When we try to implement a multi-objective genetic algorithm (MOGA) with variable weights for finding a set of Pareto optimal solutions, one difficulty lies in determining appropriate search directions for genetic search. In our MOGA, a weight value for each objective in a scalar fitness function was randomly specified. Based on the fitness function with the randomly specified weight values, a ...

fuzzy relation inequalities based on max-f composition are discussed, where f is a binary aggregation on [0,1]. for a fixed fuzzy relation inequalities system $ a circ^{f}textbf{x}leqtextbf{b}$, we characterize all matrices $ a^{'} $ for which the solution set of the system $ a^{' } circ^{f}textbf{x}leqtextbf{b}$ is the same as the original solution set. similarly, for a fixed matrix ...

In this paper we propose multi-objective variable elimination (MOVE), an efficient solution method for multi-objective collaborative graphical games (MO-CoGGs), that exploits loose couplings. MOVE computes the convex coverage set, which can be much smaller than the Pareto front. In an empirical study, we show that MOVE can tackle multi-objective problems much faster than methods that do not exp...

in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.

Real life problems involve seldom only one criterion, but multiple criteria should be optimised at the same time. The criteria can even be conflicting each other, so the classical techniques used in single criteria optimization cannot be simply reused. Many ideas have been presented in the literature for addressing multiple criteria optimization problems; one of the ideas is to provide the so-c...

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk-averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto-optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk-neutral case. We then develop coordinating contracts in thr...

We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near-pareto-optimal solutions to bi-criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density fun...

This chapter reviews methods for the assessment and comparison of Pareto set approximations. Existing set quality measures from the literature are critically evaluated based on a number of orthogonal criteria, including invariance to scaling, monotonicity and computational effort. Statistical aspects of quality assessment are also considered in the chapter. Three main methods for the statistica...