Interactive fuzzy stochastic multi-level 0–1 programming using tabu search and probability maximization

• Cooperative multi-level 0–1 programming problems involving random variable coefficients are considered.
• New optimization criterion is constructed using tabu search and probability maximization.
• An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.

In this paper, we consider interactive fuzzy programming for multi-level 0–1 programming problems involving random variable coefficients both in objective functions and constraints. Following the probability maximization model together with the concept of chance constraints, the formulated stochastic multi-level 0–1 programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating satisfactory levels of the decision makers with considerations of overall satisfactory balance among all levels. For solving the transformed deterministic problems efficiently, we also introduce novel tabu search for general 0–1 programming problems. A numerical example for a three-level 0–1 programming problem is provided to illustrate the proposed method.