stochastic approach to vehicle routing problem: development and theories abstract in this article, a chance constrained (ccp) formulation of the vehicle routing problem (vrp) is proposed. the reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. knowing that reliable computer software for lar...

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software...

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and sto...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

This paper proposes a general framework for integrating a constraint logic programming system with a stochastic constraint solver to solve constraint satisfaction problems eeciently. Stochastic solvers can solve hard constraint satisfaction problems very eeciently, and constraint logic programming allows heuristics and problem breakdown to be encoded in the same language as the constraints. Hen...

This paper deals with day-ahead programming under uncertainties in microgrids (MGs). A two-stage stochastic programming with the fixed recourse approach was adopted. The studied MG was considered in the grid-connected mode with the capability of power exchange with the upstream network. Uncertain electricity market prices, unpredictable load demand, and uncertain wind and solar power values, du...

This paper proposes a number of models for integrating stochastic constraint solvers into constraint logic programming systems in order to solve constraint satisfaction problems eeciently. Stochastic solvers can solve hard constraint satisfaction problems very eeciently, and constraint logic programming allows heuristics and problem breakdown to be encoded in the same language as the constraint...