Multi-objective Discrete Optimization Research Articles

Research on multi-objective optimisation of product form design based on kansei engineering

It is crucial to understand and meet the multi-dimensional affective image needs of users for product form in a user demand-oriented product development model. Multi-objective evolutionary algorithms based on decomposition will be introduced into the field of kansei engineering to carry out research on product form optimisation design based on multi-objective evolutionary algorithms. A constrained multi-objective discrete optimisation model was established using the kansei engineering prediction model constructed through machine learning techniques as the objective function, and a reference vector guided evolutionary algorithm was used to solve it. The superiority of this method was verified by comparing it with other commonly used solving methods in this field. Combining entropy weight method and TOPSIS, select the optimisation design scheme that best meets the multi-dimensional affective needs of users from the obtained pareto set. Taking the train as an example, the proposed method was explained. The results indicate that the optimisation scheme obtained by this method can achieve the improvement and optimisation of product form in multiple affective dimensions. Meanwhile, a comparative study on the applicability of multi-objective evolutionary algorithms in the form optimisation problem of different affective dimensions is carried out to provide reference and suggestions for subsequent product design research.

A dual-robot cooperative arc welding path planning algorithm based on multi-objective cross-entropy optimization

In this paper a novel discrete multi-objective cross-entropy optimization (CrMOCEO) algorithm is proposed to solve the path planning problem of dual-robot cooperative arc welding. We strive to find a low-cost, fast and more efficient solution for robotic welding of large complex components. Firstly, an optimization model of dual-robot welding path planning is established by considering various variables and constraints in the actual welding process. Then, three strategies are introduced to improve the multi-objective cross-entropy optimization (MOCEO) algorithm to better solve the discrete path planning problem. Finally, in order to verify feasibility and effectiveness of the proposed algorithm, it is used to solve the 2-, 3-, 5- and 7-objective WFG2–9 problems and plan some typical welding seams of a large complex component, the MOCEO, NSGA-Ⅱ, MOPSO and MOGWO are used for comparison. The simulation demonstrates that the CrMOCEO can obtain better solutions for multiple objectives than the other four algorithms, and the path solved by the CrMOCEO is tested in the Gazebo physical model and workshop site, the results further verified the effectiveness of the CrMOCEO algorithm. Particularly, a series of experiments provide more solutions for actual production.

Modelling and novel multi-level discrete optimization method for vehicle scissor door joint mechanism

An ideal theoretical model integrating four revolute joints is developed to capture the kinematic behaviour of a vehicle scissor door joint mechanism. Then, triaxial acceleration experiments are conducted to validate the effectiveness of the developed theoretical model. Furthermore, to improve dynamic responses of the mechanism, a novel discrete multi-objective optimization (DMO) method is proposed to address optimization problems where design variables cannot be parameterized. This method integrates the Taguchi method, grey relational analysis and a hybrid multi-objective decision-making approach, and iteratively updates the orthogonal array to perform optimization for handling design variables with multiple levels. Compared to the conventional non-dominated sorting genetic algorithm-II (NSGA-II), the developed DMO is capable of achieving the Pareto frontier with fewer evaluations of the objective function. The optimization results reveal that the optimized design for the electric and gas struts exhibits favourable dynamic responses of scissor door operation compared to the initial design.

Optimization of formworks shoring location as a continuous optimization problem

For the construction of reinforced concrete buildings, partial striking of props and formworks a few days after casting is frequently employed, confirming its safety based on structural calculations or analyses to improve the construction productivity. Three-dimensional finite element (FE) models are sometimes used for these kinds of structural analyses to obtain precise results. However, considerable effort is required to determine the remaining prop arrangement by trial and error via FE analysis because of time-consuming operations. This study presents continuous optimization methods for the determination of the arrangement of remaining props that can speedily provide a single valid solution based on design sensitivity; the solution guarantees local optimality. Continuous optimizations employ a function that transforms the continuous design variables into the number of remaining props at each candidate location that is inherently represented by integer values. The optimization problems have been formulated in two forms: one is to maximize the safety of the structure, and the other is to minimize the number of remaining props. These optimization methods provided valid local optimal solutions that could reduce the amount of material required for formwork and shoring by almost half within a realistic calculation time. In addition, compared with multi-objective discrete optimization by a genetic algorithm, the first method provided the optimal solution with less than half the number of FE analyses of discrete method, and the second method provided a more efficient solution than the discrete method with a total of 10,000 individuals.

Multi-scale adaptive multivariate state estimation fault detection enhancement for time-varying industrial system based on multi-output Gaussian process autoregression

Most chemical processes are time-varying and nonlinear due to load changes, product demand transitions or other causes, causing unsatisfactory performance of conventional non-parametric multivariate statistical fault detection method. In this work, a probabilistic multivariate state estimation fault detection method based on multi-output Gaussian process autoregression is first developed to overcome the linear limitation and noise information ignorance of multivariate state estimation technology-based fault detection methods. In multi-output Gaussian process regression framework, the Leave-One-Sample-Out strategy is developed to construct the dataset by leaving each historical sample from the memory matrix out as one training output in turn while regarding the corresponding remaining historical samples as one training input. Then, we design the multi-output Gaussian process autoregression model to estimate the current state of the system. Utilizing the estimation covariance information, a probabilistic index based on multivariate Kullback-Leibler divergence is developed for fault detection. Moreover, a multi-scale adaptive fault detection enhancement based on discrete multi-objective Archimedes optimization and just-in-time learning is further proposed to handle the time-varying problem. In this scheme, the memory matrix is batch-adaptively updated at monthly intervals based on discrete multi-objective Archimedes optimization to handle the slow change of system characteristics caused by equipment degradation. On the other hand, to cope with the rapid change of system characteristics caused by operation transition, the just-in-time learning is employed to select samples from the memory matrix that best match to the current system state for sample-adaptive updating. Finally, two industrial cases are used to verify the performance of the proposed method.

Self-calibration algorithm for installation angle deviation of bionic polarization compound eyes.

A self-calibration algorithm based on unsupervised optimization for polarizer installation angle deviation is proposed and used in a multi-aperture bionic polarization compound eye system. To simplify calibration operation, under the condition that the calibration-polarized light information is unknown, this algorithm fully exploits redundancy and random polarization information in the scene, and uses a non-convex multi-objective discrete parameter sorting optimization method to achieve angle self-calibration. Compared with ordinary calibration procedures, the algorithm requires less stringent conditions, achieves online calibration and is more accurate. It also can be applied to camera polarization arrays, division-of-focal-plane polarization cameras, and other polarization devices.

A novel Physarum-inspired competition algorithm for discrete multi-objective optimisation problems

Many real-world problems can be naturally formulated as discrete multi-objective optimisation (DMOO) problems. We have proposed a novel Physarum-inspired competition algorithm (PCA) to tackle these DMOO problems. Our algorithm is based on hexagonal cellular automata (CA) as a representation of problem search space and reaction–diffusion systems that control the Physarum motility. Physarum’s decision-making power and the discrete properties of CA have made our algorithm a perfectly suitable approach to solve DMOO problems. Each cell in the CA grid will be decoded as a solution (objective function) and will be regarded as a food resource to attract Physarum. The n-dimensional generalisation of the hexagonal CA grid has allowed us to extend the solving capabilities of our PCA from only 2-D to n-D optimisation problems. We have implemented a novel restart procedure to select the global Pareto frontier based on both personal experience and shared information. Extensive experimental and statistical analyses were conducted on several benchmark functions to assess the performance of our PCA against other evolutionary algorithms. As far as we know, this study is the first attempt to assess algorithms that solve DMOO problems, with a large number of benchmark functions and performance indicators. Our PCA has confirmed our assumption that individual skills of competing Physarum are more efficient in exploration and increase the diversity of the solutions. It has achieved the best performance for the Spread indicator (diversity), similar performance results compared to the strength Pareto evolutionary algorithm (SPEA2) and even outperformed other well-established genetic algorithms.

Comprehensive Utilization Model of Yarlung Zangbo River Water Resources Based on Discrete Multi-objective Optimization Model

The Yarlung Zangbo River is rich in water resources, which is of great significance to the comprehensive utilization of water resources. The reasonable development of the hydropower resources of the Yarlung Zangbo River is realized, through the water diversion project and the establishment of the trapezoidal hydropower station. A comprehensive utilization model of hydropower resources optimized by discrete objectives is constructed, based on the discrete multi-objective optimization theory. It combined with the reading of geographic data by GPS and Matlab. The number and orientation of the optimal construction of hydropower stations and the proportion of the water transfer volume of the water diversion project are obtained, combining the cost of hydropower station construction and water diversion project implementation and the benefits brought by hydropower resources.

Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems

Scalarization is a common technique to transform a multiobjective optimization problem into a scalar-valued optimization problem. This article deals with the weighted Tchebycheff scalarization applied to multiobjective discrete optimization problems. This scalarization consists of minimizing the weighted maximum distance of the image of a feasible solution to some desirable reference point. By choosing a suitable weight, any Pareto optimal image can be obtained. In this article, we provide a comprehensive theory of this set of eligible weights. In particular, we analyze the polyhedral and combinatorial structure of the set of all weights yielding the same Pareto optimal solution as well as the decomposition of the weight set as a whole. The structural insights are linked to properties of the set of Pareto optimal solutions, thus providing a profound understanding of the weighted Tchebycheff scalarization method and, as a consequence, also of all methods for multiobjective optimization problems using this scalarization as a building block.

A NSGA-II based approach for multi-objective optimization of a reconfigurable manufacturing transfer line supported by Digital Twin: A case study

In response to the wide range of customer demands, the concept of reconfigurable manufacturing systems (RMS) was introduced in the industrial sector. RMS enables producers to meet varying volumes of demand over varying time periods by swiftly adjusting its production capacity and functionality within a part family in response to abrupt market changes. In these circumstances, RMS are made to swiftly reconfigure their Reconfigurable Machine Tools (RMTs). RMTs are designed to have a variety of configurations that may be conditionally chosen and reconfigured in accordance with specific performance goals. However, the reconfiguration process is not an easy process, which entails optimization of several objectives and many of which are inherently conflictual. As a result, it necessitates real-time monitoring of the RMS's condition, which may be achieved by digital twinning, or the real-time capture of system data. The concept of using a digital replica of a physical system to provide real-time optimization is known as digital twin. This work considered a case study of discrete parts manufacturing on a reconfigurable single manufacturing transfer line (SMTL). Six manufacturing operations are required to be performed on the parts at six production stages. This work uses the Digital Twin (DT) based approach to assist a discrete multi-objective optimization problem for a reconfigurable manufacturing transfer line. This multi-objective optimization problem consists of four objective functions which is illustrated by using DT-based Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The innovative aspect of the current study is the use of a DT-based framework for RMS reconfiguration to produce the best optimum solutions. The produced real-time solutions will be of great assistance to the decision maker in selecting the appropriate real-time optimal solutions for reconfigurable manufacturing transfer lines.

FERN: Fair Team Formation for Mutually Beneficial Collaborative Learning

Automated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">team formation</i> is becoming increasingly important for a plethora of applications in open-source community projects, remote working platforms, as well as online educational systems. The latter case, in particular, poses significant challenges that are specific to the educational domain. Indeed, teaming students aims to accomplish far more than the successful completion of a specific task. It needs to ensure that all the members in the team benefit from the collaborative work, while also ensuring that the participants are not discriminated against with respect to their protected attributes, such as race and gender. Toward achieving these goals, this article introduces <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FERN</monospace> , a fair team formation approach that promotes mutually beneficial peer learning, dictated by protected group fairness as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equality of opportunity</i> in collaborative learning. We formulate the problem as a multi-objective discrete optimization problem. We show this problem to be NP-hard and propose a heuristic hill-climbing algorithm. Extensive experiments on both the synthetic and real-world datasets against well-known team formation techniques show the effectiveness of the proposed method.

Stochastic Hybrid Discrete Grey Wolf Optimizer for Multi-Objective Disassembly Sequencing and Line Balancing Planning in Disassembling Multiple Products

Recycling, reusing, and remanufacturing of end-of-life (EOL) products have been receiving increasing attention. They effectively preserve the ecological environment and promote the development of economy. Disassembly sequencing and line balancing problems are indispensable to recycling and remanufacturing EOL products. A set of subassemblies can be obtained by disassembling an EOL product. In practice, there are many different types of EOL products that can be disassembled on a disassembly line, and a high-level uncertainty exists in the disassembly process of those EOL products. Hence, this paper proposes a stochastic multi-product multi-objective disassembly-sequencing-line-balancing problem aiming at maximizing disassembly profit and minimizing energy consumption and carbon emission. A simulated annealing and multi-objective discrete grey wolf optimizer with a stochastic simulation approach is proposed. Furthermore, real cases are used to examine the efficiency and feasibility of the proposed algorithm. Comparisons with multi-objective discrete grey wolf optimization, non-dominated sorting genetic algorithm II, Multi-population multi-objective evolutionary algorithm, and multi-objective evolutionary algorithm demonstrate the superiority of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Disassembly line balancing has been widely recognized as the most ecological way of retrieving EOL products. Through in-depth research, we present a Stochastic Multi-product Multi-objective Disassembly-sequencing-line-balancing Problem. Furthermore, we consider that the uncertainty of products might cause disassembly failure. To solve this problem effectively and quickly, we combine the simulated annealing algorithm with the Grey Wolf Optimizer. The results show that the algorithm can effectively solve the proposed problem. The disassembly scheme provided by the obtained solution set offers a variety of options for decision-makers.

Integrating Energy Smart Grid’s ontologies through multi-objective particle swarm optimization algorithm with competitive mechanism

Smart city seeks safer, resource-oriented, environment friendly, and cost-effective energy solutions, and due to the distributed and independent nature of energy management systems, Energy Smart Grid (ESG) quickly evolves from a widely accepted concept to an industrial reality. To monitor the energy consumption across various domains and assist efficient energy distribution and storage, it is necessary to integrate various ESG agents’ ontologies. To this end, this work models ESG’s Ontology Matching Problem (ESG-OMP) as a discrete Multi-Objective Optimization Problem (MOOP), which simultaneously optimizes the alignment’s completeness and correctness through determining an optimal entity corresponding set. After that, a Multi-Objective Particle Swarm Optimization Algorithm With Competitive Mechanism (MOPSO-CM) is proposed to address this issue by trading off the alignment’s completeness and correctness, which introduces the CM to update the particles with the pairwise competition that performed in the swarm of current generation. Moreover, an instance-based hybrid similarity measure is used to distinguish the heterogeneous ontology entities. The experiment uses OAEI’s testing datasets, 13 smart grid’s ontology matching tasks and 5 energy smart grid’s ontology matching tasks to test MOPSO-CM’s performance. The experimental results show that MOPSO-CM can effectively address various heterogeneous ontology matching problems and determine high-quality ESG’s ontology alignments.

Thermal performance revival of composite PCM for hybrid BTMSs by architecture and formula integrated optimization

Composite phase change material (CPCM) cooling is an essential method to ensure better performance of battery thermal management system (BTMS) due to high latent heat. However, long recovery time of CPCM makes it unaffordable especially during continuous high rate discharge–charge cycles. In order to reduce the energy consumption while enhancing the latent heat recovery efficiency, a novel hybrid BTMS architecture coupling with CPCM and liquid cooling is proposed. Liquid cooling is employed to recover the latent heat of PCM. To enhance the heat transfer in BTMS, the structural layout of liquid cooling arrangement is investigated. Meanwhile, mass fraction of expanded graphite (EG) and bulk density of CPCM are considered. Specially, the experiments are conducted to verify the effectiveness of present hybrid BTMS. In solidification, temperature performance especially temperature uniformity is not ideal. Therefore, a novel successive multiple attribute decision making (MADM) algorithm is employed to achieve optimized temperature difference, maximum temperature, solidification rate and mass of CPCM. In MADM algorithm, the order preference by similarity to ideal solution (TOPSIS) is coupled with the analytic hierarchy process (AHP) to solve the multi-objective discrete optimization problem. Results indicate that the optimal solution can make the maximum temperature and temperature difference at the lowest level of 317.51 K and 3.45 K at discharge rate of 4C. Meanwhile, the latent heat of CPCM is improved by about 27.5% at charge rate of 2C. The solution can improve the long-term reliability for the BTMS and the safety and service life for battery module.

A Discrete Moth-Flame Optimization With an $l_2$-Norm Constraint for Network Clustering

Complex network clustering problems have been gained great popularity and widespread researches recently, and plentiful optimization algorithms are aimed at this problem. Among these methods, the optimization methods aiming at multiple objectives can break the limitations (e.g., instability) of those optimizing single objective. However, one shortcoming stands out that these methods cannot balance the exploration and exploitation well. In another sentence, it fails to optimize solutions on the basis of the good solutions obtained so far. Inspired by nature, a new optimized method, named multi-objective discrete moth-flame optimization (DMFO) method is proposed to achieve such a tradeoff. Specifically, we redefine the simple flame generation (SFG) and the spiral flight search (SFS) processes with network topology structure to balance exploration and exploitation. Moreover, we present the DMFO in detail utilizing a Tchebycheff decomposition method with an <inline-formula><tex-math notation="LaTeX">$l_2$</tex-math></inline-formula>-norm constraint on the direction vector (2-Tch). Besides that, experiments are taken on both synthetic and real-world networks and the results demonstrate the high efficiency and promises of our DMFO when tackling dividing complex networks.

A multiobjective discrete combination optimization method for dynamics design of engineering structures

AbstractThis paper presents a new multiobjective discrete optimization method for the engineering design of dynamic problems. A discrete combinatorial optimization problem is solved using a particle swarm optimization algorithm coupled with a stair‐form interpolation model. To address multiobjective optimization issues, a weighted average approach is implemented to convert the multiobjective optimization problem into an equivalent single‐objective optimization problem. Design constraints are taken into consideration by using the penalty function strategy. The proposed method is first verified with a 10‐bar truss structure design problem, where the cross‐sectional area of each bar is optimized to minimize both volume and node displacement. Second, the dynamic issue for hybrid composite laminates is investigated by maximizing the fundamental frequency and minimizing the cost. The results reveal that the optimized results generated by the proposed method agree well with those from other approaches.

Asynchronous parallel disassembly sequence planning method of complex products using discrete multi-objective optimization

Disassembly is a necessary link to realize the integrity of product life cycle. Asynchronous Parallel Disassembly (APD) is an important way to achieve efficient disassembly. Due to the asynchronous start of disassembly tasks by operators in APD, the calculation complexity of disassembly sequence planning optimization increases more obviously with the increase of product complexity. Further, the disassembly sequence is a discrete numerical value, which is difficult to be efficiently realized by existing optimization algorithms. To overcome these difficulties, we introduced a complex products APD description. It helped to describe the APD problem with multiple disassembly resources. Based on the APD resources overall matrix, a three-objective, viz., the total disassembly time-consuming, the disassembly direction change times, and the disassembly tools replacement times, optimization model was constructed. To obtain the optimal disassembly planning sequence, the improved discrete NSGA-II (IDNSGA-II) was proposed, which introduced a novel population restart mechanism. The proposed method was verified in a bevel gearbox disassembly process from the EAS4633 rescue inspection equipment. The optimal results showed the APD sequence planning multi-objective optimized results obtained by the IDNSGA-II algorithm can be close to the single object optimized results. For the rest objects, the optimal solution obtained from the multi-objective genetic algorithm is obviously better.

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Constrained Multi-Objective Optimization of Simulated Tree Pruning with Heterogeneous Criteria

Virtual pruning of simulated fruit tree models is a useful functionality provided by software tools for computer-aided horticultural education and research. It also enables algorithmic pruning optimization with respect to a set of quantitative objectives, which is important for analytical purposes and potential applications in automated pruning. However, the existing studies in pruning optimization focus on a single type of objective, such as light distribution within the crown. In this paper, we propose the use of heterogeneous objectives for discrete multi-objective optimization of simulated tree pruning. In particular, the average light intake, crown shape, and tree balance are used to observe the emergence of different pruning patterns in the non-dominated solution sets. We also propose the use of independent constraint objectives as a new mechanism to confine overfitting of solutions to individual pruning criteria. Finally, we perform the comparison of NSGA-II, SPEA2, and MOEA/D-EAM on this task. The results demonstrate that SPEA2 and MOEA/D-EAM, which use external solution archives, can produce better sets of non-dominated solutions than NSGA-II.

A Multiobjective Discrete Grey Wolf Optimization Approach for Transactional and QoS-driven Web Services Composition

ABSTRACT Web services facilitate reusability that allows cost-effective development of business applications using web services composition. Due to the proliferation of web services, different service providers are providing similar functionality web services. But these web services can have different values for QoS attributes and transactional properties. Thus, it is difficult to build a transactional and QoS optimal composite web service. Most of the existing works used the scalarization-based method for selecting optimal composite web service. In the scalarization-based method, the service user should have a priori knowledge of its preferences about the nonfunctional requirements of desired solutions. This paper proposes a Multiobjective Discrete Grey Wolf Optimization (MDGWO)-based approach for Transactional and QoS-driven Web Services Composition. The Pareto dominance concept is used to select optimal composite web service. Generational Distance (GD), Inverse Generational Distance (IGD), and Spread measures are used to evaluate the performance of the proposed approach. Experimental results indicate that the proposed approach performs well.