In this paper, an optimization approach was presented for the flexural strength and stiffness design of reinforced concrete beams. Surrogate modeling based on machine learning was applied to predict the responses of the structural system in three-point flexure tests. Three design input variables, the area of steel bars in the compression zone, the area of steel bars in the tension zone, and the area of steel bars in the shear zone, were adopted for the dataset and arranged by the Box-Behnken design method. The dataset was composed of thirteen specimens of reinforced concrete beams. The specimens were tested under three-points flexure loading at the age of 28 days and both the failure load and the maximum deflection values were recorded. Compression and tension tests were conducted to obtain the concrete data for the analysis and numerical modeling. Afterward, finite element modeling was performed for all the specimens using the ATENA program to verify the experimental tests. Subsequently, the surrogate models for the flexural strength and the stiffness were constructed. Finally, optimization was conducted, supporting the factorial method for the predicted responses. The adopted approach proved to be an excellent tool to optimize the design of reinforced concrete beams for flexure and stiffness. In addition, experimental and numerical results were in very good agreement in terms of both the failure type and the cracking pattern.

In this paper, we studied the scheduling of  jobs on a single machine.  Each of n jobs is to be processed without interruption and becomes available for processing at time zero. The objective is to find a processing order of the jobs, minimizing the sum of maximum earliness and maximum tardiness. This problem is to minimize the earliness and tardiness values, so this model is equivalent to the just-in-time production system. Our lower bound depended on the decomposition of the problem into two subprograms. We presented a novel heuristic approach to find a near-optimal solution for the problem. This approach depends on finding efficient solutions for two problems. The first problem is minimizing total completion time and maximum tardiness. The second is minimizing total completion time and maximum earliness. We used these efficient solutions to find a near-optimal solution for another problem which is a sum of maximum earliness and maximum tardiness. This means we eliminate the total completion time from the two problems. The algorithm was tested on a set of problems of different n. Computational results demonstrate the efficiency of the proposed method.

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In this research paper, n jobs have to be scheduled on one-machine to minimize the sum of maximum earliness and maximum tardiness. We solved a series of bi-criteria scheduling problems that related to minimize the sum of the maximum earliness and tardiness. Three new algorithms were presented, two for hierarchical objective and one for the simultaneous objective. Using the results of these algorithms, we minimize the sum of maximum earliness and maximum tardiness. This objective considered as one of the NP-hard problem, and it is also irregular, so this objective missed some helpful properties of regularity. The proposed algorithms had simple structures, and simple to implement. Lastly, they tested for different n.

In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.

Multi-objective optimization also known as multi-objective programming is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. In such circumstance, we have to be discovered out compromise arrangement which is ideal for all the objectives in a few senses. In this paper, we transformed multi-objective linear plus linear fractional programming problems to single QPP and then solved by methods of QPP. Illustrative numerical examples are displayed for exhibit reason. We have explored an arrangement to the MOLPLFP issue based on a hypothesis already considered by Dinkelbach. He clearly delineated a calculation for fractional programming with nonlinear as well as linear terms within numerator and denominator.

The problem of scheduling n jobs on a single machine is considered, where the jobs are divided into two classes and a machine set up is necessary between jobs of different classes. Jobs i (i= 1,…, n) becomes available for processing at time zero, requires a positive processing time i P. Disjoint subsets N 1 and N 2 define the partition of jobs into two classes. If two jobs in the same class are sequenced in adjacent positions, then no set up time between these jobs in necessary. We address the bicriterion (multi objective) scheduling problem, the two criteria are the minimization of flow time ( N i i c) and the minimization maximum Tardiness (max T). We characterized the set of all efficient points and the optimal solution. A modified algorithm presented to find efficient solutions for the problem with set up times. A relation found between number of efficient solutions and range of 'tardiness of shortest processing time (SPT T), tardiness of early due date (EDD T)'. This algorithm treats with a case that the set up time in  SPT rule is in increasing order. A counter example presented to show that the algorithm will fail if the set up time in  SPT rule is in decreasing order. Our task is to present the decision makers with all possible solutions and let them make the final selection. The decision maker has two objectives in mind ( N i i c) , (max T) and some solutions (efficient), we will choose the best one from the efficient solutions depending on his experiences.