An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

Abstract

We focus on multiobjective nonlinear integer programming problems with block-angular structures which are often seen as a mathematical model of large-scale discrete systems optimization. By considering the vague nature of the decision maker's judgments, fuzzy goals of the decision maker are introduced, and the problem is interpreted as maximizing an overall degree of satisfaction with the multiple fuzzy goals. For deriving a satisficing solution for the decision maker, we develop an interactive fuzzy satisficing method. Realizing the block-angular structures that can be exploited in solving problems, we also propose genetic algorithms with decomposition procedures. Illustrative numerical examples are provided to demonstrate the feasibility and efficiency of the proposed method.

Different optimisation tasks used in water quality management

“…As with the task with the cost function, task (5,6,7) can be comprised of a number of constraints (6) for the concentrations calculated in many cross sections. Maximisation of the sum of the coefficients of levels of the pollution reduction tends to lower the treatment efficiency, thereby lowering treatment costs and all other costs incurred while reducing pollution loads discharged to water.…”

“…In the case of multiobjective tasks, the extreme points are sought in a number of functions while satisfying the properly set constraints. There are many methods used for solving optimisation tasks; they have been described in detail in publications such as: [5][6][7][8][9].…”

An Algorithmic Framework for Multiobjective Optimization

“…These approaches solve MO problems by simplifying the original problem into neighbouring subproblems. Among notable techniques which involve decomposition formulations are the MO evolutionary algorithm based on decomposition (MOEA/D) [ 10 ] and genetic algorithm with decomposition procedures [ 11 ].…”