Initial Pareto Research Articles

Multi-objective simulated annealing algorithm for robotic mixed-model two-sided assembly line balancing with setup times and multiple constraints

Robotic mixed-model two-sided assembly lines (RMTALs) have become increasingly prevalent in manufacturing industries for productivity enhancement. However, only limited attention has been paid to the RMTAL balancing problems that contain both setup times and multiple constraints such as positional constraints, zoning constraints, and synchronism constraints. Given the coexistence of these aspects in real-world scenarios, this study aims to address the RMTAL balancing problem with setup times and the mentioned constraints. To formulate the problem, a mixed integer programming model is proposed to optimize cycle time and total energy consumption. To handle multiple constraints and setup times, a new method based on four-vector encoding is introduced. This method addresses the three constraints during the encoding phase using four intervals and five rules, while setup times are processed during the decoding phase. To solve the problem, a Pareto entropy-based two-mode multi-objective simulated annealing algorithm is developed. The algorithm employs variable neighborhood descent algorithm with switchable objectives to generate the initial Pareto archive. Subsequently, it selects the initial solution with minimal potential in the Pareto archive, alternating between two search modes of exploration and exploitation based on the entropy difference of Pareto solutions. Comparative experiments with four state-of-the-art algorithms on benchmark instances of varying scales demonstrate that the proposed algorithm outperforms the others in over 93% of instances for the hypervolume ratio and inverted generational distance metrics.

Nested Kriging Surrogates for Rapid Multi-Objective Optimization of Compact Microwave Components

A procedure for rapid EM-based multi-objective optimization of compact microwave components is presented. Our methodology employs a recently developed nested kriging modelling to identify the search space region containing the Pareto-optimal designs, and to construct a fast surrogate model. The latter permits determination of the initial Pareto set, further refined using a separate surrogate-assisted process. As an illustration, a three-section impedance transformer is designed for the best matching and minimum size. The set of trade-off designs is produced at the low computational cost of only a few hundred of high-fidelity EM simulations of the transformer circuit despite a large number of its geometry parameters.

A new prediction strategy combining T-S fuzzy nonlinear regression prediction and multi-step prediction for dynamic multi-objective optimization

Abstract Many dynamic multi-objective optimization problems have been widely developed to track the changing optima quickly and effectively in dynamic environments. Prediction-based methods can be used to predict future changes by learning past experience. This paper employed a new prediction strategy combining Takagi-Sugeno fuzzy nonlinear regression prediction and multi-step prediction named TSMP to estimate the new initial Pareto solutions whenever the environment changes. In TSMP, when environmental changes occur, the next initial center of Pareto solutions (PS) is predicted by a Takagi-Sugeno fuzzy nonlinear regression prediction model and then one trail population is generated by combining the predicted center and an approximate manifold of PS. Moreover, the other trail population is generated by a linear multi-step prediction model. Furthermore, the next initial PS is reinitialized by a random hybridization of these two trail populations. The proposed TSMP strategy is systematically compared with re-initialization strategy (RIS), feed-forward prediction strategy (FPS) and population prediction strategy (FPS) under different multi-objective optimizers on benchmark test problems with different features. Experimental results and performance comparisons with other state-of-the-art algorithms indicate that TSMP is effective and promising for solving dynamic multi-objective optimization problems.

A multi-objective approach for supporting wine grape harvest operations

In this paper, we present a novel multi-objective mixed-integer linear programming model to support wine grape harvesting. The proposed model considers the opposing nature of operational cost minimization and grape quality maximization, subject to several constraints, such as grape requirements and routing decisions. Based on the operations of a winery we worked with, we develop a negotiation protocol that can lead to an agreed final harvest schedule. The protocol includes an initial Pareto optimal solution obtained through the augmented weighted Tchebycheff method. Then, the solutions are presented to the two decision-makers and, if no agreement is reached, we conduct an iterative process, which includes finding Pareto optimal solutions in a neighborhood using the augmented ∊-constraint method. Finally, we choose, within this set, the solution following a substitution rate criteria. We illustrate our procedure using an educational example.

Rapid multi-objective optimization of antennas using nested kriging surrogates and single-fidelity EM simulation models

PurposeThis study aims to propose a computationally efficient framework for multi-objective optimization (MO) of antennas involving nested kriging modeling technology. The technique is demonstrated through a two-objective optimization of a planar Yagi antenna and three-objective design of a compact wideband antenna.Design/methodology/approachThe keystone of the proposed approach is the usage of recently introduced nested kriging modeling for identifying the design space region containing the Pareto front and constructing fast surrogate model for the MO algorithm. Surrogate-assisted design refinement is applied to improve the accuracy of Pareto set determination. Consequently, the Pareto set is obtained cost-efficiently, even though the optimization process uses solely high-fidelity electromagnetic (EM) analysis.FindingsThe optimization cost is dramatically reduced for the proposed framework as compared to other state-of-the-art frameworks. The initial Pareto set is identified more precisely (its span is wider and of better quality), which is a result of a considerably smaller domain of the nested kriging model and better predictive power of the surrogate.Research limitations/implicationsThe proposed technique can be generalized to accommodate low- and high-fidelity EM simulations in a straightforward manner. The future work will incorporate variable-fidelity simulations to further reduce the cost of the training data acquisition.Originality/valueThe fast MO optimization procedure with the use of the nested kriging modeling technology for approximation of the Pareto set has been proposed and its superiority over state-of-the-art surrogate-assisted procedures has been proved. To the best of the authors’ knowledge, this approach to multi-objective antenna optimization is novel and enables obtaining optimal designs cost-effectively even in relatively high-dimensional spaces (considering typical antenna design setups) within wide parameter ranges.

Expedited EM‐driven generation of Pareto‐optimal trade‐off curves for variable‐turn on‐chip inductors

This work presents a novel approach to computationally efficient Pareto front identification for variable-turn on-chip inductors. The final outcome is a set of solutions that correspond to the best trade-offs between conflicting design objectives. Here, we consider minimising inductor area and, simultaneously, maximising its quality factor, while maintaining a specified inductance value at a given operating frequency. As opposed to the typically used population-based metaheuristics requiring massive computational resources to generate the entire Pareto front in a single algorithm run, the proposed method reduces the number of necessary structure evaluations by exploiting a point-by-point strategy for determining the consecutive trade-off designs. The original design problem is a mixed-integer task involving integer and non-integer variables (here, the number of inductor windings and its geometry parameters). For the sake of computational efficiency, we develop a separate kriging interpolation model for each considered case of winding turns, and use it, instead of expensive electromagnetic simulations, to obtain the initial Pareto fronts. The non-dominated part of the concatenated initial Pareto sets is subsequently elevated (accuracy-wise) to the level of an electromagnetic analysis by means of a response correction technique. Our considerations are illustrated using a 3.5-nH variable-turn on-chip inductor realised in 65-nm CMOS technology.

Multi-objective design optimization of antennas for reflection, size, and gain variability using kriging surrogates and generalized domain segmentation

Cost-efficient multi-objective design optimization of antennas is presented. The framework exploits auxiliary data-driven surrogates, a multi-objective evolutionary algorithm for initial Pareto front identification, response correction techniques for design refinement, as well as generalized domain segmentation. The purpose of this last mechanism is to reduce the volume of the design space region that needs to be sampled in order to construct the surrogate model, and, consequently, limit the number of training data points required. The recently introduced segmentation concept is generalized here to allow for handling an arbitrary number of design objectives. Its operation is illustrated using an ultra-wideband monopole optimized for best in-band reflection, minimum gain variability, and minimum size. When compared with conventional surrogate-based approach, segmentation leads to reduction of the initial Pareto identification cost by over 20%. Numerical results are supported by experimental validation of the selected Pareto-optimal antenna designs.

An equilibrium-conserving taxation scheme for income from capital

Under conditions of market equilibrium, the distribution of capital income follows a Pareto power law, with an exponent that characterizes the given equilibrium. Here, a simple taxation scheme is proposed such that the post-tax capital income distribution remains an equilibrium distribution, albeit with a different exponent. This taxation scheme is shown to be progressive, and its parameters can be simply derived from (i) the total amount of tax that will be levied, (ii) the threshold selected above which capital income will be taxed and (iii) the total amount of capital income. The latter can be obtained either by using Piketty’s estimates of the capital/labor income ratio or by fitting the initial Pareto exponent. Both ways moreover provide a check on the amount of declared income from capital.

Pareto Ranking Bisection Algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces

A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.

Protein adsorption on ion exchange resins and monoclonal antibody charge variant modulation

A novel multicomponent adsorption equilibrium model for proteins on ion-exchange resins is developed on a statistical thermodynamic basis including surface coverage effects and protein-resin and protein–protein interactions. The resulting model exhibits a general competitive Langmuirian behavior and was applied to the study and optimization of the separation of monoclonal antibody charge variants on two strong cation exchangers. The model accounts explicitly for the effect of both pH and salt concentration, and its parameters can be determined in diluted conditions, that is, through physically sound assumptions, all model parameters can be obtained using solely experiments in diluted conditions, and be used to make predictions in overloaded conditions.The parameterization of the model and optimization of the separation is based on a two-step approach. First, gradient experiments in diluted conditions are undertaken in order to determine the model parameters. Based on these experiments and on information about the proteins of interest and the stationary phase used, all the model parameters can be estimated. Second, using the parameterized model, an initial Pareto optimization is undertaken where overloaded operating conditions are investigated. Experiments from this Pareto set are then used to refine the estimation of the model parameters. A second Pareto optimization can then be undertaken, this time with the refined parameters. This can be repeated until a satisfactory set of model parameters is found.This iterative approach is shown to be extremely efficient and to provide large amounts of knowledge based on only a few experiments. It is shown that due to the strong physical foundation of the model and the very low number of adjustable parameters, the number of iterations is expected to be at most two or three. Furthermore, the model based tool is improved as more experimental knowledge is provided, allowing for better estimations of the chromatographic processes considered at each iteration. This makes it a very suitable tool for the design and the development of preparative and industrial purification processes, including the determination of both the optimal operating conditions, as well as the allowable process operating space.

Expedited constrained multi-objective aerodynamic shape optimization by means of physics-based surrogates

In the paper, computationally efficient constrained multi-objective design optimization of transonic airfoil profiles is considered. Our methodology focuses on fixed-lift design aimed at finding the best possible trade-offs between the two objectives: minimization of the drag coefficient and maximization of the pitching moment. The algorithm presented here exploits the surrogate-based optimization principle, variable-fidelity computational fluid dynamics (CFD) models, as well as auxiliary data-driven surrogates (here, using Kriging). In order to permit computationally feasible construction of the Kriging models, initial design space reduction is also utilized. The design process has three major stages: (i) identification of the extreme points of the Pareto front through single-objective optimization (one objective at a time), (ii) construction of the Kriging model and initial Pareto front generation using multi-objective evolutionary algorithm (MOEA), and (iii) Pareto front refinement using response correction techniques and local response surface approximation (RSA) models. For the sake of computational efficiency, stages (i) and (ii) are realized at the level of coarse-discretization CFD model. The RSA models are also utilized to predict the angle of attack necessary to achieve the target lift coefficient, which considerably reduces the CFD simulation effort involved in the design process. Two design case studies are considered involving B-spline-parameterized airfoil shapes with 8 and 12 design variables. The 10-element Pareto front representations are obtained at the cost corresponding to just over two hundred of high-fidelity CFD model evaluations. This cost is not only considerably lower (up to two orders of magnitude) than the cost of direct high-fidelity model optimization using metaheuristics but, more importantly, renders multi-objective optimization of aerodynamic components computationally tractable even at the level of accurate CFD models.

Optimizing Contractor Selection for Construction Packages in Capital Projects

AbstractIn capital construction projects, the contractor selection process is executed in the front-end planning phase based on the experience and judgment of the project leadership team, whose members are considered experts. A comprehensive construction value packaging system (CVPS) is presented for assisting these project leaders in improving the efficacy, efficiency, and transparency of this process. The CVPS comprises an interface-oriented approach to work decomposition and a multicriteria approach to contractor selection. Selection is supported by software for iteratively computing and interactively visualizing the Pareto front of optimal work packages. The CVPS is validated by functional demonstration and a case study of a piping installation project in an energy infrastructure facility. The initial Pareto front had more than 100,000 optimal work packages representing different trade-offs between cost, time, contractor experience, maintenance rates, and financial stability. An iterative and interact...

Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flow, involving aerodynamics tradeoffs; and another one in low-speed flow, involving tradeoffs between the aerodynamic and the aeroacoustic performances.

Reducing the pareto set algorithm based on an arbitrary finite set of information “quanta”

In this paper, in the framework of the axiomatic approach developed by the author over the past 3 decades, we assume four axioms of "reasonable" choice, which define a rather wide class of problems of multi-criteria selection. To reduce the Pareto set we use numerical information about the preference relation of a decision maker. We propose a method for narrowing the Pareto set using an arbitrary consistent finite set of such information. The method is based on an algorithm that generates a new set of criteria (with a minimum elements number) with respect to which a new Pareto set gives o more precise upper estimate than the initial Pareto set.

A hybrid meta-learning architecture for multi-objective optimization of SVM parameters

Support Vector Machines (SVMs) have achieved a considerable attention due to their theoretical foundations and good empirical performance when compared to other learning algorithms in different applications. However, the SVM performance strongly depends on the adequate calibration of its parameters. In this work we proposed a hybrid multi-objective architecture which combines meta-learning (ML) with multi-objective particle swarm optimization algorithms for the SVM parameter selection problem. Given an input problem, the proposed architecture uses a ML technique to suggest an initial Pareto front of SVM configurations based on previous similar learning problems; the suggested Pareto front is then refined by a multi-objective optimization algorithm. In this combination, solutions provided by ML are possibly located in good regions in the search space. Hence, using a reduced number of successful candidates, the search process would converge faster and be less expensive. In the performed experiments, the proposed solution was compared to traditional multi-objective algorithms with random initialization, obtaining Pareto fronts with higher quality on a set of 100 classification problems.

Reducing the Pareto set based on set-point information

An axiomatic approach to reducing the Pareto set in the problem of multicriteria choice based on an information set obtained from the decision maker is considered. The information reflects the degree up to which the decision maker is ready to lose values of one group of criteria to improve values of several other groups of criteria. It is proved that using this information one can eliminate a whole number of elements from the initial Pareto set, simplifying the subsequent choice.

NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point

Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates.