Discrete Optimization Research Articles

Cooperative target allocation for heterogeneous agent models using a matrix-encoding genetic algorithm

Heterogeneous platforms collaborate to execute tasks through different operational models, resulting in the task allocation problem that incorporates different agent models. In this paper, we address the problem of cooperative target allocation for heterogeneous agent models, where we design the task-agent matching model and the multi-agent routing model. Since the heterogeneity and cooperativity of agent models lead to a coupled allocation problem, we propose a matrix-encoding genetic algorithm (MEGA) to plan reliable allocation schemes. Specifically, an integer matrix encoding is resorted to represent the priority between targets and agents in MEGA and a ranking rule is designed to decode the priority matrix. Based on the proposed encoding-decoding framework, we use the discrete and continuous optimization operators to update the target-agent match pairs and task execution orders. In addition, to adaptively balance the diversity and intensification of the population, a dynamical supplement strategy based on Hamming distance is proposed. This strategy adds individuals with different diversity and fitness at different stages of the optimization process. Finally, simulation experiments show that MEGA algorithm outperforms the conventional target allocation algorithms in the heterogeneous agent scenario.

Pairwise Distances and the Problem of Multiple Optima.

Discrete optimization problems arise in many biological contexts and, in many cases, we seek to make inferences from the optimal solutions. However, the number of optimal solutions is frequently very large and making inferences from any single solution may result in conclusions that are not supported by other optimal solutions. We describe a general approach for efficiently (polynomial time) and exactly (without sampling) computing statistics on the space of optimal solutions. These statistics provide insights into the space of optimal solutions that can be used to support the use of a single optimum (e.g., when the optimal solutions are similar) or justify the need for selecting multiple optima (e.g., when the solution space is large and diverse) from which to make inferences. We demonstrate this approach on two well-known problems and identify the properties of these problems that make them amenable to this method.

Finite variation sensitivity analysis in the design of isotropic metamaterials through discrete topology optimization

AbstractThis article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

Ship base vibration reduction design technology based on visualization of power flow and discrete optimization

The ship base is a structure that connects the equipment to the hull and may play a role in restraining and isolating the dynamic load. Adding damping on the base to improve the vibration isolation performance is an important measure to control ship vibration. In this research, the energy transfer route and vector cloud of the ship base were analyzed employing the power flow theory, and then the placement of the particle damper was determined. Through the discrete optimization of different particle parameters including the particle material, diameter and filling rate, the best vibration reduction effect was acquired. The simulation and experiment results show that the particle damping has obvious damping effect, and the steel particle has better damping effect than the lead particle and the aluminum particle. The change of particle filling rate influences the vibration characteristics, and the best effect is achieved when the filling rate is 82%. The vibration reduction performance relies strongly on particle diameters, and they all exert obvious vibration suppression effect at the peak acceleration admittance. The proposed discrete optimization strategy effectively saves experiment cost, and the presented particle damper may be traded as an optional scheme in vibration reduce treatment of ship base.

Topological derivative based sensitivity analysis for three-dimensional discrete variable topology optimization

This study introduces a novel Topological Derivative-based Sensitivity Analysis (TDSA) methodology for three-dimensional (3D) discrete variable topology optimization. Recently, the authors pointed out that the discrete variable sensitivity can be related to the topological derivative, and thus can be rationally approximated by the specially customized topological derivative for plane stress problems. However, the 3D discrete variable sensitivity requires the 3D topological derivative with element-shaped (e.g., unit cube) domain perturbation, whose analytical solution is not available in the literature. This paper proposes a unified parameter fitting framework to calculate the 3D topological derivative with arbitrary shape 3D domain perturbation. The formula for spherical hole perturbation obtained through this parameter fitting framework is identical to the well-known analytical topological derivative formula. Further, the 3D discrete variable sensitivity can be easily obtained through element-shaped domain perturbation. With the recently proposed Sequential Approximate Integer Programming (SAIP), numerical examples demonstrate that TDSA is precise not only for the self-adjoint 3D minimum compliance problems but also for the non-adjoint 3D compliant mechanism design problems. In sum, numerical examples have been conducted by feeding the derived sensitivity to the SAIP optimization algorithms, and the correctness of the sensitivity information has been well demonstrated. This research further solidifies the foundation of rational discrete variable sensitivity analysis in 3D topology optimization.

The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems

Many solution algorithms for multiobjective optimization problems are based on scalarization methods that transform the multiobjective problem into a scalar-valued optimization problem. In this article, we study the theory of weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm scalarizations. These methods minimize the distance induced by a weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm between the image of a feasible solution and a given reference point. We provide a comprehensive theory of the set of eligible weights and, in particular, analyze the topological structure of the normalized weight set. This set is composed of connected subsets, called weight set components which are in a one-to-one relation with the set of optimal images of the corresponding weighted p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-norm scalarization. Our work generalizes and complements existing results for the weighted sum and the weighted Tchebycheff scalarization and provides new insights into the structure of the set of all Pareto optimal solutions.

A Dual-Polarization Programmable Metasurface for Green and Secure Wireless Communication.

Dual-polarization programmable metasurfaces can flexibly manipulate electromagnetic (EM) waves while providing approximately twice the information capacity. Therefore, they hold significant applications in next-generation communication systems. However, there are three challenges associated with the existing dual-polarization programmable metasurfaces. This article aims to propose a novel design to address them. First, the design overcomes the challenge of element- and polarization-independent controls, enabling more powerful manipulations of EM waves. Second, by using more energy-efficient tunable components and reducing their number, the design can be nearly passive (maximum power consumption of 27.7mW), leading to a significant decrease in the cost and power consumption of the system (at least two orders of magnitude lower than the power consumption of conventional programmable metasurfaces). Third, the design can operate in a broad bandwidth, which is attractive for practical engineering applications. Both the element and array of the metasurface are meticulously designed, and their performance has been carefully studied. The experiments demonstrate that 2D wide-angle beam scanning can be realized. Moreover, secure communication based on directional information modulation can be implemented by exploiting the metasurface and an efficient discrete optimization algorithm, showing its programmable, multiplexing, broadband, green, and secure features.

A novel path planning approach to minimize machining time in laser machining of irregular micro-holes using adaptive discrete grey wolf optimizer

As an essential technique in fabricating substrates for flexible printed circuit boards, laser drilling of polyimide films facilitates the production of smaller holes of superior quality, which is crucial for preserving the structural integrity and functional reliability of materials. This advanced technology is increasingly critical in sectors demanding high performance, such as high-speed communications and biomedical devices. However, challenges such as the diverse sizes of micro-holes, their irregular placement, and the inherent limitations of scanning components on speed and operational range make efficient and rapid laser drilling a complex endeavor. In this paper, we develop a processing time evaluation model and present a new adaptive discrete grey wolf optimizer (A-D-GWO). The A-D-GWO utilizes exchange, shift, and 2-opt operations to enhance search efficiency and includes an adaptive parameter mechanism, improving its adaptability to various problem sizes and ensuring faster convergence. Experimental results confirmed the algorithm’s effectiveness, reducing processing times by 38.9%, 53.6%, and 55.5% for files containing 90, 286, and 649 holes, respectively. When compared to traditional algorithms, A-D-GWO showed better stability and accuracy, suggesting its suitability for inclusion in laser processing technologies.

Blind parameter identification of implicit differential equations using the collocation discretization and homotopy optimization methods

In this paper, our objectives are to estimate the moments of inertia and reconstruct the inputs of a two-link pendulum that models a human arm. A blind parameter identification routine to determine the inertia properties of human limbs without input data based on a combination of collocation discretization and homotopy optimization is suggested. Without the input data, inertia parameters are structurally unidentifiable. Complementary equations in terms of the ratio of inertia parameters in the cost function and the rate of change of the inputs in the constraints are introduced to make the problem structurally identifiable. Numerous simulations are performed to validate our approach. Experiments to record human upper arm and forearm oscillatory movements were also performed, and moment of inertia terms were evaluated. The significance of the proposed method is that the method can be used to evaluate the moments of inertia of human body segments only from the experimental kinematic data. The advantages of the method are: numerical integration of dynamic and sensitivity equations is avoided and the record of the inputs to the system is not needed.

Integrated optimization of well placement and perforation layer selection using a modified dung beetle algorithm

In the oilfield development process, a proper well pattern plays a crucial role in improving oil recovery and economic benefits. However, traditional well pattern optimization mainly focuses on two-dimensional plane well placement, overlooking the spatial alignment of perforated layers and well placements. This oversight presents significant challenges, especially in meeting the demands for fine development of high water-cut oilfields. Therefore, this paper introduces an innovative approach to well pattern optimization, termed integrated well pattern optimization (WPO–I), which couples well placements with perforation positions. By maximizing net present value, a novel mathematical model for well pattern optimization is established, considering the location of infill wells, the status and type of existing wells, and the perforation position of working wells as co-optimization variables. Besides, an improved discrete dung beetle optimization (IDDBO) algorithm is developed, utilizing multi-layer integer coding and an opposition-based learning strategy. To evaluate the proposed method's performance, the Egg model is used to compare it with five optimization algorithms. Furthermore, this study assesses the development effects of conventional plane well placement optimization (WPO–P) compared to WPO-I. The results highlight the distinct advantages of the IDDBO algorithm in solving discrete nonlinear programming problems. Particularly, the WPO-I method enables spatial matching of the well pattern with reservoir heterogeneity and remaining oil distribution, effectively utilizing spatial residual oil. This method provides a new development optimization strategy in mature oilfields, especially for fine adjustment of well patterns during the secondary recovery stage of water flooding.

A discrete moth-flame optimization algorithm for multiple automated guided vehicles scheduling problem in a matrix manufacturing workshop

The growing need for customized and varied production has highlighted the significance of smart and automated factories in the manufacturing sector. In this particular context, the scheduling of multiple Automated Guided Vehicles (AGVs) plays a pivotal role in enhancing the efficiency of operations within an intelligent manufacturing shop. This study centers on the material handling process within a matrix manufacturing shop with the objective of identifying the most cost-effective transportation routes for materials. To accomplish the specified objective, this research aims to identify an optimal solution for reducing transportation costs. In particular, this study formulates a mixed-integer linear programming model and introduces a novel discrete variant of the moth-flame optimization (MFO) algorithm, named DMFO, to address the scheduling problem. The DMFO algorithm incorporates several significant enhancements. Firstly, a population initialization method is proposed, which combines a nearest-neighbor-based adaptive heuristic and a random sorting technique to ensure the formation of a well-structured population. Secondly, the flame generation mechanism and spiral flight search processes within the MFO have been redefined to achieve a more optimal balance between exploration and exploitation. A neighborhood search mechanism is subsequently devised, employing the concept of neighborhood relevance to accelerate the convergence process. Additionally, a heuristic approach is introduced to reduce the computational cost. Moreover, a population regeneration mechanism is proposed to avoid the algorithm falling into a local optimum. To validate the effectiveness of the DMFO, a comparative analysis is conducted using a dataset of 110 real-world factory instances. In this analysis, eight well-established optimization algorithms are employed. The simulation results consistently demonstrate that the relative percentage deviation (RPD) value of the DMFO tends to approach 0% more closely compared to other algorithms, thereby substantiating the effectiveness of the proposed algorithm.

Fast unsupervised multi-modal hashing based on piecewise learning

Unsupervised hashing has been extensively applied in large-scale multi-modal retrieval by mapping original data from heterogeneous modalities into unified binary codes. However, there still remain challenges especially how to balance the individual modality-specific representations and common representation preserving intrinsic linkages among heterogeneous modalities. In this paper, we propose a novel fast Unsupervised Multi-modal Hashing based on Piecewise Learning, denoted as UMHPL, to deal with the mentioned issue. Initially, we formulate the problem as matrix factorization to derive the individual modality-specific latent representations and common latent representation with consensus matrices in a brief time. To maintain the integrality of multi-modal data, we integrate them by adaptive weight factors and nuclear norm minimization. Subsequently, we establish a connection between the individual modality-specific latent representations and common latent representation based on the piecewise hash learning framework to reinforce the discriminative competency of model, which leads the hash codes more compact. Finally, an effective discrete optimization algorithm in mathematical logic and functional analysis is proposed. Comprehensive experiments on Wiki, MIRFlirck, NUS-WIDE, and MSCOCO datasets demonstrate the superior performance of UMHPL to state-of-the-art hashing methods.

Research on the Human–Robot Collaborative Disassembly Line Balancing of Spent Lithium Batteries with a Human Factor Load

The disassembly of spent lithium batteries is a prerequisite for efficient product recycling, the first link in remanufacturing, and its operational form has gradually changed from traditional manual disassembly to robot-assisted human–robot cooperative disassembly. Robots exhibit robust load-bearing capacity and perform stable repetitive tasks, while humans possess subjective experiences and tacit knowledge. It makes the disassembly activity more adaptable and ergonomic. However, existing human–robot collaborative disassembly studies have neglected to account for time-varying human conditions, such as safety, cognitive behavior, workload, and human pose shifts. Firstly, in order to overcome the limitations of existing research, we propose a model for balancing human–robot collaborative disassembly lines that take into consideration the load factor related to human involvement. This entails the development of a multi-objective mathematical model aimed at minimizing both the cycle time of the disassembly line and its associated costs while also aiming to reduce the integrated smoothing exponent. Secondly, we propose a modified multi-objective fruit fly optimization algorithm. The proposed algorithm combines chaos theory and the global cooperation mechanism to improve the performance of the algorithm. We add Gaussian mutation and crowding distance to efficiently solve the discrete optimization problem. Finally, we demonstrate the effectiveness and sensitivity of the improved multi-objective fruit fly optimization algorithm by solving and analyzing an example of Mercedes battery pack disassembly.

Success-History Based Adaptive Differential Evolution Algorithm for Discrete Structural Optimization

Success-History Based Adaptive Differential Evolution Algorithm for Discrete Structural Optimization

A powerful local government's optimal discretion in simple menu contract of monopoly regulation

We analyse the optimal discretion of a powerful local government (LG) in deciding the instrument choice and setting standards of simple menu contracts (composed of a fixed price and a cost reimbursement) of monopoly regulation. Between the two, a fixed-price contract entails more incentives for efficiency than a cost-reimbursement contract, but ensures more profits for the firm. Due to a preference bias towards the firm's benefits between governments, an incentive reward, offered by the federal government (FG) to the powerful LG with informational advantage of efficiency gain from the regulation, is considered to induce an efficient regulatory policy. We find that under the FG's delegation mechanism, upper-level government conflict leads to a compromised policy as an exchange payoff and additional informational rent to the LG for part of their information value. For the remaining information, the reward is rejected, and the LG has the discretionary power to set policy criteria for simple contracts. The results suggest that bureaucratic political issues still lead to an excessive tendency towards either a fixed price or cost reimbursement scheme, depending on the bias direction of the LG's preferences regarding the monopoly. However, the delegation mechanism of hierarchical bureaucracy can effectively alleviate the influence of policy distortions caused by political factors.

A Probabilistic Reformulation Technique for Discrete RIS Optimization in Wireless Systems

A Probabilistic Reformulation Technique for Discrete RIS Optimization in Wireless Systems

Real-time shape sensing of large-scale honeycomb antennas with a displacement-gradient-based variable-size inverse finite element method

Real-time thermal deformation monitoring plays a crucial role in calibrating phase signals and maintaining satellite performance for large spaceborne antennas. The inverse finite element method (iFEM) represents a promising shape-sensing methodology applicable to monitor the three-dimensional displacement of structures through surface-measured strain. However, the high-accuracy reconstruction of large-scale structures involves a large number of inverse elements, which leads to the low level of computational efficiency. To address this issue, a displacement-gradient-based variable-size iFEM is proposed in this paper. According to the characteristics of deformation, this method optimizes the size of each inverse element to reduce the number of inverse elements required, which improves real-time performance and maintains the high accuracy of reconstruction. The real-time performance of the proposed method is verified by conducting a simulation test on a large-scale honeycomb antenna. According to the simulation results, the variable-size iFEM is applicable to achieve the same accuracy of reconstruction using fewer inverse elements than conventional iFEM. An experimental test is performed and the optimal variable-size discretization that balances accuracy and efficiency is determined. The results show that the maximum error of reconstructed displacement is less than 7.3 % and the reconstruction time is in no excess of 0.1 s.

Systematic solution for multi-model control approaches in nonlinear dynamic systems based on the s-gap metric

This paper proposes a systematic approach for optimizing the distribution of local models in multi-model control systems (MMCS) to enhance overall robustness. While existing literature discusses this method for linear parameter varying (LPV) and uncertain linear time-invariant (LTI) systems, significant limitations persist in addressing nonlinear dynamic systems. Robust control tools like the gap metric and generalized stability margin (GSM) have limited effectiveness in analyzing the robustness of nonlinear feedback systems. To address these challenges, novel concepts of the gap metric and GSM are introduced to determine central operating points (COPs) within local operating areas (LOAs) across the total operating area (TOA). These COPs guide the extraction of affine disturbance local models (ADLMs). Additionally, an optimization problem based on the s-gap metric and GSM is presented to optimize COPs placement and LOAs boundaries. Challenges such as non-monotonic behavior of the cost function and complexity arising from the s-gap metric formulation necessitate novel solution methods. To address these, constraints are applied to the cost function, and a novel discrete optimization approach is introduced. Finally, theoretical findings are applied to the Duffing system, pH neutralization process, and continuous stirred tank reactor (CSTR) plant to evaluate the proposed method's effectiveness. This comprehensive validation across different systems underscores the versatility and practical utility of the proposed approach.

An ultra-weak space-time variational formulation for the Schrödinger equation

We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time Petrov-Galerkin discretization with optimal discrete inf-sup stability.We show norm-preservation of the ultra-weak formulation. The inf-sup optimal Petrov-Galerkin discretization is shown to be asymptotically norm-preserving, where the deviation is shown to be in the order of the discretization. In addition, we introduce a Galerkin discretization, which has suboptimal inf-sup stability but exact norm-preservation.Numerical experiments underline the performance of the ultra-weak space-time variational formulation, especially for non-smooth initial data.

Identifying top-k influential nodes in social networks: a discrete hybrid optimizer by integrating butterfly optimization algorithm with differential evolution

Identifying top-k influential nodes in social networks: a discrete hybrid optimizer by integrating butterfly optimization algorithm with differential evolution