Machine scheduling problems (MSP) are     considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as  are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutio

The presented study investigated the scheduling regarding  jobs on a single machine. Each  job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness  which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions  is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two

In this paper, the problem of scheduling jobs on one machine for a variety multicriteria
are considered to minimize total completion time and maximum late work. A set of n
independent jobs has to be scheduled on a single machine that is continuously available from
time zero onwards and that can handle no more than one job at a time. Job i,(i=1,…,n)
requires processing during a given positive uninterrupted time pi, and its due date d
i.
For the bicriteria problems, some algorithms are proposed to find efficient (Pareto)
solutions for simultaneous case. Also for the multicriteria problem we proposed general
algorithms which gives efficient solutions within the efficient range

     In this paper, the bi-criteria machine scheduling problems (BMSP) are solved, where the discussed problem is represented by the sum of completion and the sum of late work times  simultaneously. In order to solve the suggested BMSP, some metaheurisitc methods are suggested which produce good results. The suggested local search methods are simulated annulling and bees algorithm. The results of the new metaheurisitc methods are compared with the complete enumeration method, which is considered an exact method, then compared results of the heuristics with each other to obtain the most efficient method.

In this paper we investigate the use of two types of local search methods (LSM), the Simulated Annealing (SA) and Particle Swarm Optimization (PSO), to solve the problems ( ) and . The results of the two LSMs are compared with the Branch and Bound method and good heuristic methods. This work shows the good performance of SA and PSO compared with the exact and heuristic methods in terms of best solutions and CPU time.

In this paper, the main work is to minimize a function of three cost criteria for scheduling n jobs on a single machine. We proposed algorithms to solve the single machine scheduling multiobjective problem. In this problem, we consider minimizing the total completion times, total tardiness and maximum tardiness criteria. First a branch and bound (BAB) algorithm is applied for the 1//∑Ci+∑Ti+Tmax problem. Second we compare two multiobjective algorithms one of them based on (BAB) algorithm to find the set of efficient (non dominated) solutions for the 1//(∑Ci ,∑Ti ,Tmax) problem. The computational results show that the algorithm based on (BAB) algorithm is better than the other one for generated the total number of

This paper proposes a new algorithm (F2SE) and algorithm (Alg(n – 1)) for solving the
two-machine flow shop problem with the objective of minimizing total earliness. This
complexity result leads us to use an enumeration solution approach for the algorithm (F2SE)
and (DM) is more effective than algorithm Alg( n – 1) to obtain approximate solution.

Scheduling problems have been treated as single criterion problems until recently. Many of these problems are computationally hard to solve three as single criterion problems. However, there is a need to consider multiple criteria in a real life scheduling problem in general. In this paper, we study the problem of scheduling jobs on a single machine to minimize total tardiness subject to maximum earliness or tardiness for each job. And we give algorithm (ETST) to solve the first problem (p1) and algorithm (TEST) to solve the second problem (p2) to find an efficient solution.  

Human beings are greatly inspired by nature. Nature has the ability to solve very complex problems in its own distinctive way. The problems around us are becoming more and more complex in the real time and at the same instance our mother nature is guiding us to solve these natural problems. Nature gives some of the logical and effective ways to find solutions to these problems. Nature acts as an optimized source for solving the complex problems.  Decomposition is a basic strategy in traditional multi-objective optimization. However, it has not yet been widely used in multi-objective evolutionary optimization.   

Although computational strategies for taking care of Multi-objective Optimization Problems (MOPs) h