Search For Pareto-optimal Solutions Research Articles

An optimization framework for achieving optimal hydrocyclone's performance aligning with decision-makers' preferences

Previous hydrocyclone optimization often neglected interactions among key performance objectives, which limits hydrocyclone wide applications to meet increasingly diverse industry demands. This study proposes an optimization framework to identify the most suitable hydrocyclone design and operating conditions with conflicting key performance objectives. An advanced multi-objective evolutionary algorithm (PICEA-g) is employed to generate Pareto-optimal solutions that capture trade-offs among multiple conflicting objectives. A novel data-driven predictive algorithm, INFO-ELM, is introduced to establish nonlinear relationships between key variables and performance objectives, thereby accelerating the search for Pareto-optimal solutions by PICEA-g. Furthermore, a multi-criteria decision-making method (TOPSIS) is utilized to determine the optimal solution based on decision-makers' preferences, ensuring consistency between preference information and decision outcomes. The framework's effectiveness is validated across various separation scenarios using two decision-making strategies. This study offers a comprehensive approach to address trade-offs in hydrocyclone optimization, widening its application in diverse separation scenarios.

Evolutionary multimodal multiobjective optimization guided by growing neural gas

Evolutionary multimodal multiobjective optimization aims to search for a set of Pareto optimal solutions that are well distributed in both the objective and decision spaces. In recent years, there has been a growing interest in enhancing the search ability of evolutionary algorithms using machine learning techniques. However, there are few studies on machine learning-assisted evolutionary multimodal multiobjective optimization. In this paper, we propose an evolutionary multimodal multiobjective algorithm guided by growing neural gas, which learns the topological structure of the obtained good solutions during the evolution process. These good solutions are well-converged and well-distributed in the decision space, which indicate the shape of the Pareto optimal solution set. The proposed algorithm employs three novel mating selection operators based on the topological structure to efficiently and effectively search for Pareto optimal solutions. The first operator exploits Pareto optimal solutions within the topological structure, while the others explore Pareto optimal solutions around and far away from the topological structure, respectively. The proposed algorithm is compared with eight state-of-the-art evolutionary multimodal multiobjective algorithms on 20 test problems. Experimental results demonstrate that the proposed algorithm is competitive in solving these problems.

Multi-Objective Adapted Binary Bat for Test Suite Reduction

Regression testing is an essential quality test technique during the maintenance phase of the software. It is executed to ensure the validity of the software after any modification. As software evolves, the test suite expands and may become too large to be executed entirely within a limited testing budget and/or time. So, to reduce the cost of regression testing, it is mandatory to reduce the size of the test suite by discarding the redundant test cases and selecting the most representative ones that do not compromise the effectiveness of the test suite in terms of some predefined criteria such as its fault-detection capability. This problem is known as test suite reduction (TSR); and it is known to be as nondeterministic polynomial-time complete (NP-complete) problem. This paper formulated the TSR problem as a multi-objective optimization problem; and adapted the heuristic binary bat algorithm (BBA) to resolve it. The BBA algorithm was adapted in order to enhance its exploration capabilities during the search for Pareto-optimal solutions. The effectiveness of the proposed multi-objective adapted binary bat algorithm (MO-ABBA) was evaluated using 8 test suites of different sizes, in addition to twelve benchmark functions. Experimental results showed that, for the same fault discovery rate, the MO-ABBA is capable of reducing the test suite size more than each of the multi-objective original binary bat (MO-BBA) and the multi-objective binary particle swarm optimization (MO-BPSO) algorithms. Moreover, MO-ABBA converges to the best solutions faster than each of the MO-BBA and the MO-BPSO.

Multicriteria optimization in the problem of computer-aided design of hybrid solar energy systems

This paper reports an approach to optimizing the structure of a hybrid solar energy system (HSES), used in the task of automated design, under two modes: independent and connected to the network. The proposed HSES includes a solar energy system (SES), an energy storage system (ESS) powered by rechargeable batteries (RBs), a set of diesel generators (DGs), and a network-connecting system. This paper has identified models of the HSES elements' power and proposed a control algorithm based on rules that assess the state of the system during operation. The energy models in conjunction with the control algorithm make it possible to model the system's operation stage over a predefined time interval. The proposed approach is based on solving a multicriteria optimization problem (MCO). MCO takes into consideration the minimization of system costs and the total cost of the system, minimizing fuel use, maximizing reliability, and minimizing the use of non-renewable energy sources. A solution to the MCO problem is based on using a Pareto-optimal solution search algorithm, underlying which is the NSGA-II genetic algorithm employing the proposed set of crossbreeding, mutation, and breeding operators. The devised procedure makes it possible to determine the structure of HSES, which includes a set of the number of solar panels, RBs, and DGs. The result is three variants of HSES for a household for two people (Kyiv, Ukraine), under an autonomous mode and in the regime connected to the electricity grid. Given the possibility of selling electricity at a green tariff during the year, the reported solution makes it possible to reduce the estimated cost of the system by up to 45 %. The use of simulation has helped conduct a detailed analysis of the system's performance throughout the year

Balancing assembly lines operating with heterogeneous workers under uncertainty in task processing times

PurposeThis paper considers the assembly line worker assignment and balancing problem of type-2 (ALWABP-2) with fuzzy task times. This problem is an extension of the (simple) SALBP-2 in which task times are worker-dependent and concurrently uncertain. Two criteria are simultaneously considered for minimization, namely, fuzzy cycle time and fuzzy smoothness index.Design/methodology/approachFirst, we show how fuzzy concepts can be used for managing uncertain task times. Then, we present a multiobjective genetic algorithm (MOGA) to solve the problem. MOGA is devoted to the search for Pareto-optimal solutions. For facilitating effective trade-off decision-making, two different MO approaches are implemented and tested within MOGA: a weighted-sum based approach and a Pareto-based approach.FindingsExperiments over a set of fuzzified test problems show the effect of these approaches on the performance of MOGA while verifying its efficiency in terms of both solution and time quality.Originality/valueTo the author’s knowledge, no previous published work in the literature has studied the biobjective assembly line worker assignment and balancing problem of type-2 (ALWABP-2) with fuzzy task times.

Modeling design information systems with multi-criteria

This work is devoted to the development of a new method for modeling information systems of multi-criteria design, based on expert ranking of criteria. The possibilities of the fuzzy-set theory and the possibility theory allow for a comprehensive analysis of criteria by reducing numerical indicators to a qualitative form, passing to the corresponding fuzzy relations of preference. Some of the information may be lost, therefore conclusions should be applied, both on the basis of “quantitative” processing of the results of measuring the criteria, and on the basis of “qualitative” processing. If these conclusions coincide, then their adequacy will be confirmed based on the initial data. Since the modeling of complex design systems is determined by several criteria defined on different base sets, and the problem of determining the multi-criteria efficiency in conditions of incompleteness of the initial data remains relevant, within the framework of this article, an optimization method is proposed simultaneously according to many criteria with incompleteness of the initial data. The difference between the described method lies in the fact that the expert ranking of criteria enables to formally set fuzzy preference graphs that make it possible to obtain comprehensive information about estimates in the rank scale during pairwise comparisons, with the aim of subsequent search for Pareto-optimal solutions in multi-criteria problems.

Decision-making and multi-objectivization for cost sensitive robust optimization over time

Most existing research on dynamic optimization focuses on tracking the moving global optimum (TMO). Recently, a new paradigm for handling dynamic optimization, known as robust optimal over time (ROOT), has been proposed to avoid frequent changes in the optimal solutions. To explicitly minimize the costs incurred in switching solutions, a multi-objective ROOT algorithm has also been suggested. In practice, however, only one Pareto optimal solution can be adopted when the environment changes. To automate the decision-making process, this paper proposes a new approach that combines a ROOT/SCII algorithm with a policy to handle dynamic optimization problems. In the proposed approach, ROOT/SCII is used to simultaneously maximize the robustness and minimize the costs of switching solutions, and the policy is used to select a solution from the obtained Pareto set to be used in the new environment. In addition, multi-objectivization is introduced to enhance the efficiency in search for Pareto optimal solutions trading off between the robustness over time and the switching costs for the high dimension of decision space. Simulation results demonstrate that multi-objectivization is effective and the proposed approach is able to find a sequence of preferred solutions guided by the policy, considerably reducing the total switching costs while satisfying the user’s robustness requirement, and outperforming TMO and ROOT in terms of switching cost minimization.

Multi-objective clustering algorithm using particle swarm optimization with crowding distance (MCPSO-CD)

Clustering, an unsupervised method of grouping sets of data, is used as a solution technique in various fields to divide and restructure data to become more significant and transform them into more useful information. Generally, clustering is difficult and complex phenomenon, where the appropriate numbers of clusters are always unknown, comes with a large number of potential solutions, and as well the datasets are unsupervised. These problems can be addressed by the Multi-Objective Particle Swarm Optimization (MOPSO) approach, which is commonly used in addressing optimization problems. However, MOPSO algorithm produces a group of non-dominated solutions which make the selection of an “appropriate” Pareto optimal or non-dominated solution more difficult. According to the literature, crowding distance is one of the most efficient algorithms that was developed based on density measures to treat the problem of selection mechanism for archive updates. In an attempt to address this problem, the clustering-based method that utilizes crowding distance (CD) technique to balance the optimality of the objectives in Pareto optimal solution search is proposed. The approach is based on the dominance concept and crowding distances mechanism to guarantee survival of the best solution. Furthermore, we used the Pareto dominance concept after calculating the value of crowding degree for each solution. The proposed method was evaluated against five clustering approaches that have succeeded in optimization that comprises of K-means Clustering, MCPSO, IMCPSO, Spectral clustering, Birch, and average-link algorithms. The results of the evaluation show that the proposed approach exemplified the state-of-the-art method with significant differences in most of the datasets tested.

Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm

In today’s manufacturing industry more than one performance criteria are considered for optimization to various degrees simultaneously. To deal with such hard competitive environments it is essential to develop appropriate multicriteria scheduling approaches. In this paper consideration is given to the problem of scheduling n independent jobs on a single machine with due dates and objective to simultaneously minimize three performance criteria namely, total weighted tardiness (TWT), maximum tardiness and maximum earliness. In the single machine scheduling literature no previous studies have been performed on test problems examining these criteria simultaneously. After positioning the problem within the relevant research field, we present a new heuristic algorithm for its solution. The developed algorithm termed the hybrid non-dominated sorting differential evolution (h-NSDE) is an extension of the author’s previous algorithm for the single-machine mono-criterion TWT problem. h-NSDE is devoted to the search for Pareto-optimal solutions. To enable the decision maker for evaluating a greater number of alternative non-dominated solutions, three multiobjective optimization approaches have been implemented and tested within the context of h-NSDE: including a weighted-sum based approach, a fuzzy-measures based approach which takes into account the interaction among the criteria as well as a Pareto-based approach. Experiments conducted on existing data set benchmarks problems show the effect of these approaches on the performance of the h-NSDE algorithm. Moreover, comparative results between h-NSDE and some of the most popular multiobjective metaheuristics including SPEA2 and NSGA-II show clear superiority for h-NSDE in terms of both solution quality and solution diversity.

Bi-criteria single-machine batch scheduling with machine on/off switching under time-of-use tariffs

The industrial sector is the largest consumer of the world’s total energy and most of its consumption is in form of electricity. In recent years, to strengthen the peak load regulation capability, time-of-use (TOU) pricing has been implemented in many countries to encourage consumers to shift their use from peak to mid- and off-peak periods such that their energy bills can be reduced. In this paper, we study a new single-machine batch scheduling problem with machine on/off switching under TOU tariffs, which aims to simultaneously minimize total electricity cost and makespan. For the problem, we first develop a bi-objective mixed-integer linear programming model. Based on optimal batch rule analysis, an improved model is further provided which greatly reduces Pareto optimal solution search space. To efficiently solve large-size problems, we propose a heuristic based ε-constraint method. The results from extensive computational experiments confirm the effectiveness and efficiency of the proposed model and the algorithm.

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

ABSTRACTIn multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.

Multi-objective optimization of turning process of hardened material for energy efficiency

Improving the energy efficiency of machining processes is one way to reduce manufacturing costs in an effort to resolve environmental issues. The objective of this work is to optimize the machining parameters of the turning process for hardened AISI 4140 steel to reduce the consumed cutting energy and improve energy efficiency. The machining parameters evaluated include cutting speed, feed rate, nose radius, edge radius, rake angle, and relief angle. Firstly, numerical simulations were applied in conjunction with the Box- Behnken design (BBD) experimental method and response surface methodology (RSM) to render the relationships of the machining parameters with the specific required cutting energy as well as energy efficiency. Subsequently, a non-dominated sorting genetic algorithm-II (NSGA-II) was used to solve multi-objective optimization problems and search for Pareto optimal solutions. Finally, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was adopted to determine the best solution compromised from the Pareto set. The results show that the specific required cutting energy decreased by approximately 16%, and the energy efficiency could be improved by about 11% compared to the non-optimized system. Therefore, this research is intended to contribute toward making machining processes of hardened steels more green and efficient.

A hybrid method of evolutionary algorithm and simple cell mapping for multi-objective optimization problems

A hybrid method is proposed to take advantages of evolutionary algorithms (EAs) and the simple cell mapping (SCM) for multi-objective optimization problems (MOPs). The hybrid method starts with a random search for Pareto optimal solutions with an EA, and follows up with a neighborhood based search and recovery algorithm using the SCM. The non-dominated sorting genetic algorithm-II (NSGA-II) is used as an example of EAs. It is found that the SCM based search and recovery algorithm can reconstruct the branches of the Pareto set even when only one point in the vicinity of the set is available from the random search by the EA. We have chosen several benchmark MOPs to compare NSGA-II and SCM separately with the EA\(+\)SCM hybrid method while using the Hausdorff distance as a performance metric, and applied the method to develop multi-objective optimal designs of PID controls for a nonlinear oscillator with time delay. The results show that the EA\(+\)SCM hybrid method is very promising.

Function approximation with LWPR and XCSF: a comparative study

Function approximation, also called regression, is an important tool in numerical mathematics and engineering. The most challenging approximation problems arise, when the function class is unknown and the surface has to be approximated online from incoming samples. One way to achieve good approximations of complex non-linear functions is to cluster the input space into small patches, apply linear models in each niche, and recombine these models via a weighted sum. While it is rather simple to optimally fit a linear model to given data, it is fairly complex to find a reasonable structuring of the input space in order to exploit linearities in the underlying function. We compare two non-parametric regression algorithms that are able to approximate multi-dimensional, non-linear functions online. The XCSF Learning Classifier System is a modified version of XCS, which is a genetics-based machine learning algorithm. Locally Weighted Projection Regression is a statistics-based machine learning technique that is mainly used for function approximation tasks in robotics. For both algorithms the relevant, conflicting performance criteria are accuracy and population size, that is, the number of local models. We explore the trade-off between those criteria on three benchmark problems by means of intense grid search for Pareto optimal solutions. Detailed learning behavior is investigated using selected Pareto optimal parameters. The illustration of final input space clusterings sheds light on the structuring capabilities. A discussion of advantages and drawbacks completes this comparative study.

Optimization methods for complex sheet metal stamping computer aided engineering

Nowadays, sheet metal stamping processes design is not a trivial task due to the complex issues to be taken into account (complex shapes forming, conflicting design goals and so on). Therefore, proper design methodologies to reduce times and costs have to be developed mostly based on computer aided procedures. In this paper, a computer aided approach is proposed with the aim to offer a methodology able to solve very complex sheet metal stamping processes, in particular a progressive design approach based on the integration between numerical simulations and optimization methodologies is presented. In particular, Response Surface Method, Moving Least Squares approximation and Pareto optimal solutions search techniques were applied in order to design two different complex 3D stamping operations. The proposed design procedure is able to verify the necessity of a spatially differentiated restraining forces approach and to design the best policy for them. In particular, different part “quality” indicators were monitored such as springback occurrence and thinning. An explicit/forming-implicit/springback approach was utilized to develop the numerical simulations. To sum up, a new and flexible design methodology is proposed, able to: deal with complex sheet metal stamping processes; investigate many possible technological scenarios; carry out a set of reliable solutions able to satisfy different design requirements; offer different optimization possibilities in order to take in to account all the sheet metal stamping design issues.

Design of Complex Sheet Metal Forming Processes: A New Computer Aided Progressive Approach

The growing interest in sheet metal stamping processes, particularly in automotive industry, led to three main issues in this field: request of very complex shapes; growing interest in springback control; solution of multi-objective problems. This makes the design of the sheet metal stamping processes very difficult, since the number of both design variables and design objectives are progressively increased; therefore, proper design methodologies to reduce times and costs are highly required. In this paper, an innovative design approach able to manage and optimize complex stamping operations is proposed. In particular, a progressive design approach based on the integration between numerical simulations, Response Surface Methodology (RSM) and Pareto optimal solutions search techniques was applied in order to design a complex automotive sheet stamping operation.

Design of sheet stamping operations to control springback and thinning: A multi-objective stochastic optimization approach

The aim of this paper is to develop a design tool for stamping processes, which is able to deal with the scattering of the final part quality due to the inner variability of such operations. Such variability is one of the main drawbacks for a robust process design. It results in a scattering of the most significant process results and depends on several parameters. The so called noise factors greatly influence final result variability, which often means rejecting parts and anyway achieving final properties different from the specified ones. The process investigated in the paper is an S-shaped U-channel stamping operation carried out on a lightweight aluminum alloy of automotive interest. The main topic of the paper is the prevention of excessive part thinning and the control of springback phenomena; thus, thinning and springback are the objective functions taken into account. The blank holder force (BHF) value was considered as process design variable while two noise factors were considered: lubricating conditions (represented by the friction coefficient μ) and strain-hardening index of the material (exponent n in material flow rule). The approach proposed in this paper is a multi-objective optimization problem consisting of an integration among finite element (FEM) numerical simulation, Response Surface Methodology (RSM) and Monte Carlo Simulation (MCS) method. The developed tool starts from a Pareto optimal solutions search technique and takes into account noise factors. The design procedure is able to foresee the potential direction along which a Pareto solution may move due to the effects of the noise factors. In this way, the proposed design tool is fully able to take into account process variability effects and to provide a precise overview of the possible perturbations the analyzed objective functions may undergo.

A new progressive design methodology for complex sheet metal stamping operations: Coupling spatially differentiated restraining forces approach and multi-objective optimization

The growing interest in sheet metal stamping processes, particularly in the automotive industry has led to three main issues in this field:*request of very complex shapes; *growing interest in springback control; *solution of multi-objective problems. These issues make a sheet metal stamping processes design very difficult and proper design methodologies to reduce times and costs are highly required. In this paper, a computer aided approach aiming to satisfy the mentioned issues is proposed. In particular, a progressive design approach based on the integration between numerical simulations, Response Surface Methodology (RSM) and Pareto optimal solutions search techniques was applied in order to design a complex 3D automotive stamping operation. An explicit/forming-implicit/springback approach was utilized to develop the numerical simulations. The proposed design approach is able to verify the necessity of a spatially differentiated restraining forces approach and to design the best policy for them. Pareto optimal solutions search techniques were applied in two different phases: the former Pareto frontier was built using an uniform restraining forces policy while the latter, which is the final process design tool, was based on a differentiated restraining forces strategy. Two different restraining force policies were applied: the former focused on drawbeads utilization, the latter utilized a segmented blankholder. As the optimization objective functions are concerned, indicators related both to thinning distribution and to springback amount were taken into account. The obtained Pareto curves can be used in order to discriminate which conditions have to be expected once a desired value of one of the objective functions is fixed. A new and flexible design methodology is proposed, able to:*deal with complex sheet metal stamping processes; *investigate many possible technological scenarios; *carry out a set of reliable solutions able to satisfy different design requirements.

A Pareto optimal design approach for simultaneous control of thinning and springback in stamping processes

One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. In this way, a strong research effort is developed on high strength steels which are widely utilized and they require a proper springback control. Springback reduction in sheet metal forming is a typical goal to be pursued which is conflicting with thinning reduction for instance. Thus, such problems can be considered as multi-objective ones characterized by conflicting objectives. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an industrial environment. In this paper, integration between numerical simulations, response surface methodology and Pareto optimal solutions search techniques was applied in order to design a DP 600 U-channel shape stamping operation. In particular the friction conditions and blank holder force were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid excessive geometrical distortions due to springback occurrence.

Analysis of stamping performances of dual phase steels: A multi-objective approach to reduce springback and thinning failure

The industrial interest on light weight components has contributed in the last years to a significant research effort on new materials able to guarantee high mechanical properties, good formability and reasonable costs together with reduced weights when compared to traditional mild steels. Among such materials advanced high strength steels (AHSS) such as transformations induced plasticity (TRIP) and dual phase (DP), and light weight alloys proved their usefulness in stamping of automotive components. As AHSS are concerned, one of the main drawbacks is related to springback occurrence. Many aspects have to be taken into account when springback reduction is investigated: material behavior issues, process conditions, numerical simulations parameters calibration, geometrical aspects and so on. Moreover, springback minimization problems are typically multi-objective ones because springback reduction may conflict with other goals in stamping design such as thinning reduction. In this paper, such problem was investigated through integration between numerical simulations, Response Surface Methodology and Pareto optimal solutions search techniques. The design of a U-channel stamping operation was investigated utilizing two different dual phase steel grades: DP 1000 and DP 600. An explicit/forming-implicit/springback approach was utilized for the numerical simulations. Friction conditions and blank holder force were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid excessive geometrical distortions due to springback occurrence.