The capacitated arc routing problem (CARP) is one of the most important routing problems with many applications in real world situations. In some real applications such as urban waste collection and etc., decision makers have to consider more than one objective and investigate the problem under uncertain situations where required edges have demand for more than one type of commodity. So, in thi...

Hubs are facilities to collect arrange and distribute commodities in telecommunication networks, cargo delivery systems, etc. In this paper, an uncapacitated phub center problem in case of single allocation and also multiple allocation will be introduced in which travel times or transportation costs are considered as fuzzy parameters. Then, by proposing new methods, the presented problem is con...

Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play significant role in mechanical civil engineering design. The concept direct methods aims to determine the ultimate load carrying capacity structures beyond elastic range. In practical problems, lead nonlinear convex optimization problems with large number variables constraints. If strengt...

This paper is concerned with chance constrained programming to deal with nonlinear optimization problems with random parameters. Specific Monte Carlo methods to evaluate the gradient and Hessian of probabilistic constraints are proposed and discussed. These methods are implemented in penalization optimization routines adapted to stochastic optimization. They are shown to reduce the computationa...

This paper presents a multi-objective fuzzy chance constrained capacitated transportation problem based on fuzzy goal programming problem with capacity restrictions on commodities which are shipped from different sources to different destinations. The capacity of each origin and the demand of each destination are considered random in nature with fuzzy normal stochastic parameters following norm...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (FMDVRP-SPD) is investigated. The FMDVRP-SPD is the problem of allocating customers to several depots, so that the optimal set of routes is determined simultaneously to serve the pickup and the delivery demands of each customer within scattered depots. In the problem, both pickup and delivery dema...