Stochastic Approach versus Multiobjective Approach for Obtaining Efficient Solutions in Stochastic Multiobjective Programming Problems

In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions, which involves transforming the multiobjective problem into a problem with only one objective function. Our aim is to determine whether the order in which these two transformations are carried out influences, in any way, the efficient solution obtained. Our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem, the order can have an influence on the final set of efficient solutions obtained for a given problem.Stochastic Multiobjective Programming, Efficiency, Stochastic Approach, Multiobjective Approach.

The capacitated vehicle routing problem with soft time windows and stochastic travel times

A full multiobjective approach is employed in this paper to deal with a stochastic multiobjective capacitated vehicle routing problem (CVRP). In this version of the problem, the demand is considered to be deterministic, but the travel times are assumed to be stochastic. A soft time window is tied to every customer and there is a penalty for starting the service outside the time window. Two objectives are minimized, the total length and the time window penalty. The suggested solution method includes a non-dominated sorting genetic algorithm (NSGA) together with a variable neighborhood search (VNS) heuristic. It was tested on instances from the literature and compared to a previous solution approach. The suggested method is able to find solutions that dominate some of the previously best known stochastic multiobjective CVRP solutions

A risk-aversion approach for the Multiobjective Stochastic Programming problem

Multiobjective stochastic programming is a field well located to tackle problems arising in emergencies, given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this work, especially designed for risk-aversion solutions. A linear programming model is presented to obtain such solution.Comment: 29 pages, 3 figures, 17 table

Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems

In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions, which involves transforming the multiobjective problem into a problem with only one objective function. Our aim is to determine whether the order in which these two transformations are carried out influences, in any way, the efficient solution obtained. Our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem, the order can have an influence on the final set of efficient solutions obtained for a given problem

Mathematical programming with uncertainty and multiple objectives for sustainable development and wildfire management

Mathematical Programming is a field of Operations Research well located for tackling problems as diverse as those arising in Logistics and Disaster Management. The main objective of Mathematical Programming is the selection of an optimal alternative satisfying a series of constraints. Traditionally alternatives are usually judged by a single criterion (for example, minimizing cost); however, it is also common that multiple objectives have to be considered simultaneously, leading to Multicriteria Decision Making. When the conditions to be satisfied by an alternative, or the evaluation of that alternative relies on random or unknown factors, there is a context of Optimization under uncertainty. The first chapters of this thesis study the field of Multicriteria Decision Making and Optimization under uncertainty, in two application in the context of sustainable development and disaster management. Optimization with uncertainty is presented with an application to rural electrification. It is common, especially in rural areas, that the access to electricity is provided via solar systems installed on the homes of the users. These systems have to be repaired when they malfunction. Consequently, the decision of how to size and locate a maintenance network is affected by uncertainty. A mathematical programming model is developed, treating the uncertainty in a non-explicit way, whose goal is to obtain a maintenance network at minimum cost. Such model is then used as a tool for obtaining more straightforward rules that are able to predict maintenance cost using limited information. The model is validated using information from a real program implemented in Morocco. When studying Multicriteria Decision Making a problem in wildfire management is considered. To mitigate the effect of wildfires, it is common the modification of forest, with what is known as fuel management. This technique, consisting in the felling or controlled burns of vegetation in selected areas, results on more manageable fires when they inevitably occur. Unfortunately, modifying flora can affect existing fauna, and thus it is sensible to search for solutions that improve the landscape wildfire-related, without substantial damage to existing species. That is, there are multiple criteria to take into account when optimizing. A mathematical programming model is developed, suggesting which areas to burn and when, taking into account the conflicting criteria. This model is applied to a series of realistic simulated cases. After that, a theoretical study of the field of Multiobjective Stochastic Programming (MSP) is performed, in which problems which simultaneously have multiple criteria and uncertainty are considered. In that chapter, a new concept of solution for MSP problems with risk-aversion is developed, its properties are studied, and a linear programming model is formulated for obtaining such a solution. A computational study of the model is also performed, applying it to a variant of the well-known knapsack problem. Finally, prescribed burning is studied again, considering this time the existing uncertainty due to not knowing how many prescribed burns can be completed within a year, caused by the limited time-window in which prescribed burns can be performed. The problem is solved using the risk-averse multiobjective stochastic methodology developed in the previous chapter. Lastly, the resulting model is applied to a real case located in the south of Spain