An Interactive Fuzzy Satisficing Method for Fuzzy Random Multiobjective 0-1 Programming Problems through Probability Maximization Using Possibility

In this paper, we focus on multiobjective 0-1 programming problems under the situation where stochastic uncertainty and vagueness exist at the same time. We formulate them as fuzzy random multiobjective 0-1 programming problems where coefficients of objective functions are fuzzy random variables. For the formulated problem, we propose an interactive fuzzy satisficing method through probability maximization using of possibility

Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

This paper considers stochastic two-level linear programming problems. Using the concept of chance constraints and probability maximization, original problems are transformed into deterministic ones. An interactive fuzzy programming method is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance

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

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

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

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

A simheuristic algorithm for solving an integrated resource allocation and scheduling problem

Modern companies have to face challenging configuration issues in their manufacturing chains. One of these challenges is related to the integrated allocation and scheduling of resources such as machines, workers, energy, etc. These integrated optimization problems are difficult to solve, but they can be even more challenging when real-life uncertainty is considered. In this paper, we study an integrated allocation and scheduling optimization problem with stochastic processing times. A simheuristic algorithm is proposed in order to effectively solve this integrated and stochastic problem. Our approach relies on the hybridization of simulation with a metaheuristic to deal with the stochastic version of the allocation-scheduling problem. A series of numerical experiments contribute to illustrate the efficiency of our methodology as well as their potential applications in real-life enterprise settings

A two-phase procedure for a multi-objective programming problem with fuzzy coefficients based on group decision making for project selection

Regional Development Agencies (RDAs) play a major role in ensuring sustainability and reducing inter-regional and intra-regional development disparities in line with the principles and policies set in the National Development Plan and Programs. This is done by enhancing cooperation among the public and private sectors, as well as non-governmental organizations. To achieve these targets, RDAs use certain tools such as financial support programs, technical support programs, and the like. Accordingly, an effective evaluation mechanism is crucial in selecting projects that have more added value and higher multiplier effects. In this regard, determining the right parameters that assist in choosing the best projects should be clearly demonstrated. In this study, the selection of projects according to the evaluating criteria of support mechanisms considered by RDAs are discussed through the procedure provided by a practical solution methodology, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP). Later, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems

Advancing Model Diagnostics To Support Hydrologic Prediction And Water Resources Planning Under Uncertainty

Computational models are essential tools for prediction and planning in water resources systems to ensure human water security and environmental health. Water systems models merely approximate the processes by which water moves through natural and built environments; their value depends on assumptions regarding climate, demand, land use, and other uncertain factors that may influence decision making. Numerical techniques to explore the role of these uncertain factors, known as diagnostic methods, can highlight opportunities to improve the accuracy of prediction as well as identify influential uncertainties to inform additional research and policy. This dissertation advances diagnostic methods for water resources models to identify (1) time-varying dominant processes driving modeled hydrologic predictions in flood forecasting, and (2) tradeoffs and vulnerabilities to changing climate and demands in regional urban water supply systems planning for drought. This work proposes diagnostic methods as a key element of a posteriori decision support, in which decision alternatives and vulnerable scenarios are identified following computational modeling and data analysis. Consistent with this theme, this work follows a multi-objective approach in which stakeholders can analyze tradeoffs between conflicting objectives as part of an iterative constructive learning process. For a spatially distributed flood forecasting model, results show that dominant uncertainties vary in space and time, and can inform model-based scientific inference as well as decision making. Similarly, the results of the urban water supply study indicate that sensitivity analysis can suggest costeffective paths to mitigate vulnerability to deeply uncertain future scenarios, for which likelihoods remain unknown or disputed. The multi-objective approach allows stakeholders to explore tradeoffs in their modeled robustness to inform intra-regional policies such as transfer contracts and shared infrastructure investments. Bridging the areas of hydrology and water systems planning is increasingly valuable, as hydrologic modelers begin to incorporate anthropogenic influences on the water cycle, and water systems planners begin to explore uncertainty in hydrologic process representation. In summary, this work develops diagnostic methods to identify time-varying dominant processes in distributed flood forecasting as well as tradeoffs and vulnerabilities under change in regional urban water supply, ultimately seeking to improve model-based planning for extreme floods and droughts in water resources systems