the markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. considering real world limits and conditions, the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. therefore, the use of meta-heuristic methods such as neural networks and evolutionar...

Despite existing various integer programming for sequencing problems, there is not enoughinformation about practical values of the models. This paper considers the problem of minimizing maximumlateness with release dates and presents four different mixed integer programming (MIP) models to solve thisproblem. These models have been formulated for the classical single machine problem, namely sequ...

The Vehicle Routing Problem (VRP), a famous problem of operation research, holds a central place in combinatorial optimization problems. In this problem, a fleet vehicles with Q capacity start to move from depot and return after servicing to customers in which visit only ones each customer and load more than its capacity not at all. The objective is to minimize the number of used vehicles and t...

We introduce strong formulations for robust mixed 0–1 programming with uncertain objective coefficients. We focus on a polytopic uncertainty set described by a “budget constraint” for allowed uncertainty in the objective coefficients. We show that for a robust 0–1 problem, there is an α–tight linear programming formulation with size polynomial in the size of an α–tight linear programming formul...

In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0-1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of ...

in this paper a new method is proposed for path planning of planar manipulators amid obstacles through mathematical programming in a way that the robot’s links avoid collision with obstacles throughout their motion from an initial to a goal configuration. after inputting the workspace geometry, the shortest feasible path for the robot’s end-effector is planned toward its goal position using gen...

Each of n items (products) is to be processed on two, capacity limited machines in order to satisfy known demands in each of T periods. Only one item can be processed on each machine at any given time and period. Each switch from one item to another requires sequence dependent setup time. The object is to minimize the sum of the costs of production, storage and setup. We define a quadratic mixe...

This paper surveys complexity and approximability results for the Maximum Solution (Max Sol) problem. Max Sol is an optimisation variant of the constraint satisfaction problem. Many important and well-known combinatorial optimisation problems are instances of Max Sol: for example, Max Sol restricted to the domain {0, 1} is exactly the Max Ones problem (which, in turn, captures problems such as ...