Making Robust Decisions in Discrete Optimization Problems as a Game against Nature

In this paper a discrete optimization problem under uncertainty is discussed. Solving such a problem can be seen as a game against nature. In order to choose a solution, the minmax and minmax regret criteria can be applied. In this paper an extension of the known minmax (regret) approach is proposed. It is shown how different types of uncertainty can be simultaneously taken into account. Some exact and approximation algorithms for choosing a best solution are constructed.Discrete optimization, minmax, minmax regret, game against nature

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto's front which is a set of scenarios that are helpful for guiding the decision's maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization

Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance