Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to...

This paper presents an adaptive PSO algorithm whose numerical parameters can be updated following a scheduled protocol respecting some known criteria of convergence in order to enhance the chances to reach the global optimum of a hard combinatorial optimization problem, such those encountered in global optimization problems of composite laminates. Some examples concerning hard design problems a...

This paper presented a mixed integer programming for integrated scheduling and process planning. The presented process plan included some orders with precedence relations similar to Multiple Traveling Salesman Problem (MTSP), which was categorized as an NP-hard problem. These types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...

Reliability optimization problem has a wide application in engineering area. One of the most important problems in reliability is redundancy allocation problem (RAP). In this research, we worked on a RAP with repairable components and k-out-of-n sub-systems structure. The objective function was to maximize system reliability under cost and weight constraints. The aim was determining optimal com...

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called extremal optimization (EO), is compared with simulated annealing (SA) in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult...

the capacitated vehicle routing problem (cvrp) is a well-known combinatorial optimization problem that holds a central place in logistics management. the vehicle routing is an applied task in the industrial transportation for which an optimal solution will lead us to better services, save more time and ultimately increase in customer satisfaction. this problem is classified into np-hard problem...

Most interesting real-world optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a near-optimal solution to a large-scale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization prob...

Travelling Salesman Problem is an intensively studied problem in the field of Combinatorial Optimization. Being an NP-Hard problem it is widely studied in the area of optimization. A problem is NP-Hard if its approximate solution is derived from the solution of NP problem, i.e. an algorithm that is used to solve NP problem can be modified to find the approximate solution to NP-hard problem.The ...