China
Africa
Explore chapters and articles related to this topic
Simple Multi-Attribute Rating Technique — SMART
Published in Maria Isabel Gomes, Nelson Chibeles Martins, Mathematical Models for Decision Making with Multiple Perspectives, 2022
Maria Isabel Gomes, Nelson Chibeles Martins
After the procedures presented in the previous sections all Alternatives’ performances according to all Criteria will be valued in a reference increasing scale where the lowest and highest possible values for each Criteria corresponds to 0 and 100, respectively. To get the final classification of one Alternative is necessary to combine the obtained values in each Criterion. But how to combine them? If all Criteria had the same relative importance for the DM a simple average could be a good way to integrate all values in a single indicator. Unfortunately, that equal importance seldom happens. So, in this step it will be necessary to translate the DM’ opinion concerning the Criteria relative importance into Weights that will be used to calculate a weighted sum for each Alternative.
Multi Objective Bacterial Foraging Optimization: A Survey
Published in Ranjeet Kumar Rout, Saiyed Umer, Sabha Sheikh, Amrit Lal Sangal, Artificial Intelligence Technologies for Computational Biology, 2023
R. Vasundhara Devi, S. Siva Sathya
are the weights provided to the corresponding n objectives. In this approach, the MOO problem is converted into a single objective problem. In weighted sum approach, the objectives are provided with weight values based upon the importance or the priority of the objective in the corresponding real-world problems. In the case of [47], the BFO algorithm is modified to solve the multiple objectives of the single phase transformer design. Transformers are the electrical equipment used in the transmission and distribution of electricity in a stable and reliable manner. They help in the successful operation of electrical utilities. The transformers should be designed with high quality, highly efficient transformers with a minimal cost. This single-phase transformer design needs to minimize the cost while improving the performance. As there are two objectives that need to be simultaneously solved, the weighted sum method is used. The first objective is the cost involved represented as f1, and the second objective is the efficiency represented as f2. The weighting values associated with cost (Rs) and efficiency (%) are w1 and w2, respectively. The solutions obtained should minimize the cost and the objective values are represented as ff1,f2=fw1,w2=w1f1+w21/f2
Frequently Used Multicriteria Decision-Making Methods
Published in Mohamed El Alaoui, Fuzzy TOPSIS, 2021
Despite its computational ease, the weighted sum suffers from many limitations. First, it requires that the entry elements be both numerical and comparable. Second, its compensatory nature may not be desirable; a good performance in accordance with a certain criterion with a relatively high weight can mask other underperformances while still producing a satisfactory result (El Alaoui & Ben-azza, 2017a).
Tool path generation for five-axis machining of blisks with barrel cutters
Published in International Journal of Production Research, 2019
Yaoan A. Lu, Ye Ding, Chengyong Wang, Limin Zhu
The weighted sum method for multi-objective optimizations continues to be used extensively because it can provide a single solution point that reflects the preferences presumably incorporated in the selection of a single set of weights (Marler and Arora 2010). The weighted sum method allows the user to specify preferences, articulating the relative importance of the different objectives, and there are many different approaches for determining the weights. During the search process of the optimal tool path, the values of Wmin, Fpt, FA, FC for each path are calculated and normalised, so that they are comparable at a same level. Then the weighted sum method is used to determine the total cost value of this path. Therefore, the objective function becomes
Integrated design of emergency shelter and medical networks considering diurnal population shifts in urban areas
Published in IISE Transactions, 2019
Qing-Mi Hu, Laijun Zhao, Huiyong Li, Rongbing Huang
Typically, the decision-maker has managerial preferences for different objective functions in the strategic emergency preparedness network design. In the weighted sum method, the weight itself reflects the relative importance (preference) among the objective functions under consideration. Moreover, the weighted sum method is simple to understand and easy to implement by emergency managers. Thus, this article applies the weighted sum method to solve the established bi-objective optimization model, despite its drawbacks in depicting the Pareto-optimal set (Kim and Weck, 2005).
A multi-objective, bilevel sensor relocation problem for border security
Published in IISE Transactions, 2019
Aaron M. Lessin, Brian J. Lunday, Raymond R. Hill
Numerous solution techniques exist to solve multi-objective optimization and facility relocation problems, ranging from the Weighted Sum and ε-constraint Methods to genetic algorithms and other metaheuristics. The Weighted Sum Method involves selecting weights for each objective that represent their relative importance and subsequently optimizing the resulting weighted objective function (Ehrgott, 2006). However, prespecifying appropriate weights for each objective may be unrealistic, and the objectives may be incommensurable (Sherali and Soyster, 1983). Detailed surveys of systematic weight selection techniques are presented by Eckenrode (1965), Hobbs (1980), and Hwang and Yoon (1981). Similarly, the Lexicographic Method requires preemptively ranking the objectives in order of importance such that an incremental improvement in a particular objective preempts arbitrarily large improvements in the less important objectives (Sherali and Soyster, 1983). This method iteratively solves a sequence of single-objective problems, optimizing one objective at a time and assigning previously determined optimal objective function values as constraints (Ehrgott, 2006). Alternatively, one can develop preemptive weights for a single objective function that includes all objectives as shown by Sherali and Soyster (1983), but potential scaling issues in practice may induce premature termination in a commercial solver, resulting in the identification of a solution that is not Pareto optimal. As such, herein we utilize the ε-constraint Method, which bounds the respective values for all but one of the objective function values while optimizing the remaining objective. The respective bounds may be iteratively relaxed (w.l.o.g.) with the corresponding identification of optimal solutions for each combination of bounds used to identify non-inferior solutions (Mavrotas, 2009). Additionally, goal programming has been applied to multi-objective optimization and facility relocation problems, such as in research conducted by by Min (1988), Bhattacharya et al. (1993), and Badri (1999). Goal programming requires specification of goals for each objective function, upon which the total absolute deviation from the goals is typically minimized (Marler and Arora, 2004). Lee and Olson (1999) provide a review of goal programming formulations and applications.