Improved two-phase solution strategy for multiobjective fuzzy stochastic linear programming problems with uncertain probability distribution

Multiobjective Fuzzy Stochastic Linear Programming (MFSLP) problem where the linear inequalities on the probability are fuzzy is called a Multiobjective Fuzzy Stochastic Linear Programming problem with Fuzzy Linear Partial Information on Probability Distribution (MFSLPPFI). The uncertainty presents unique difficulties in constrained optimization problems owing to the presence of conflicting goals and randomness surrounding the data. Most existing solution techniques for MFSLPPFI problems rely heavily on the expectation optimization model, the variance minimization model, the probability maximization model, pessimistic/optimistic values and compromise solution under partial uncertainty of random parameters. Although these approaches recognize the fact that the interval values for probability distribution have important significance, nevertheless they are restricted by the upper and lower limitations of probability distribution and neglected the interior values. This limitation motivated us to search for more efficient strategies for MFSLPPFI which address both the fuzziness of the probability distributions, and the fuzziness and randomness of the parameters. The proposed strategy consists two phases: fuzzy transformation and stochastic transformation. First, ranking function is used to transform the MFSLPPFI to Multiobjective Stochastic Linear Programming Problem with Fuzzy Linear Partial Information on Probability Distribution (MSLPPFI). The problem is then transformed to its corresponding Multiobjective Linear Programming (MLP) problem by using a-cut technique of uncertain probability distribution and linguistic hedges. In addition, Chance Constraint Programming (CCP), and expectation of random coefficients are applied to the constraints and the objectives respectively. Finally, the MLP problem is converted to a single-objective Linear Programming (LP) problem via an Adaptive Arithmetic Average Method (AAAM), and then solved by using simplex method. The algorithm used to obtain the solution requires fewer iterations and faster generation of results compared to existing solutions. Three realistic examples are tested which show that the approach used in this study is efficient in solving the MFSLPPFI

Multi-criteria reliability optimization for a complex system with a bridge structure in a fuzzy environment : A fuzzy multi-criteria genetic algorithm approach

Abstract: Optimizing system reliability in a fuzzy environment is complex due to the presence of imprecise multiple decision criteria such as maximizing system reliability and minimizing system cost. This calls for multi-criteria decision making approaches that incorporate fuzzy set theory concepts and heuristic methods. This paper presents a fuzzy multi-criteria nonlinear model, and proposes a fuzzy multi-criteria genetic algorithm (FMGA) for complex bridge system reliability design in a fuzzy environment. The algorithm uses fuzzy multi-criteria evaluation techniques to handle fuzzy goals, preferences, and constraints. The evaluation approach incorporates fuzzy preferences and expert choices of the decision maker in regards to cost and reliability goals. Fuzzy evaluation gives the algorithm flexibility and adaptability, yielding near-optimal solutions within short computation times. Results from computational experiments based on benchmark problems demonstrate that the FMGA approach is a more reliable and effective approach than best known algorithm, especially in a fuzzy multi-criteria environment

System reliability optimization : a fuzzy genetic algorithm approach

System reliability optimization is often faced with imprecise and conflicting goals such as reducing the cost of the system and improving the reliability of the system. The decision making process becomes fuzzy and multi-objective. In this paper, we formulate the problem as a fuzzy multi-objective nonlinear program (FMOOP). A fuzzy multiobjective genetic algorithm approach (FMGA) is proposed for solving the multi-objective decision problem in order to handle the fuzzy goals and constraints. The approach is able flexible and adaptable, allowing for intermediate solutions, leading to high quality solutions. Thus, the approach incorporates the preferences of the decision maker concerning the cost and reliability goals through the use of fuzzy numbers. The utility of the approach is demonstrated on benchmark problems in the literature. Computational results show that the FMGA approach is promising

A multi-objective optimisation approach applied to offshore wind farm location selection

This paper compares the three state-of-the-art algorithms when applied to a real-world case of the wind energy sector. Optimum locations are suggested for a wind farm by considering only Round 3 zones around the UK. The problem comprises of some of the most important techno-economic life cycle cost-related factors, which are modelled using the physical aspects of each wind farm location (i.e., the wind speed, distance from the ports, and water depth), the wind turbine size, and the number of turbines. The model is linked to NSGA II, NSGA III, and SPEA 2 algorithms, to conduct an optimisation search. The performance of these three algorithms is demonstrated and analysed, so as to assess their effectiveness in the investment decision-making process in the wind sector, more importantly, for Round 3 zones. The results are subject to the specifics of the underlying life cycle cost model

Satisficing solutions for multiobjective stochastic linear programming problems

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out.Decision Science

Developing collaborative planning support tools for optimised farming in Western Australia

Land-use (farm) planning is a highly complex and dynamic process. A land-use plan can be optimal at one point in time, but its currency can change quickly due to the dynamic nature of the variables driving the land-use decision-making process. These include external drivers such as weather and produce markets, that also interact with the biophysical interactions and management activities of crop production.The active environment of an annual farm planning process can be envisioned as being cone-like. At the beginning of the sowing year, the number of options open to the manager is huge, although uncertainty is high due to the inability to foresee future weather and market conditions. As the production year reveals itself, the uncertainties around weather and markets become more certain, as does the impact of weather and management activities on future production levels. This restricts the number of alternative management options available to the farm manager. Moreover, every decision made, such as crop type sown in a paddock, will constrains the range of management activities possible in that paddock for the rest of the growing season.This research has developed a prototype Land-use Decision Support System (LUDSS) to aid farm managers in their tactical farm management decision making. The prototype applies an innovative approach that mimics the way in which a farm manager and/or consultant would search for optimal solutions at a whole-farm level. This model captured the range of possible management activities available to the manager and the impact that both external (to the farm) and internal drivers have on crop production and the environment. It also captured the risk and uncertainty found in the decision space.The developed prototype is based on a Multiple Objective Decision-making (MODM) - á Posteriori approach incorporating an Exhaustive Search method. The objective set used for the model is: maximising profit and minimising environmental impact. Pareto optimisation theory was chosen as the method to select the optimal solution and a Monte Carlo simulator is integrated into the prototype to incorporate the dynamic nature of the farm decision making process. The prototype has a user-friendly front and back end to allow farmers to input data, drive the application and extract information easily

Advances in Methodology and Applications of Decision Support Systems

These Proceedings are composed of a selection of papers of the Workshop on Advances in Methodology and Applications of Decision Support Systems, organized by the System and Decision Sciences (SDS) Program of IIASA and the Japan Institute of Systems Research (JISR). The workshop was held at IIASA on August 20-22, 1990. The Methodology of Decision Analysis (MDA) Project of the SDS Program focuses on a system-analytical approach to decision support and is devoted to developing methodology, software and applications of decision support systems concentrated primarily around interactive systems for data analysis, interpretation and multiobjective decisionmaking, including uncertainty analysis and group decision making situations in both their cooperative and noncooperative aspects. The objectives of the research on decision support systems (DSS) performed in cooperation with the MDA Project are to: compare various approaches to decision support systems; advance theory and methodology of decision support; convert existing theories and methodologies into usable (simple to use, user-friendly and robust) tools that could easily be used in solving real-life problems. A principal characteristic of decision support systems is that they must be tuned to specific decision situations, to complex real-life characteristics of every application. Even if the theory and methodology of decision support is quite advanced, every application might provide impulses for further theoretical and methodological advances. Therefore the principle underlying this project is that theoretical and methodological research should be strongly connected to the implementation and applications of its results to sufficiently complicated, real-life examples. This approach results in obtaining really applicable working tools for decision support. The papers for this Proceedings have been selected according to the above summarized framework of the research activities. Therefore, the papers deal both with theoretical and methodological problems and with real-life applications

Evolutionary algorithms with average crossover and power heuristics for aquaculture diet formulation

The aquaculture farming industry is one of the most important industries in Malaysia since it generates income to economic growth and produces main source of food for the nation. One of the pillars in aquaculture farming industries is formulation of food for the animal, which is also known as feed mix or diet formulation. However, the feed component in the aquaculture industry incurs the most expensive operational cost, and has drawn many studies regarding diet formulation. The lack of studies involving modelling approaches had motivated to embark on diet formulation, which searches for the best combination of feed ingredients while satisfying nutritional requirements at a minimum cost. Hence, this thesis investigates a potential approach of Evolutionary Algorithm (EA) to propose a diet formulation solution for aquaculture farming, specifically the shrimp. In order to obtain a good combination of ingredients in the feed, a filtering heuristics known as Power Heuristics was introduced in the initialization stage of the EA methodology. This methodology was capableof filtering certain unwanted ingredients which could lead to potential poor solutions. The success of the proposed EA also relies on a new selection and crossover operators that have improved the overall performance of the solutions. Hence, three main EA model variants were constructed with new initialization mechanism, diverse selection and crossover operators, whereby the proposed EAPH-RWS-Avg Model emerged as the most effective in producing a good solution with the minimum penalty value. The newly proposed model is efficient and able to adapt to changes in the parameters, thus assists relevant users in managing the shrimp diet formulation issues, especially using local ingredients. Moreover, this diet formulation strategy provides user preference elements to choose from a range of preferred ingredients and the preferred total ingredient weights