Multiple Criteria Optimization Problem Research Articles

On the Advantages of Searching Infeasible Regions in Constrained Evolutionary-Based Multi-Objective Engineering Optimization

Abstract Solving a multiple-criteria optimization problem with severe constraints remains a significant issue in multi-objective evolutionary algorithms. The problem primarily stems from the need for a suitable constraint handling technique. One potential approach is balancing the search in feasible and infeasible regions to find the Pareto front efficiently. The justification for such a strategy is that the infeasible region also provides valuable information, especially in problems with a small percentage of feasibility areas. To that end, this paper investigates the potential of the infeasibility-driven principle based on multiple constraint ranking-based techniques to solve a multi-objective problem with a small feasibility ratio. By analyzing the results from intensive experiments on a set of test problems, including the realistic multi-objective car structure design and actuator design problem, it is shown that there is a significant improvement gained in terms of convergence by utilizing the generalized version of the multiple constraint ranking techniques.

Application of integrated CRITIC and GRA-based Taguchi method for multiple quality characteristics optimization in laser-welded blanks

There is a need to study the multi-objective optimization technique as the appropriate method to enhance welding qualities under optimal process conditions. Therefore, this study investigated the application of the integrated Criteria Importance Through Intercriteria Correlation (CRITIC), which is an objective weighting technique, and the Grey Relational Analysis (GRA)-based Taguchi method to solve multiple criteria optimization problem in the Nd:YAG laser welding process. The Taguchi-based L36 orthogonal array table was employed in this study to optimize six process parameters, including the beam diameter, laser power, flow rate, welding speed, laser offset, and pulse shape, with the aim to simultaneously achieve maximum weld strength and minimum weld width. The base metal JIS G3141 SPCC steel with 0.5 and 1.0 mm thicknesses was used in the present experiment. Following the welding process and optimization, the weld strength was measured using a Cometech QC-506M1 universal testing machine, while the weld width was determined under a Nikon SMZ25 stereomicroscope. Based on the results, the weight fractions of the weld strength and weld width from the applied CRITIC method were equal to 0.4157 and 0.5843, respectively. Meanwhile, the GRA revealed that the process parameters recorded an optimal setting for beam diameter of 0.8 mm, flow rate of 8 L/min, laser power of 0.6 kW, welding speed of 2.5 mm/s, laser offset of 0.2 mm, and pulse shape I. Furthermore, the weld strength and the weld width were enhanced from 236 to 328 MPa and from 1.13 to 1.04 mm, respectively. Additionally, the Analysis of Variance (ANOVA) indicated that the laser power and welding speed were the most influential parameters on the welding qualities. Most importantly, the findings of the confirmation experiment showed that the proposed approach was able to effectively identify the optimal laser welding parameters, which ultimately improved the multiple quality characteristics.

Economic Analysis of LNG Distribution for Power Plant and City Gas in Bali

Indonesia is a country that contains great potential for economic development and it is also impact on increased electricity demand in Indonesia. Ministry of Energy and Mineral Resources stated that increasing demand for electricity in Indonesia have reached 6,9% annually. PT. PLN as the electrical company in Indonesia has designed long term strategic development of power plant to anticipate increasing demand for electricity in Indonesia as documented at “Rencana Usaha Penyediaan Tenaga Listrik” (RUPTL) PT. PLN on 2018-2027[7]. The government has plan to convert the energy that will be used in power plants to become natural gas energy for utilization of power plants in Indonesia. PT. PLN is prioritizing the power plant that will operate by using Liquefied Natural Gas (LNG) as the main energy. PT.PLN also want to build the new Power Plant (PLTGU) in Celukan Bawang, Bali. The power plant will have 350 MWx2 as the additional power supply to reduce deficit of electrical power in Bali. Analyzing economic indicators is an important point to determined requirement Infrastructure and distribution Natural Gas at every district in Bali. In this study MCDM (Multiple Criteria Decision Making) is applied to model and solve multiple criteria optimization problems in economic process. The AHP method is presented to compare the best alternatives route of distribution LNG, the requirement to construct mini Natural Gas filling station, economical value of the distribution, and supply-demand at every district in Bali. Payback period (PP) and Return of Investment (ROI) calculation must be considered to develop economic value and fulfil the needs at every district by establishing a new mini LNG filling station in certain locations. The result of this research is expected to provide recommendation on best LNG distribution, which will assume lowest gas price at the end user. Accordingly, this will support the program of Bali clean and green.

A Compact Representation of Preferences in Multiple Criteria Optimization Problems

A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization.

A Pareto approach to resolve the conflict between information gain and experimental costs: Multiple-criteria design of carbon labeling experiments.

Science revolves around the best way of conducting an experiment to obtain insightful results. Experiments with maximal information content can be found by computational experimental design (ED) strategies that identify optimal conditions under which to perform the experiment. Several criteria have been proposed to measure the information content, each emphasizing different aspects of the design goal, i.e., reduction of uncertainty. Where experiments are complex or expensive, second sight is at the budget governing the achievable amount of information. In this context, the design objectives cost and information gain are often incommensurable, though dependent. By casting the ED task into a multiple-criteria optimization problem, a set of trade-off designs is derived that approximates the Pareto-frontier which is instrumental for exploring preferable designs. In this work, we present a computational methodology for multiple-criteria ED of information-rich experiments that accounts for virtually any set of design criteria. The methodology is implemented for the case of 13C metabolic flux analysis (MFA), which is arguably the most expensive type among the ‘omics’ technologies, featuring dozens of design parameters (tracer composition, analytical platform, measurement selection etc.). Supported by an innovative visualization scheme, we demonstrate with two realistic showcases that the use of multiple criteria reveals deep insights into the conflicting interplay between information carriers and cost factors that are not amendable to single-objective ED. For instance, tandem mass spectrometry turns out as best-in-class with respect to information gain, while it delivers this information quality cheaper than the other, routinely applied analytical technologies. Therewith, our Pareto approach to ED offers the investigator great flexibilities in the conception phase of a study to balance costs and benefits.

A Selection of Important Genes and Their Correlated Behavior in Alzheimer's Disease.

In 2017, approximately 5 million Americans were living with Alzheimer’s disease (AD), and it is estimated that by 2050 this number could increase to 16 million. In this study, we apply mathematical optimization to approach microarray analysis to detect differentially expressed genes and determine the most correlated structure among their expression changes. The analysis of GSE4757 microarray dataset, which compares expression between AD neurons without neurofibrillary tangles (controls) and with neurofibrillary tangles (cases), was casted as a multiple criteria optimization (MCO) problem. Through the analysis it was possible to determine a series of Pareto efficient frontiers to find the most differentially expressed genes, which are here proposed as potential AD biomarkers. The Traveling Sales Problem (TSP) model was used to find the cyclical path of maximal correlation between the expression changes among the genes deemed important from the previous stage. This leads to a structure capable of guiding biological exploration with enhanced precision and repeatability. Ten genes were selected (FTL, GFAP, HNRNPA3, COX1, ND2, ND3, ND4, NUCKS1, RPL41, and RPS10) and their most correlated cyclic structure was found in our analyses. The biological functions of their products were found to be linked to inflammation and neurodegenerative diseases and some of them had not been reported for AD before. The TSP path connects genes coding for mitochondrial electron transfer proteins. Some of these proteins are closely related to other electron transport proteins already reported as important for AD.

Multiple Criteria Optimization of the Joint Vehicle and Transportation Jobs Selection and Vehicle Routing Problems for a Small Road Freight Transportation Fleet

Abstract We consider a joint problem of selecting transportation jobs and designing transportation routes for small freight transportation fleet owners. The problem is formulated as a multiple criteria optimization problem with several stakeholders: the driver, the fleet owner and the clients. The problem formulation includes driving and work time regulation constraints, takes into account driver comfort and safety, as well as the lateness of the job execution and the time constraints on the pickup and the delivery. Furthermore, the selection of the vehicle is included as a part of the decision making process. The problem is heavily constrained and cannot be solved exactly in reasonable time. We propose an iterative solution algorithm which we evaluate in a series of computational experiments performed on a subset of the transportation network of Poland.

Multiple-criteria Decision-making Support Based on the Multi-Indicator Evaluation of the Pareto-Approximation Quality

The paper considers a problem, which is defined as multi-indicator finding the "best" algorithm to solve a multiple-criteria optimization (MCO) problem. Of a large number of known algorithms for solving the MCO, we deal with the algorithms based on the preliminary construction of its Pareto front (set) approximation and called P-algorithms.Because of a large number of P-algorithms, a problem of choosing the "best" algorithm for the given MCO problem (and / or this class of these problems) arises, i.e. a meta-optimization problem. We pose the problem of structural meta-optimization of P-algorithms, which suggests a simultaneous P-approximation construction and optimization of this approximation according to one or several P-indicators.The paper presents basic MCO-problem formulation and describes used P-approximation quality indicators. Considers several methods to choose the "best" P-algorithm such as a method based on using one or another method to visualize multi-indicator estimates of P-approximation quality, a method based on the scalar convolution of P-approximation quality indicators, chosen by a decision-maker (DM), and an author's automated method that supposes a preliminary approximation of the function of preference. Provides mathematical description, considers advantages and disadvantages, as well as shows the ways to overcome these shortcomings.The main research result involves a development of the original PREF-I method to solve the MCO problem based on identification of so-called DM’s function of preference. This method may be thought as evolution of the PREF method aimed at solving the initial MCO problem.

Evaluation of Optimum Turning Process of Process Parameters Using DOE and PCA Taguchi Method

In order to build up a bridge between quality and productivity, the present study highlights optimization of turning process parameters to provide good surface finish as well as high hardness. The objective of this paper is to solve the multi- response parameter optimization problems of turning process. By applying Taguchi method the quality of manufactured goods, and engineering designs are developed by studying variations. In this work, an attempt has been made to solve the correlated multiple criteria optimization problem of turning process by considering the major performance characteristics hardness and surface roughness. The corresponding machining parameters are cutting-speed, feed and depth of cut. Traditional Taguchi based hybrid optimization approaches rely on the assumption that quality indices are uncorrelated or independent. But it is felt that, in practice, there may be some correlation among various quality indices (responses) under consideration. To overcome this limitation of Taguchi approach, the present study proposes application of PCA to convert correlated responses into uncorrelated quality indices called individual principal components. The Composite Principle Component has been optimized by using Taguchi method. Analysis of variance (ANOVA) has been conducted for Composite Principle Component to find the optimal process parameters. Signal to Noise (S/N) Ratio has been found for PCA to find the optimal levels of the process parameters. Finally a conformation test has been made for three different materials and the results have been plotted.

Weights balancing method using entropy values in solving MCDM problem

The article shows how multiple criteria optimization problems could be solved by application of modified KEMIRA method, when there are three groups of criteria. Criteria priorities are determined by the entropy, criteria weights are calculated by solving optimization task. The proposed method allows to find one of several possible local extrema.

Quaisidifferentials in Kantorovich Spaces

This is an overview of the quasidifferential calculus for the mappings that arrive at Kantorovich spaces. The necessary optimality conditions are also derived for multiple criteria optimization problems with quasidifferentiable data.

Optimization of turning process parameters by using grey-Taguchi

The main objective of this study is to improve toughness and hardness of engineering material by changing the machining parameters of turning process. By applying Taguchi method the quality of manufactured goods, and engineering designs are developed by studying variations. In this work, an attempt has been made to solve the correlated multiple criteria optimization problem of turning process by considering three different process parameters viz. cutting-speed, feed and depth of cut.. Grey Relational Analysis has been adopted to convert multiple objectives of the optimization problem into a single objective function, denoted as Grey Relational Grade. The overall Grey Relational Grade has been optimized by using Taguchi method. Analysis of variance (ANOVA) has been conducted for Grey relational grade (GRG) to find the optimal process parameters. Signal to Noise (S/N) Ratio has been found for GRG to find the optimal levels of the process parameters. Finally a conformation test has been made for three different materials and the results have been plotted. Keywords: Turning, Optimization, Grey-Taguchi and ANOVA

Solving Multicriteria Optimization Problems with WebOptim Software System

Abstract This paper is a presentation of a web based decision support system “WebOptim” for solving single and multiple criteria optimization problems. It targets a wide range of user typeseducators, researchers, managers and business people. It also provides two types of communication interfaces user friendly graphical interface for human interaction and programming interface for machine communication with other third party software systems. The interfaces facilitate the problem solving process of different types of optimization problems, mainly single and multi-objective programming optimization problems with continuous or integer variables.

Selection of Materials Using Multi Criteria Decision Making Method by Considering Physical and Mechanical Properties of Jute/Al<sub>2</sub>O<sub>3</sub> Composites

Multi-Criteria Decision Making (MCDM) method plays a key role to find out the best option from all possible alternatives. From different application areas Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the Multi-Criteria Decision Making (MCDM) method to find out the correct result. TOPSIS is a real-world and valuable procedure for ranking and selection of a number of externally determined substitutes through distance measures. In this paper, application of techniques for order preference by similarity of an ideal solution (TOPSIS) method is applied for solving multiple criteria (objective) optimization problem in mechanical and physical properties of jute/Al2O3 fiber based hybrid composites. The best performance value of composite is designed from ideal solution and as well as the worst performance value of composite is designed for negative-ideal solution. The results have demonstrated the model to be both robust and efficient.

Predicting Student Retention by Linear Programming Discriminant Analysis

The goal of the paper is to predict student retention with an ensemble method by combining linear programming (LP) discriminant analysis approaches together with bootstrapping and feature salience detection. In order to perform discriminant analysis, we linearize a fractional programming method by using Charnes-Cooper transformation (CCT) and apply linear programming, while comparing with an approach that uses deviation variables (DV) to tackle a similar multiple criteria optimization problem. We train a discriminatory hyperplane family and make the decision based on the average of the histograms created, thereby reducing variability of predictions. Feature salience detection is performed by using the peeling method, which makes the selection based on the proportion of variance explained in the correlation matrix. While the CCT method is superior in detecting true-positives, DV method excels in finding true-negatives. The authors obtain optimal results by selecting either all 14 (CCT) or the 8 (DV) most important student study related and demographic dimensions. They also create an ensemble. A quantitative course along with the age at accession are deemed to be the most important, whereas the two courses resulting in less than 2% of failures are amongst the least important, according to peeling. A five-fold Kolmogorov-Smirnov test is undertaken, in order to help university staff in devising intervention measures.

10.5937/industrija42-5731 = Fuzzy models in measuring competitiveness of agroindustry

Over the past three decades, competitiveness has become an integral part of modern management and business development. The authors observe 18 enterprises in Vojvodina in the period 2009-2013 from Agriculture and Manufacturing sectors and measure their competitiveness based on the involvement of intellectual capital. The authors also propose the construction of a portfolio by solving the multiple criteria optimization problem. Fuzzy methodology has been applied: yields are modeled with trapezoidal fuzzy numbers, and the risk is measured by semi-deviation. Results of the study indicate a deviation from the Markowitz model which assumes that the yields are normally distributed, and that the appropriate risk measure is the variance of returns. Portfolios obtained by fuzzy methodology are characterized by higher values of intellectual capital, when compared to its counterparts obtained from Markowitz optimization.

Identification of potential biomarkers from microarray experiments using multiple criteria optimization

Microarray experiments are capable of determining the relative expression of tens of thousands of genes simultaneously, thus resulting in very large databases. The analysis of these databases and the extraction of biologically relevant knowledge from them are challenging tasks. The identification of potential cancer biomarker genes is one of the most important aims for microarray analysis and, as such, has been widely targeted in the literature. However, identifying a set of these genes consistently across different experiments, researches, microarray platforms, or cancer types is still an elusive endeavor. Besides the inherent difficulty of the large and nonconstant variability in these experiments and the incommensurability between different microarray technologies, there is the issue of the users having to adjust a series of parameters that significantly affect the outcome of the analyses and that do not have a biological or medical meaning. In this study, the identification of potential cancer biomarkers from microarray data is casted as a multiple criteria optimization (MCO) problem. The efficient solutions to this problem, found here through data envelopment analysis (DEA), are associated to genes that are proposed as potential cancer biomarkers. The method does not require any parameter adjustment by the user, and thus fosters repeatability. The approach also allows the analysis of different microarray experiments, microarray platforms, and cancer types simultaneously. The results include the analysis of three publicly available microarray databases related to cervix cancer. This study points to the feasibility of modeling the selection of potential cancer biomarkers from microarray data as an MCO problem and solve it using DEA. Using MCO entails a new optic to the identification of potential cancer biomarkers as it does not require the definition of a threshold value to establish significance for a particular gene and the selection of a normalization procedure to compare different experiments is no longer necessary.

Adapting the Hypervolume Quality Indicator to Quantify Trade‐offs and Search Efficiency for Multiple Criteria Decision Making Using Pareto Fronts

When choosing a best solution based on simultaneously balancing multiple objectives, the Pareto front approach allows promising solutions across the spectrum of user preferences for the weightings of the objectives to be identified and compared quantitatively. The shape of the complete Pareto front provides useful information about the amount of trade‐off between the different criteria and how much compromise is needed from some criterion to improve the others. Visualizing the Pareto front in higher (3 or more) dimensions becomes difficult, so a numerical measure of this relationship helps capture the degree of trade‐off. The traditional hypervolume quality indicator based on subjective scaling for multiple criteria optimization method comparison provides an arbitrary value that lacks direct interpretability. This paper proposes an interpretable summary for quantifying the nature of the relationship between criteria with a standardized hypervolume under the Pareto front (HVUPF) for a flexible number of optimization criteria, and demonstrates how this single number summary can be used to evaluate and compare the efficiency of different search methods as well as tracking the search progress in populating the complete Pareto front. A new HVUPF growth plot is developed for quantifying the performance of a search method on completeness, efficiency, as well as variability associated with the use of random starts, and offers an effective approach for method assessment and comparison. Two new enhancements for the algorithm to populate the Pareto front are described and compared with the HVUPF growth plot. The methodology is illustrated with an optimal screening design example, where new Pareto search methods are proposed to improve computational efficiency, but is broadly applicable to other multiple criteria optimization problems. Copyright © 2012 John Wiley & Sons, Ltd.

Parametric optimization of wire electrical discharge machining using TOPSIS method

In this paper, application of techniques for order preference by similarity to ideal solution (TOPSIS) method is applied for solving multiple criteria (objective) optimization problem in wire electrical discharge machining (WEDM) process. Three examples are included to illustrate the approach. In all the cases, it is found that, the results obtained using the TOPSIS method almost match with those derived by the past researchers which prove the applicability of this method while solving various complex decision-making problems in present day manufacturing environment.

Optimization of the urban line network using a mathematical programming approach

The paper deals with the line-planning problem related to urban public transport. Given the transportation network in a city, the origin–destination matrix of travel demands, and the fl eet of available vehicles, the goal is to design the routes and frequencies of lines. The proposed solution method is a combination of the exact mathematical programming algorithm and a trip assignment procedure. The solution process consists of three stages: (i) initialization, (ii) designing the line network and setting the initial frequencies of selected lines, (iii) solution improvement. In the fi rst stage, an initial set of feasible lines is proposed. In the second stage, an optimal subset of candidate lines is selected and initial frequencies of lines are computed by solving a mathematical programming model of the line-planning problem. The problem is formulated as a multiple criteria optimization problem, where the criteria refl ect travelers’ demand for a high quality service, operator’s interest in an effective service, and the environmental impact of the vehicles. The solution of this problem specifi es the number of vehicles of the given mode and type operating on the lines. The lines which are not assigned a vehicle will not operate. The assigned number of vehicles determines the frequency of a given line. At the same time, the solution specifi es optimal passengers’ routes in the line network. The third stage consists of an iterative process, which computes new line frequencies with regard to in-vehicle and waiting times, transfers, and passengers’ behavior in a situation when they have multiple travel alternatives. The approach has been verifi ed using real transportation data of a middle-sized city in the Slovak Republic. The paper presents the results of the case study.