Entropy-Based Weighting for Multiobjective Optimization: An Application on Vertical Turning

Abstract

In practical situations, solving a given problem usually calls for the systematic and simultaneous analysis of more than one objective function. Hence, a worthwhile research question may be posed thus: In multiobjective optimization, what can facilitate for the decision maker choosing the best weighting? Thus, this study attempts to propose a method that can identify the optimal weights involved in a multiobjective formulation. The proposed method uses functions of Entropy and Global Percentage Error as selection criteria of optimal weights. To demonstrate its applicability, this method was employed to optimize the machining process for vertical turning, maximizing the productivity and the life of cutting tool, and minimizing the cost, using as the decision variables feed rate and rotation of the cutting tool. The proposed optimization goals were achieved with feed rate = 0.37 mm/rev and rotation = 250 rpm. Thus, the main contributions of this study are the proposal of a structured method, differentiated in relation to the techniques found in the literature, of identifying optimal weights for multiobjective problems and the possibility of viewing the optimal result on the Pareto frontier of the problem. This viewing possibility is very relevant information for the more efficient management of processes.

Robust Multi-Objective Optimization for Response Surface Models Applied to Direct Low-Value Natural Gas Conversion Processes

“…Following a different approach, some authors (see [ 50 , 51 , 52 ]) used the Shannon entropy index [ 53 ] associated with an error measure, to determine the most preferred Pareto ideal point in a MOP in a vertical turning process, resolved using the NBI method. The authors state that Shannon’s entropy index can provide a more reliable assessment of the relative weights of objectives in the absence of analyst preferences.…”

“…Furthermore, the authors state that when combined with an error measure, it minimized the error of Pareto’s preferred point related to individual optimal responses. The weighting metric ξ is obtained by [ 50 , 52 ]: where w i are the weights to be assigned to the objectives that are to be optimized.…”

“…In the search for an optimization model that allows for the simultaneous conversion of CH 4 , C 2 selectivity , and C 2 yield, the decision-making process, based on multiple criteria, proposed by Rocha et al [ 52 ] can be used. The authors sought to build a uniformly distributed Pareto frontier and a way to select the preferred Pareto optimal points as the ideal solution to a given problem.…”

Entropic Data Envelopment Analysis: A Diversification Approach for Portfolio Optimization

“…According Rocha et al [49], among the many desirable properties of the Shannon entropy index, we can highlight: (a) the entropy of a probability distribution representing a completely certain result is 0, and the entropy of any probability distribution representing uncertain results is positive; and (b) its measure is concave. Property 1 is desirable, since the entropy index guarantees non-zero solutions.…”

Train Operation Strategy Optimization Based on a Double-Population Genetic Particle Swarm Optimization Algorithm

“…To obtain the weight of each index more accurately, linear combination weights based on entropy (LCWBE) is used, which is both subjectivity and objectivity [30,31]. The steps of LCWBE is as follows.…”