multi-objective

This paper presents a multi-objective mathematical model which aims to optimize and harmonize a supply chain to reduce costs, improve quality, and achieve a competitive advantage and position using meta-heuristic algorithms. The purpose of optimization in this field is to increase quality and customer satisfaction and reduce production time and related prices. The present research simultaneously optimized the supply chain in the multi-product and multi-period modes. The presented mathematical model was firstly validated. The algorithm's parameters are then adjusted to solve the model with the multi-objective simulated annealing (MOSA) algorithm. To validate the designed algorithm's performance, we solve some examples with General Algebraic Modeling System (GAMS). The MOSA algorithm has achieved an average error of %0.3, %1.7, and %0.7 for the first, second, and third objective functions, respectively, in average less than 1 minute. The average time to solve was 1847 seconds for the GAMS software; however, the GAMS couldn't reach an optimal solution for the large problem in a reasonable computational time. The designed algorithm's average error was less than 2% for each of the three objectives under study. These show the effectiveness of the MOSA algorithm in solving the problem introduced in this paper.

Home Health Care (HHC) is characterized as preparing medical and paramedical services for patients at their place of residence. In the HHC industry, it is imperative for decision-makers to appoint nurses to patients and plan visiting patterns to confront with conflicting objectives and boost service quality. This study offers important insights into Home Health Care Routing and Scheduling Problem (HHCRSP) by dealing with three patient-oriented objectives. Moreover, the proposed model accounts for real-life constraints such as emergency patients, nurses’ proficiency and patients’ preferences. Owing to the multi-objective nature of the model, the Augmented Epsilon Constraint approach and Fuzzy Goal Programming are used for trading off the objectives. Further, getting as close as possible to the real-world problems, some parameters are considered uncertain and consequently a robust approach along with three dissimilar uncertainty sets are used to control uncertainty. Numerical results demonstrate that, regardless of the type of the uncertainty set, increasing control parameters make objective values farther than ideal ones, and the comparison performed among the sets also highlights the stringency of the Box space. A unique indicator, presented to validate the robust approaches, features all sets are almost the same in terms of equal optimality and feasibility criteria.

This paper presents a multi-objective daily voltage and reactive (Volt/VAr) control in radial distribution systems including distributed generation (DG) units. The main purpose is to determine optimum dispatch schedules for on-load tap changer (OLTC) settings at substations, substation switched capacitors and feeder-switched capacitors based on the day-ahead load forecast. The objectives are selected to minimize the voltage deviation on the secondary bus of the main transformer, total electrical energy losses, the reactive power flow through the OLTC and voltage fluctuations in distribution systems, for the next day. Since the objectives are not the same, a fuzzy system is used to calculate the best solution. In order to simplify the control actions for OLTC at substations, a time-interval based control strategy is used for decomposition a daily load forecast into several sequential load levels. A binary ant colony optimization (BACO) method is used to solve the daily voltage and reactive control which is a non-linear mixed-integer problem. To illustrate the effectiveness of the proposed method, the Volt/VAr control is performed in IEEE 33-bus and 69-bus distribution systems and its performance is compared with genetic algorithm and hybrid binary genetic algorithm and particle swarm optimization algorithms. Simulation results show the BACO algorithm has better outperforms than other algorithms.

Weapon-Target Assignment (WTA) as an important part of aerial defense cycle has long been ‎studied. Challenges are usually finding fast-computing methods to search optimal or near-‎optimal solution in cases of a large number of weapons and targets. This viewpoint is more ‎mathematically considerable but practically has limited usage in the mentioned context. A ‎real-time search algorithm is proposed which decomposes the WTA problem and by ‎decreasing the size of solution space and deleting impossible solutions, enables real-time ‎exhaustive search algorithm. Implementation of the algorithm for three typical scenarios shows ‎excellent real-time performance and the possibility of finding exact solutions for large-scale ‎problems.‎

Learning models and related results depend on the quality of the input data. If raw data is not properly cleaned and structured, the results are tending to be incorrect. Therefore, discretization as one of the preprocessing techniques plays an important role in learning processes. The most important challenge in the discretization process is to reduce the number of features’ values. This operation should be applied in a way that relationships between the features are maintained and accuracy of the classification algorithms would increase. In this paper, a new evolutionary multi-objective algorithm is presented. The proposed algorithm uses three objective functions to achieve high-quality discretization. The first and second objectives minimize the number of selected cut points and classification error, respectively. The third objective introduces a new criterion called the normalized cut, which uses the relationships between their features’ values to maintain the nature of the data. The performance of the proposed algorithm was tested using 20 benchmark datasets. According to the comparisons and the results of nonparametric statistical tests, the proposed algorithm has a better performance than other existing major methods.

The Shuffled Complex Evolution (SCE-UA) method developed at the University of Arizona is a global optimization algorithm, initially developed by [1] for the calibrationof conceptual rainfall-runoff (CRR) models. SCE-UA searches for the global optimumof a function by evolving clusters of samples drawn from the parameter space, via a systematiccompetitive evolutionary process. Being a general purpose global optimization algorithm, it has found widespread applications across a diverse range of science and engineering fields. Here, we recount the history of the development of the SCE-UA algorithm and its later advancements. We also present a survey of illustrative applications of the SCE-UA algorithm and discuss its extensions to multi-objective problems and touncertainty assessment. Finally, we suggest potential directions for future investigation.

A dynamic integrated solution for three main problems through integrating all metrics using SCOR are proposed in this research. This dynamic solution comprises strategic decisions in high-level, operational decisions in low-level and alignment of these two decision levels. In this regard, a human intelligence-based process for high level decisions and machine-intelligence based decision support systems (DSSs) for low-level decisions is then proposed using a novel approach. The operational presented model considers important supply chain features thoroughly such as different echelons, several suppliers, several manufacturers and several products during multiple periods. A multi-objective mathematical programming model is then developed to yield the operational decisions with Pareto efficient performance values and solved using a well-known meta-heuristic algorithm, i.e., NSGAII where its parameters is tuned using Taguchi method. Afterward, an intermediate machine-intelligence module is used to determine the best operational solution based on the strategic decision maker’s idea. The efficiency of the proposed framework is shown through numerical example where a sensitivity analysis is then conducted over the obtained results so as to show the impact of the strategic scenario planning on the considered supply chain’s performance.

This study considers a multi-objective combined budget constrained facility location/network design problem (FL/NDP) in which the system uncertainty is considered. The most obvious practical examples of the problem are territorial designing and locating of academies, airline networks, and medical service centers. In order to assure the network reliability versus uncertainty, an efficient robust optimization approach is applied to model the proposed problem. The formulation is minimizing the total expected costs, including, transshipment costs, facility location (FL) costs, fixed cost of road/link utilization as well as minimizing the total penalties of uncovered demand nodes. Then, in order to consider of several system uncertainty, the proposed model is changed to a fuzzy robust model by suitable approaches. An efficient Sub-gradient based Lagrangian relaxation algorithm is applied. In addition, a practical example is studied. At the following, a series of experiments, including several test problems, is designed and solved to evaluate of the performance of the algorithm. The obtained results emphasize that considering of practical factors (e.g., several uncertainties, system disruptions, and customer satisfaction) in modelling of the problem can lead to significant improvement of the system yield and subsequently more efficient utilization of the established network.

The Optimal Power Flow (OPF) is one of the most important issues in the power systems. Due to the complexity and discontinuity of some parameters of power systems, the classic mathematical methods are not proper for this problem. In this paper, the objective function of OPF is formulated to minimize the power losses of transmission grid and the cost of energy generation and improve the voltage stability and voltage profile, considering environmental issues. Therefore, the OPF problem is a nonlinear optimization problem consisting of continuous and discontinuous variables. To solve it, Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and a new hybrid algorithm combining modified Particle Swarm Optimization (PSO) and Genetic algorithm (GA) methods are proposed. In this method, each of the algorithms is performed in its procedure and generates the primary population; then, the populations are ordered and from among them, populations with the highest propriety function are selected. The first population that guesses will enter the two algorithms’ procedures for generating the new population. Note that the inputs of the two algorithms are the same; then, generates a new population. Now, there are three groups of populations: one created by modified GA, one created by modified PSO, and the other is the first initial population, and then sorted with the described sorting method.

The optimal reactive power dispatch (ORPD) is a very important problem aspect of power system planning and is a highly nonlinear, non-convex optimization problem because consist of both continuous and discrete control variables. Since the power system has inherent uncertainty, hereby, this paper presents both of the deterministic and stochastic models for ORPD problem in multi objective and single objective formulation, respectively. The deterministic model consider three main issues in ORPD problem as real power loss, voltage deviation and voltage stability index, but, in the stochastic model the uncertainty on the demand and the equivalent availability of shunt reactive power compensators have been investigated. To solve them, propose a new modified harmony search algorithm (HSA) which implemented in single and multi objective forms. Since, like many other general purpose optimization methods, the original HSA often traps into local optima, to aim with this cope, an efficient local search method called chaotic local search (CLS) and global search operator are proposed in the internal architecture of the original HSA algorithm to improve its ability in finding of best solution because ORPD problem is very complex problem with different types of continuous and discrete constrains i.e. excitation settings of generators, sizes of fixed capacitors, tap positions of tap changing transformers and the amount of reactive compensation devices. Moreover, fuzzy decision-making method is employed to select the best solution from the set of Pareto solutions.

This paper proposes per unit coding for combined economic emission load dispatch problem. In the proposed coding, it is possible to apply the percent effects of elements in any number and with high accuracy in objective function. In the proposed per unit coding, each function is transformed into per unit form based on its own maximum value and has a value from 0 to 1. In this paper, particle swarm optimization is used for solving economic emission load dispatch problem. In order to show the advantages of the proposed method, 25 independent case studies are conducted on systems holding three and six power units with different influence percentages of each function are investigated. The obtained results are compared with those of other methods such as Biogeography Based Optimization, Tabu Search, NSGA-II and etc. The obtained results properly show the superiority of the proposed method to combine economic emission dispatch problem over the penalty factor technique and other conventional combined approaches.

In this paper, a novel multi-objective bus stop location model is proposed, which considers not only the coverage of demand and minimization of access time but also the necessities of suitable stops for transit network design phase. Three objective functions are considered including minimizing (I) sum of the total access distance (time), (II) the weighted combination of stops, and (III) the number of stops. A sum-weighted method is used to solve the proposed multi-objective model considering the different scenarios of weights. A detailed analysis is carried out Tehran CBD to generate sensible stops results.