Robust optimization
Mohamad Ali Movafaghpour
Abstract
Purpose: In many real-world optimization problems, we are facing uncertainties in parameters describing the problem. In general, as a simplifying assumption, uncertainty is ignored. In the school bus routing problem, there are uncertain parameters that are assumed to have deterministic values. As a result ...
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Purpose: In many real-world optimization problems, we are facing uncertainties in parameters describing the problem. In general, as a simplifying assumption, uncertainty is ignored. In the school bus routing problem, there are uncertain parameters that are assumed to have deterministic values. As a result of this simplifying assumption, the obtained solutions may be mismatched with the real world. This issue arose by violating some hard constraints.Methodology: In this research, a mixed linear integer programming for school bus routing with mixed loading by using a heterogeneous fleet is presented. The uncertainty of travel times is modeled as interval numbers. We propose a heuristic algorithm to generate extreme scenarios. Each scenario is generated in order to make the last found optimal solution into an infeasible one as much as possible.Findings: Experimental results show that deploying this novel algorithm for generating extreme scenarios, efficiently produces diverse scenarios. After the scenario generation algorithm is converged, the intersection of the feasible optimal solutions under diverse scenarios is extracted as robust sub-tours or robust trips.Originality/Value: It is the first time to apply the notions of robust optimization using the extreme scenarios generation scheme. At each iteration of the extreme scenario’s generation, the most conflicting scenario against a given optimum solution is generated. The main advantage of this method over other present robust optimization methods is its emphasis on maintaining the feasibility of the optimal solution when dealing with the most diverse set of uncertainty scenarios while keeping the computational effort needed as low as desired.
Robust optimization
Shima Roosta; Seyed Milad Mirnajafi Zadeh; Hamid Bazargan Harandi
Abstract
Purpose: Location-Routing Problem (LRP) is a strategic supply chain design problem aimed at meeting customer demands. LRPs involve selecting one or more depot sites from a set of potential locations and determining the best routes to connect them to demand points. With the rising awareness about the ...
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Purpose: Location-Routing Problem (LRP) is a strategic supply chain design problem aimed at meeting customer demands. LRPs involve selecting one or more depot sites from a set of potential locations and determining the best routes to connect them to demand points. With the rising awareness about the environmental impacts of transportation over the past years, using green logistics to mitigate these impacts has become increasingly important.Methodology: To compensative a gap in the literature, this paper presents a robust bi-objective Mixed-Integer Linear Programming (MILP) model for the Green Capacitated Location-Routing Problem (G-CLRP) with demand uncertainty and the possibility of failure in depots and routes.Findings: The final result of this robust multi-objective model is to set up the depots and select the routes that offer the highest reliability (maximizing network service) while imposing the lowest cost and environmental pollution. The paper also provides a numerical analysis and a sensitivity analysis of the solutions of the model.Originality/Value: Determining backup depots and increasing network serviceability for LRPs.
Robust optimization
Amin Ghaseminejad; Mohammad Fallah; Hamed Kazemipoor
Abstract
Purpose: The present paper deals with modeling and solving a multi-objective problem of robust facility layout problem under uncertainty with NSGA-II, MOPSO and MOGWO algorithms. Since the problem of facility layout is NP-Hard, the need to use meta-algorithms by providing a suitable chromosome to achieve ...
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Purpose: The present paper deals with modeling and solving a multi-objective problem of robust facility layout problem under uncertainty with NSGA-II, MOPSO and MOGWO algorithms. Since the problem of facility layout is NP-Hard, the need to use meta-algorithms by providing a suitable chromosome to achieve near-optimal solutions has been investigated in this article. The issue under consideration in this article includes several departments that are based on 5 different aspects (minimizing the flow time between departments, maximizing the number of equipment and facilities, minimizing the distance traveled to access firefighting equipment, minimizing the distance to access optimal climatic conditions and maximization of noisy departments from each other) should be arranged in different parts of the hall. In order to achieve the above objective functions at the same time, assigning departments to each section, equipping each section with different equipments and arranging the departments together are among the main objectives of the article.Methodology: In this paper, GA, PSO and GWO single-objective meta-heuristic algorithms and NSGA-II, MOPSO and MOGWO multi-objective meta-heuristic algorithms have been used to solve the problem.Findings: Computational results show that GA, PSO and GWO single-objective algorithms have high efficiency in achieving the optimal value of the objective function in a much shorter time, and their multi-objective methods show the high efficiency of the NSGA-II algorithm in achieving the average value of the objective function. First, second and fifth; the MOPSO algorithm has the highest expansion and metric distance in achieving the average number of efficient answers and computational time, and finally the MOGWO algorithm in obtaining the average value of the third and fourth objective functions. Statistical comparisons also showed a significant difference between the means of computational time. To evaluate and rank the algorithms, the TOPSIS method is used and the results show the high efficiency of the MOGWO algorithm in solving the model.Originality/Value: In this paper, a new model of the multi-objective robust facility layout problem under uncertainty conditions is modeled with respect to health and environmental safety aspects.
Robust optimization
Fahimeh Baroughi; Soudabeh Seyyedi Ghomi
Abstract
In this paper the robust path centdian problem is investigated on tree networks with the same interval vertex weights for the both path center and path median problems. The used objective function in this paper is the simple sum of path median and path center problems. In the past research works the ...
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In this paper the robust path centdian problem is investigated on tree networks with the same interval vertex weights for the both path center and path median problems. The used objective function in this paper is the simple sum of path median and path center problems. In the past research works the vertex weights for the both path median and path center location problems are disjoint. The used approach to compute the robust solution is the minmax regret criterion. In this method for any selected path on the tree, the maximum value of regret is minimized for all possible events of vertex weights. Using the minmax regret criterion, an algorithm with O(n^5) time complexity is presented to obtain a robust solution of the robust path centdian problem on tree networks. In this paper using the worst case scenarios for the path median and path center we obtain the worst case scenarios of robust centdian problem. Then we obtain a robust solution for this problem.
Robust optimization
Masomeh Hoseinpour; Alireza Fakharzadeh Jahromi
Abstract
In recent decades, the theory of robust optimization has been introduced as a powerful tool for optimizing uncertain processes. Regarding the Uncertainty of the glycemic load of consumed food, the main purpose of this article is to provide an optimal Iranian diet using a robust optimization to adjust ...
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In recent decades, the theory of robust optimization has been introduced as a powerful tool for optimizing uncertain processes. Regarding the Uncertainty of the glycemic load of consumed food, the main purpose of this article is to provide an optimal Iranian diet using a robust optimization to adjust the glycemic load in patients with type 2 diabetes. Diabetes type 2 is a devastating disease, in addition to cardiovascular disease, infectious and kidney diseases, causes insulin resistance and cancer and drugs of cholesterol-lowering have an increased risk of cardiovascular complications and incidence of cancer. Indeed, adjustment of nutrition is important to prevent and control or reduce the complications of diabetes. In this paper, due to the uncertainty of the glycemic load of foods, with collecting necessary nutritional information, the Iranian diet model is determined and analyzed by a robust optimization method. According to this, 75 cases of food (42 Iranian food, 10 Foodstuffs for breakfast, 20 types of fruits and fruit juices and 3 types of dairy products) have been studied locally. The benefits of this model are the ability to adapt according to the person's tastes and opinion of the nutritionist with minimizing changes for the current diet of the individual.