A Distance Based Method for Solving Multi-Objective Optimization Problems

Kamal, Murshid; Jalil, Syed Aqib; Muneeb, Syed Mohd; Ali, Irfan

doi:10.22237/jmasm/1532525455

Cited by 13 publications

(8 citation statements)

References 28 publications

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“…A preference-based method is employed to convert this MOOP into a single objective optimisation problem using preference factors w 1 and w 2 assigned to each objective [14,16,17]. Thus:…”

Section: Defining Cost Functionmentioning

confidence: 99%

“…This is to choose w 1 and w 2 in Equation ( 27) which may be the same or different. Considering the empirical knowledge regarding the optimisation problem, differential weights are preferable [17]. The weighted sum in Equation ( 27) uses a priori articulation of preferences, with the weights assigned directly based on their relative importance, as per the rating method [18].…”

Section: Objective Function Weightingsmentioning

confidence: 99%

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Constrained optimised flexible power control for grid‐connected converters under unbalanced faults

Rufa'I

Zhang

Chong

2021

J. eng.

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This paper presents a constrained multi-objective optimisation scheme for a gridconnected voltage source converter operating under unbalanced voltage conditions in a three-phase three-wire system. The scheme is aimed at evaluating the converter reference currents required to supply all the power generated by the connected source to the grid, whilst simultaneously suppressing oscillations of both real and reactive powers. The tradeoff between these two conflicting requirements is achieved by setting a single cost function with variable weightings. Two constraints are set to restrict the converter instantaneous phase current and maintain low DC-bus voltage percentage ripple. A genetic algorithm is applied to search for the optimal solution. Simulation results are presented and confirm the effectiveness of the proposed method.

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“…A preference-based method is employed to convert this MOOP into a single objective optimisation problem using preference factors w 1 and w 2 assigned to each objective [14,16,17]. Thus:…”

Section: Defining Cost Functionmentioning

confidence: 99%

Section: Objective Function Weightingsmentioning

confidence: 99%

Constrained optimised flexible power control for grid‐connected converters under unbalanced faults

Rufa'I

Zhang

Chong

2021

J. eng.

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“…Quddoos [13] proposed a method of finding a compromise variant of the route by determining the weight of different possible variants. In [14], multi-objective linear programming is used to minimize the distances between ideal objectives to a possible target space by transforming intermediate targets into constraints. Kamal [14] also uses a balanced method of programming goals and minimizing the distances between ideal goals to a possible target space by solving subtasks of the general problem of linear programming.…”

Section: Introductionmentioning

confidence: 99%

“…In [14], multi-objective linear programming is used to minimize the distances between ideal objectives to a possible target space by transforming intermediate targets into constraints. Kamal [14] also uses a balanced method of programming goals and minimizing the distances between ideal goals to a possible target space by solving subtasks of the general problem of linear programming. In Fleischmann's article [15], various variants of mathematical modeling and a search for optimal solutions of reverse logistics are considered.…”

Section: Introductionmentioning

confidence: 99%

Entropy as an Objective Function of Optimization Multimodal Transportations

Bazaluk

Kotenko

Ніценко

2021

Entropy

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This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks.

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“…FGP technique is used for achieving the highest degree of each of the defined membership goals to the extent possible in the decision-making. Kamal et al (2018) considered a MOTP and developed a new technique called the distance-based method for solving it.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

et al. 2021

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The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

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A Distance Based Method for Solving Multi-Objective Optimization Problems

Cited by 13 publications

References 28 publications

Constrained optimised flexible power control for grid‐connected converters under unbalanced faults

Constrained optimised flexible power control for grid‐connected converters under unbalanced faults

Entropy as an Objective Function of Optimization Multimodal Transportations

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

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