainty is inevitable in real world. It has to be taken into consideration, especially in engineering optimization; otherwise the obtained optimal solution may become infeasible. Robust optimization (RO) approaches have been proposed to deal with this issue. Most existing RO algorithms use double-looped structures in which a large amount of computational efforts have been spent in the inner loop optimization to determine the robustness of candidate solutions. In this paper, an advanced approach is presented where no optimization run is required to be performed for robustness evaluations in the inner loop. Instead, a concept of Utopian point is proposed and the corresponding maximum variable/parameter variation will be obtained by just solving a set of linear equations. The obtained robust optimal solution from the new approach may be conservative, but the deviation from the true robust optimal solution is very small given the significant improvement in the computational efficiency. Six numerical and engineering examples are tested to show the applicability and efficiency of the proposed approach, whose solutions and computational time are compared with those from a similar but double-looped approach, SQP-RO, proposed previously.

scholarly journals Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 211
Author(s):  
Lijun Xu ◽  
Yijia Zhou ◽  
Bo Yu
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Model ◽  
Multi Stage ◽  
Proposed Model ◽  
Dual Forms

In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.

The Value of Randomized Solutions in Mixed-Integer Distributionally Robust Optimization Problems

2021 ◽  
Author(s):  
Erick Delage ◽  
Ahmed Saif
Keyword(s):  
Robust Optimization ◽  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Optimization Problems ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Distributionally Robust Optimization ◽  
Continuous Relaxation ◽  
Distributionally Robust

Randomized decision making refers to the process of making decisions randomly according to the outcome of an independent randomization device, such as a dice roll or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, in which deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has recently been shown that using a randomized, rather than a deterministic, strategy in nonconvex distributionally robust optimization (DRO) problems can lead to improvements in their objective values. It is still unknown, though, what is the magnitude of improvement that can be attained through randomization or how to numerically find the optimal randomized strategy. In this paper, we study the value of randomization in mixed-integer DRO problems and show that it is bounded by the improvement achievable through its continuous relaxation. Furthermore, we identify conditions under which the bound is tight. We then develop algorithmic procedures, based on column generation, for solving both single- and two-stage linear DRO problems with randomization that can be used with both moment-based and Wasserstein ambiguity sets. Finally, we apply the proposed algorithm to solve three classical discrete DRO problems: the assignment problem, the uncapacitated facility location problem, and the capacitated facility location problem and report numerical results that show the quality of our bounds, the computational efficiency of the proposed solution method, and the magnitude of performance improvement achieved by randomized decisions. Summary of Contribution: In this paper, we present both theoretical results and algorithmic tools to identify optimal randomized strategies for discrete distributionally robust optimization (DRO) problems and evaluate the performance improvements that can be achieved when using them rather than classical deterministic strategies. On the theory side, we provide improvement bounds based on continuous relaxation and identify the conditions under which these bound are tight. On the algorithmic side, we propose a finitely convergent, two-layer, column-generation algorithm that iterates between identifying feasible solutions and finding extreme realizations of the uncertain parameter. The proposed algorithm was implemented to solve distributionally robust stochastic versions of three classical optimization problems and extensive numerical results are reported. The paper extends a previous, purely theoretical work of the first author on the idea of randomized strategies in nonconvex DRO problems by providing useful bounds and algorithms to solve this kind of problems.

An Efficient Multi-Objective Robust Optimization Method by Sequentially Searching From Nominal Pareto Solutions

2021 ◽  
Vol 21 (4) ◽  
Author(s):  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Time ◽  
Pareto Solutions ◽  
Worst Case ◽  
Multi Objective ◽  
Pareto Points ◽  
Single Objective

Abstract Multi-objective optimization problems (MOOPs) with uncertainties are common in engineering design. To find robust Pareto fronts, multi-objective robust optimization (MORO) methods with inner–outer optimization structures usually have high computational complexity, which is a critical issue. Generally, in design problems, robust Pareto solutions lie somewhere closer to nominal Pareto points compared with randomly initialized points. The searching process for robust solutions could be more efficient if starting from nominal Pareto points. We propose a new method sequentially approaching to the robust Pareto front (SARPF) from the nominal Pareto points where MOOPs with uncertainties are solved in two stages. The deterministic optimization problem and robustness metric optimization are solved in the first stage, where nominal Pareto solutions and the robust-most solutions are identified, respectively. In the second stage, a new single-objective robust optimization problem is formulated to find the robust Pareto solutions starting from the nominal Pareto points in the region between the nominal Pareto front and robust-most points. The proposed SARPF method can reduce a significant amount of computational time since the optimization process can be performed in parallel at each stage. Vertex estimation is also applied to approximate the worst-case uncertain parameter values, which can reduce computational efforts further. The global solvers, NSGA-II for multi-objective cases and genetic algorithm (GA) for single-objective cases, are used in corresponding optimization processes. Three examples with the comparison with results from the previous method are presented to demonstrate the applicability and efficiency of the proposed method.

scholarly journals Robust Optimization Model and Algorithm for Railway Freight Center Location Problem in Uncertain Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xing-cai Liu ◽  
Shi-wei He ◽  
Rui Song ◽  
Yang Sun ◽  
Hao-dong Li
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Location Problem ◽  
Clonal Selection ◽  
Expected Value ◽  
Clonal Selection Algorithm ◽  
Selection Algorithm ◽  
Railway Freight ◽  
Center Location ◽  
Robust Model

Railway freight center location problem is an important issue in railway freight transport programming. This paper focuses on the railway freight center location problem in uncertain environment. Seeing that the expected value model ignores the negative influence of disadvantageous scenarios, a robust optimization model was proposed. The robust optimization model takes expected cost and deviation value of the scenarios as the objective. A cloud adaptive clonal selection algorithm (C-ACSA) was presented. It combines adaptive clonal selection algorithm with Cloud Model which can improve the convergence rate. Design of the code and progress of the algorithm were proposed. Result of the example demonstrates the model and algorithm are effective. Compared with the expected value cases, the amount of disadvantageous scenarios in robust model reduces from 163 to 21, which prove the result of robust model is more reliable.

scholarly journals Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Sayuri Maldonado-Pinto ◽  
Martha-Selene Casas-Ramírez ◽  
José-Fernando Camacho-Vallejo
Keyword(s):  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Location Problem ◽  
Facility Location Problem ◽  
Computational Time ◽  
Benchmark Instances ◽  
Crossover Phase ◽  
Bilevel Problems ◽  
Feasible Solutions ◽  
The Impact

The problem addressed here is a combinatorial bilevel programming problem called the uncapacitated facility location problem with customer’s preferences. A hybrid algorithm is developed for solving a battery of benchmark instances. The algorithm hybridizes an evolutionary algorithm with path relinking; the latter procedure is added into the crossover phase for exploring the trajectory between both parents. The proposed algorithm outperforms the evolutionary algorithm already existing in the literature. Results show that including a more sophisticated procedure for improving the population through the generations accelerates the convergence of the algorithm. In order to support the latter statement, a reduction of around the half of the computational time is obtained by using the hybrid algorithm. Moreover, due to the nature of bilevel problems, if feasible solutions are desired, then the lower level must be solved for each change in the upper level’s current solution. A study for illustrating the impact in the algorithm’s performance when solving the lower level through three different exact or heuristic approaches is made.

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