Multi-objective Optimization Task Research Articles

Selective laser sintering of carbon fiber–reinforced PA12: Gaussian process modeling and stochastic optimization of process variables

This work presents an in-depth investigation of the influence of the individual laser sintering parameters on density, mechanical, and dimensional properties of carbon fiber–reinforced PA12 parts manufactured by selective laser sintering (SLS) . A space-filling design of experiments method was used to plan the experiments and SLS trials were conducted to manufacture test samples that were characterized in terms of dimensional accuracy, density, and mechanical properties. Gaussian process–supervised learning was used to model the interaction between laser sintering parameters and quality properties. Stochastic optimization via evolutionary algorithm was employed to obtain trade-off solutions for several multi-objective optimization tasks. The Gaussian process presented excellent model quality for the majority of response variables evaluated. Laser sintering parameters had a significant influence on physical and mechanical properties, exhibiting complex and non-linear behavior. Multi-objective optimization showed a wide range of optimized laser sintering parameters available, depending on the trade-off objective desired.

A novel hybrid particle swarm optimization and gravitational search algorithm for multi-objective optimization of text mining

Big-data is one of the milestones on the web especially on social media (SM). Due to the widespread popularity of SM on the web, it is a painful task to capture the essence of SM. In this study, mining big social media data is re-formulated into a multi-objective optimization (MOO) task for an extractive summary. A Gravitational Search Algorithm (GSA) is utilized for optimizing several expressive objectives for generating a concise summary of SM. Moreover, particle swarm optimization (PSO) is mixed with GSA in a new shape to strengthen a local search ability and slow convergence speed in standard GSA. Whereas some users may demand the brief at any moment, several groups are constituted for incremental updating process during real-time based on naïve Bayes algorithm. From experimental results, the proposed approach outperformed other notable and state-of-art comparative methods.

A Multitasking Electric Power Dispatch Approach With Multi-Objective Multifactorial Optimization Algorithm

Electric power dispatch issue mainly consists of two optimization tasks: active and reactive power dispatches, each of which is a non-linear multi-objective optimization problem with a series of constraints. Traditional evolutionary algorithms are focused on single-task optimization for active or reactive power dispatch and they are not able to deal with several (single- or multi-objective) optimization tasks simultaneously. In this paper, to solve this problem, a multitasking electric power dispatch approach is proposed by introducing the multi-objective multifactorial optimization (MO-MFO) algorithm and integrating it with the characteristics of power system. The approach exhibits the great potential to be developed as a cloud-computing solver or platform for future large-scale smart grid applications involving different market entities because of its implicit parallel computation mechanism. The multitasking approach is thoroughly tested and benchmarked with IEEE-30-bus and IEEE-118-bus standard systems and exhibits generally better performances as compared to previously proposed Pareto heuristic approaches for electric power dispatch.

Multi-objective trajectory design for overtaking maneuvers of automated vehicles

Abstract The paper proposes a trajectory design method for overtaking maneuvers, in which several performances are incorporated. Thus, it leads to a multi-objective optimization task. It is based on a simple mathematical representation of feasible trajectories by using a potential field approach. The solution of the complex computations in the optimization is approximated by neural networks. The proposed solution is based on the idea that there are a large number of collision free feasible trajectories. The goal of the method is to find the trajectory, which is suitable for the specified objectives. The result of the paper is an integrated decision for both longitudinal and lateral directions, such as longitudinal acceleration command and the values of the defined path. The effectiveness of the method is presented through CarMaker simulation environment.

A Multi-Objective Task Scheduling Method for Fog Computing in Cyber-Physical-Social Services

Fog computing provides users with data storage, computing, and other services by using fog layer devices close to edge devices. Tasks and resource scheduling in fog computing has become a research hotspot. For the multi-objective task-scheduling problem in fog computing, an adaptive multi-objective optimization task scheduling method for fog computing (FOG-AMOSM) is proposed in this paper. In this method, the total execution time and the task resource cost in the fog network are taken as the optimization target of resource allocation, and a multi-objective task scheduling model is designed. Since the objective model is a Pareto optimal solution problem, the global optimal solution can be obtained by using multi-objective optimization theory and the improved multi-objective evolutionary heuristic algorithm. Moreover, to obtain a better distribution of the current task scheduling group, the neighborhood is adaptively changed according to the current situation of the task scheduling group in fog computing, which avoids the problem that the neighborhood value caused by the neighborhood policy in the multi-objective algorithm affects the distribution of the task scheduling population. This algorithm is used to solve the non-inferior solution set of the utility function index of fog computing task scheduling to try to solve the multi-objective cooperative optimization problem in fog computing task scheduling. The results show that the proposed method has better performance than other methods in terms of total task execution time, resource cost and load dimensions.

Pymoo: Multi-Objective Optimization in Python

Python has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related frameworks have arisen in the past few years. Only a few of them support optimization of multiple conflicting objectives at a time, but do not provide comprehensive tools for a complete multi-objective optimization task. To address this issue, we have developed pymoo, a multi-objective optimization framework in Python. We provide a guide to getting started with our framework by demonstrating the implementation of an exemplary constrained multi-objective optimization scenario. Moreover, we give a high-level overview of the architecture of pymoo to show its capabilities followed by an explanation of each module and its corresponding sub-modules. The implementations in our framework are customizable and algorithms can be modified/extended by supplying custom operators. Moreover, a variety of single, multi and many-objective test problems are provided and gradients can be retrieved by automatic differentiation out of the box. Also, pymoo addresses practical needs, such as the parallelization of function evaluations, methods to visualize low and high-dimensional spaces, and tools for multi-criteria decision making. For more information about pymoo, readers are encouraged to visit: https://pymoo.org

New hybrid NSGA-III&SPEA/R to multi-object optimization in a half-car dynamic model

In this article, we conducted a new hybrid method between Non-dominated Sorting Genetic Algorithm II (NSGA-III) and SPEA/R (HNSGA-III&SPEA/R). This method is implemented to find the optimal values of the powertrain mount system stiffness parameters. This is the task of finding multi-objective optimization involving six simultaneous optimization goals: mean square acceleration and mean square displacement of the powertrain mount system. A hybrid HNSGA-III&SPEA/R has proposed with the integration of Strength Pareto evolutionary algorithm-based reference direction for Multi-objective (SPEA/R) and Many-objective optimization genetic algorithm (NSGA-III). Several benchmark functions are tested, and results reveal that the HNSGA-III&SPEA/R is more efficient than the typical SPEA/R and NSGA-III. Powertrain mount system stiffness parameters optimization with HNSGA-III&SPEA/R is simulated. It proved the potential of the HNSGA-III&SPEA/R for powertrain mount system stiffness parameter optimization problem.

Smoothing, deep, or mixed diamond burnishing of low-alloy steel components – optimization procedures

Diamond burnishing (DB) is a static mechanical surface treatment based on severe surface plastic deformation aimed at significant improvement in the surface integrity and operating properties of the treated component. Very often, DB is unjustifiably perceived of as typical smoothing burnishing. In the present article, it is shown that DB can be conducted as smoothing, deep, or mixed burnishing depending on the particular combination of process governing factors employed. Optimizations of the DB process for 41Cr4 steel under different criteria are conducted in order to obtain the optimal parameters of different DB processes. The choices of governing factors and objective functions (roughness and fatigue limits), which are obtained on the basis of planned experiments and regression analyses, are fully justified. By means of one-objective optimizations, the uncompromising optimum values of the objective functions and the corresponding optimum values of the governing factors of smoothing and deep DB processes are obtained. A new optimization procedure for solving a multi-objective optimization task is developed in order to obtain compromise optimal values simultaneously with the objective functions and governing factors of the mixed DB process. In order to highlight the advantages of the proposed optimization procedure, the multi-objective task solution is compared with the results obtained via some known methods, i.e., the compromise weight vector and function of the losses methods.

A Multiobjective multifactorial optimization algorithm based on decomposition and dynamic resource allocation strategy

Multiobjective multifactorial optimization (MO-MFO), i.e., multiple multiobjective tasks are simultaneously optimized by a single population, has received considerable attention in recent years. Traditional algorithms for the MO-MFO usually allocate equal computing resources to each task, however, this may not be reasonable due to the fact that different tasks usually have different degrees of difficulty. Motivated by the idea that the limited computing resources should be adaptively allocated to different tasks according to their difficulties, this paper proposes an algorithm for the MO-MFO based on decomposition and dynamic resource allocation strategy (denoted as MFEA/D-DRA). In the MFEA/D-DRA, each multiobjective optimization task is firstly decomposed into a series of single-objective subproblems. Thereafter, a single population is used to evolve all the single-objective subproblems. In the process of evolution, subproblems with fast evolution rate will have the opportunity to get more rewards, i.e., computing resources. The evolution rate is measured by a utility function and updated periodically. Moreover, different multiobjective optimization tasks can communicate with each other according to a random mating probability. Finally, a set of evenly distributed approximate Pareto optimal solutions is obtained for each multiobjective optimization task. The statistical analysis of experimental results illustrates the superiority of the proposed MFEA/D-DRA algorithm on a variety of benchmark MO-MFO problems.

Real-time data text mining based on Gravitational Search Algorithm

Short messages are one of the milestones on the web especially on social media (SM). Due to the widespread circulation of SM, it already turns into excessively painful capturing outmost relevant and significant information for certain users. One of the main motivations of this work is that many users may need an inclusive brief of all comments without reading the entire list of short messages for decision making. In this work, mining in big social media data is formulated for the first time into a multi-objective optimization (MOO) task to extract the essence of a text. Since some users may demand the brief at any moment, several groups of dissimilar short messages are established based on graph coloring mechanism. Six interesting feature are formalized to exhibit more interactive messages. A Gravitational Search Algorithm (GSA) is employed to satisfy several important objectives for generating a concise summary. The problem was picked by using the Normal Boundary Intersection (NBI) mechanism to trade-off among different features. Additionally, to satisfy real-time needs, an inventive incremental grouping task is modelled to update the existing colors. From exhaustive experimental results, the proposed approach outperformed other strong comparative methods.

GuacaMol: Benchmarking Models for de Novo Molecular Design.

De novo design seeks to generate molecules with required property profiles by virtual design-make-test cycles. With the emergence of deep learning and neural generative models in many application areas, models for molecular design based on neural networks appeared recently and show promising results. However, the new models have not been profiled on consistent tasks, and comparative studies to well-established algorithms have only seldom been performed. To standardize the assessment of both classical and neural models for de novo molecular design, we propose an evaluation framework, GuacaMol, based on a suite of standardized benchmarks. The benchmark tasks encompass measuring the fidelity of the models to reproduce the property distribution of the training sets, the ability to generate novel molecules, the exploration and exploitation of chemical space, and a variety of single and multiobjective optimization tasks. The benchmarking open-source Python code and a leaderboard can be found on https://benevolent.ai/guacamol .

Speckle noise removal in SAR images using Multi-Objective PSO (MOPSO) algorithm

SAR images are inherently affected by speckle noise, and although attempts made earlier to remove speckle succeeded, there is still the challenge of preserving the edges of images. This is due to the smoothing effect of most of the earlier algorithms that work on thresholding coefficients in the transform domain. There exists a trade-off between denoising and the ability to preserve edges in selecting a suitable threshold. Estimation of an optimal threshold is a major concern and is compounded by the requirement for concurrent smoothing of noise and preservation of structural/edge information in an image. Considering the search for an optimal threshold as exhaustive and the requirements as contradictory, we model this as a Multi-Objective Particle Swarm Optimization (MOPSO) task and propose a MOPSO framework for despeckling an SAR image using a Dual-Tree Complex Wavelet Transform (DTCWT) in the frequency domain. Two counteractive reference metrics, such as Peak Signal-to-Noise Ratio (PSNR) and Mean Structural Similarity Index Metric (MSSIM), and non-reference metrics such as the alpha-beta (αβ) and Despeckling Evaluation Index (DEI) have been used as the objective functions of MOPSO. An optimal threshold derived from this multi-objective optimization is chosen for despeckling the SAR images. The proposed solution has been found to outperform state-of-the-art filters such as Lee, Kaun, Frost and SAR-BM3D filters. Also, the proposed MOPSO framework superior than the competing optimization technique Multi-Objective Evolutionary Algorithm (MOEA) based on Differential Evolution (DE) framework for despeckling.

Efficient Robust Design Optimization of Optical Systems

To accelerate the virtual product development of using optical simulation software, the Robust Design Optimization approach is very promising. Optical designs can be explored thoroughly by means of sensitivity analysis. This includes the identification of relevant input parameters and the modelling of inputs vs. outputs to understand their dependencies and interactions. Furthermore, the intelligent definition of objective functions for an efficient subsequent optimization is of high importance for multi-objective optimization tasks. To find the best trade-off between two or more merit functions, a Pareto optimization is the best choice. As a result, not only one design, but a front of best designs is obtained and the most appropriate design can be selected by the decision maker. Additionally, the best trade-off between output variation of the robustness (tolerance) and optimization targets can be found to secure the manufacturability of the optical design by several advanced approaches. The benefit of this Robust Design Optimization approach will be demonstrated.

The optimality of the standard genetic code assessed by an eight-objective evolutionary algorithm

BackgroundThe standard genetic code (SGC) is a unique set of rules which assign amino acids to codons. Similar amino acids tend to have similar codons indicating that the code evolved to minimize the costs of amino acid replacements in proteins, caused by mutations or translational errors. However, if such optimization in fact occurred, many different properties of amino acids must have been taken into account during the code evolution. Therefore, this problem can be reformulated as a multi-objective optimization task, in which the selection constraints are represented by measures based on various amino acid properties.ResultsTo study the optimality of the SGC we applied a multi-objective evolutionary algorithm and we used the representatives of eight clusters, which grouped over 500 indices describing various physicochemical properties of amino acids. Thanks to that we avoided an arbitrary choice of amino acid features as optimization criteria. As a consequence, we were able to conduct a more general study on the properties of the SGC than the ones presented so far in other papers on this topic. We considered two models of the genetic code, one preserving the characteristic codon blocks structure of the SGC and the other without this restriction. The results revealed that the SGC could be significantly improved in terms of error minimization, hereby it is not fully optimized. Its structure differs significantly from the structure of the codes optimized to minimize the costs of amino acid replacements. On the other hand, using newly defined quality measures that placed the SGC in the global space of theoretical genetic codes, we showed that the SGC is definitely closer to the codes that minimize the costs of amino acids replacements than those maximizing them.ConclusionsThe standard genetic code represents most likely only partially optimized systems, which emerged under the influence of many different factors. Our findings can be useful to researchers involved in modifying the genetic code of the living organisms and designing artificial ones.

A survey of multiple types of text summarization with their satellite contents based on swarm intelligence optimization algorithms

Due to the tremendous increment of data on the web, extracting the most important data as a conceptual brief would be valuable for certain users. Therefore, there is a massive enthusiasm concerning the generation of automatic text summary frameworks to constitute abstracts automatically from the text, web, and social network messages associated with their satellite content. This survey highlights, for the first time, how the swarm intelligence (SI) optimization techniques are performed to solve the text summarization task efficiently. Additionally, a convincing justification of why SI, especially Ant Colony Optimization (ACO), has been presented. Unfortunately, three types of text summarization tasks using SI indicate bit utilizing in the literature when contrasted with the other summarization techniques as machine learning and genetic algorithms, in spite of the fact that there are seriously promising outcomes of the SI methods. On the other hand, it has been noticed that the summarization task with multiple types has not been formalized as a multi-objective optimization (MOO) task before, despite that there are many objectives which can be considered. Moreover, the SI was not employed before to support the real-time summary approaches. Thus, a new model has been proposed to be adequate for achieving many objectives and to satisfy the real-time needs. Eventually, this study will enthuse researchers to further consider the various types of SI when solving the summarization tasks, particularly, in the short text summarization (STS) field.

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

Granulating linguistic information in decision making under consensus and consistency

This study is concerned with group decision making contexts in which linguistic preference relations are used to provide the evaluations of results. On the one hand, granulation of linguistic terms, which are used as entries of the preference relations, is carried out for the purpose of dealing with the linguistic information. Formally, the problem is expressed as a multi-objective optimization task in which a performance index composed of the weighted averaging of the criteria of consensus and consistency is maximized via an appropriate association of the linguistic terms with information granules formed as intervals. On the other hand, once the linguistic terms are made operational by mapping them to the corresponding intervals, a selection process, in which the consistency achieved by each agent is also considered, is employed with intent to construct the solution to the decision problem under consideration. An experimental study is reported by demonstrating the main features of the proposed approach. Furthermore, some drawbacks and advantages are also analyzed.

Multi-stage optimization method for air-intake system of hovercraft based on autonomous optimization

In this study, an optimal structural design program was designed and developed for Computational Fluid Dynamics based on self-optimization, effectively reducing the time required for structural optimization. Through experimental design using this program, the effects of various design variables on the optimization objectives were evaluated, and an adaptive simulated annealing algorithm was used for global optimization. Furthermore, response surface methodology and a nonlinear quadratic programming algorithm were utilized to obtain a global optimum solution after repeated iterations. Moreover, using a hovercraft air-intake system as the optimized object, the total pressure loss of the system was completely optimized by using a porous medium model and Matlab analysis program, and the accuracy of the structural design optimization program was validated. After the global optimization, the total pressure loss of the air-intake system was reduced by 20.5% compared to the original model. An average nonuniformity of 4.36% of engine inlet speed and 5% local nonuniformity of 11.19% satisfy the design requirements of the hovercraft engine. This method can be directly applied to engineering optimization problems as well as multiobjective optimization tasks after improving the relevant methodologies.

Gender approaches to evolutionary multi-objective optimization using pre-selection of criteria

ABSTRACTA novel idea to perform evolutionary computations (ECs) for solving highly dimensional multi-objective optimization (MOO) problems is proposed. Following the general idea of evolution, it is proposed that information about gender is used to distinguish between various groups of objectives and identify the (aggregate) nature of optimality of individuals (solutions). This identification is drawn out of the fitness of individuals and applied during parental crossover in the processes of evolutionary multi-objective optimization (EMOO). The article introduces the principles of the genetic-gender approach (GGA) and virtual gender approach (VGA), which are not just evolutionary techniques, but constitute a completely new rule (philosophy) for use in solving MOO tasks. The proposed approaches are validated against principal representatives of the EMOO algorithms of the state of the art in solving benchmark problems in the light of recognized EC performance criteria. The research shows the superiority of the gender approach in terms of effectiveness, reliability, transparency, intelligibility and MOO problem simplification, resulting in the great usefulness and practicability of GGA and VGA. Moreover, an important feature of GGA and VGA is that they alleviate the ‘curse’ of dimensionality typical of many engineering designs.

Multi objective particle swarm optimization of hybrid micro-grid system: A case study in Sweden

Distributed energy resources DERs are small scale energy system which could provide local supply when placed at customers' premises. They aggregate multiple local and diffuse production installations, consumer facilities, storage facilities and monitoring tools and demand management. The main challenges when assessing the performance of an off-grid hybrid micro-grid system HMGS are the reliability of the system, the cost of electricity production and the operation environmental impact. Hence the tradeoff between three conflicting objectives makes the design of an optimal HMGS seen as a multi-objective optimization task. In this paper, we consider the optimization and the assessment of a HMGS in different Swedish cities to point out the potential of each location for HMGS investment. The HMGS consists of photovoltaic panels, wind turbines, diesel generator and battery storage. The HMGS model was simulated under one-year weather conditions data. A multi objective particle swarm optimization is used to find the optimal system configuration and the optimal component size for each location. An energy management system is applied to manage the operation of the different component of the system when feeding the load. The techno economics analysis shows the potential of HMGS in the Swedish rural development.