Discrete Constraints Research Articles

Nonlinear strategic human resource management based on organisational mathematical model

Abstract Human resource management organisation's goal must be achieved by regulating employee behaviour through a restraint system. We conduct quantitative research on employee behaviour under organisational constraints, which is an essential means to ensure the organisation's healthy and stable development. The employees themselves adapt to the organisational goals, obey the organisation's constraint system and allocate their resources so that there is less research on optimising their behaviour. This article briefly reviews the research and application of economic theory, organisational behaviour, human resource management and other aspects of optimising employee resource allocation behaviour. The thesis defines organisational resources and divides them into three types. Based on the constraint system, we turn the organisation's control, requirements or incentives on employee behaviour into above or below employee operating constraints; we believe that the constraint system has the characteristics of discrete and hanging river effects, and we have obtained an evaluation. Two algorithms of the organisational constraint system. The article discusses employee resources and behaviours. At the same time, it attempts to construct a quantitative model based on the employee's multi-objective, nonlinear, continuous and discrete constraints, on the allocation of resources and behaviour optimisation and on the employee's adaptation to the organisational constraints. Under the premise of optimisation, several situations in which the model solves the optimal solution are studied. The research found that this article can fill the gaps in employees’ self-adaptation to organisational goals and behaviour optimisation quantitative models.

Robust Beamforming for RIS-Assisted Wireless Communications With Discrete Phase Shifts

In this letter, we study the robust beamforming design for the reconfigurable intelligent surface (RIS)-assisted communication systems from a multi-antenna access point (AP) to a single-antenna user under imperfect channel state information (CSI), where the RIS has only a finite number of phase shifts at each element. In particular, considering the cascaded AP-RIS-user channel estimation error, we aim to jointly optimize the transmit beamforming at the AP and discrete phase shifts of RIS to minimize the transmission power of AP, subject to a signal-to-noise ratio constraint at the user. To tackle the non-convex optimization problem, we decouple it into two subproblems and propose a novel alternative optimization framework. More specifically, the robust beamforming of AP is first obtained through S-Procedure and semidefinite relaxation. Then we recast the discrete phase shift constraint at RIS into an equivalent convex one, and propose an efficient algorithm to obtain a near optimal solution. Finally, the two subproblems are iteratively optimized to obtain joint robust beamforming. Simulation results show that the proposed scheme can approach the performance of the perfect CSI counterpart and substantially outperform traditional non-robust methods.

A MILP model for optimal renewable wind DG allocation in smart distribution systems considering voltage stability and line loss

This paper introduces a new model for optimal wind distributed generation (WDG) allocation based on mixed integer linear programming (MILP) in todays' smart grids considering on-load tap changing (OLTC) and power factor control (PFC) strategies. The objectives of the proposed optimization model are improving voltage stability and energy loss minimization subject to power flow constraints, line thermal limits, maximum number and size of WDG units, penetration limit, discrete OLTC tap position constraints, and PFC constraints. An efficient voltage phasor-information-based probabilistic voltage stability index (VSI) is extracted to measure the improvement of voltage stability with WDGs. Besides energy losses, reduction index is used to measure the energy loss reduction with the integration of renewable WDGs in the distribution system. An efficient linearized power flow (LPF) model as well as piecewise linearized model of the quadratic terms associated to the PFC constraints are represented to convert the original nonconvex problem into the form of a well-known MILP problem, which guarantees optimal solution and computationally is efficient to be solved using powerful commercial solvers. The effectiveness and validity of proposed model is investigated in compared to the state-of-the-art population-based methods and classical models.

An improved mixed-coded hybrid firefly algorithm for the mixed-discrete SSCGR problem

Reducers play a particularly important role in mechanical transmission field, and even a slight reduction in the material consumption would bring considerable economic and social benefits. With the goal of the minimum volume of consumables, a general mathematical model for the widely used single-stage cylindrical gear reducer (SSCGR), is established. When some real and discrete parameters are selected as the design variables, the SSCGR problem becomes a mixed-discrete SSCGR problem. To minimize the mixed-discrete SSCGR problem and make discrete design variables always satisfy discrete constraints, an improved mixed-coded hybrid firefly algorithm (IMCHFA) is proposed. The proposed approach uses new mixed-coded method to encode the position structure, and uses sorting group selection to select paired fireflies for position update, then uses combinatorial mutation to accelerate convergence of the algorithm. Meanwhile, the rounding technique is adopted to make the position structure meet the coding rules. 28 modified CEC 2017 mixed-discrete problems and two practical mixed-discrete engineering optimization problems are tested by the IMCHFA and other improved algorithms. The results show that the solution quality of IMCHFA is significantly better than other improved algorithms examined in this study. Finally, the proposed IMCHFA is applied to optimize the mixed-discrete SSCGR problem. Compared to the solution quality of other improved algorithms examined in this study, the proposed IMCHFA can obtain more efficient and economic solutions.

Discrete Semantics-Guided Asymmetric Hashing for Large-Scale Multimedia Retrieval

Cross-modal hashing technology is a key technology for real-time retrieval of large-scale multimedia data in real-world applications. Although the existing cross-modal hashing methods have achieved impressive accomplishment, there are still some limitations: (1) some cross-modal hashing methods do not make full consider the rich semantic information and noise information in labels, resulting in a large semantic gap, and (2) some cross-modal hashing methods adopt the relaxation-based or discrete cyclic coordinate descent algorithm to solve the discrete constraint problem, resulting in a large quantization error or time consumption. Therefore, in order to solve these limitations, in this paper, we propose a novel method, named Discrete Semantics-Guided Asymmetric Hashing (DSAH). Specifically, our proposed DSAH leverages both label information and similarity matrix to enhance the semantic information of the learned hash codes, and the ℓ2,1 norm is used to increase the sparsity of matrix to solve the problem of the inevitable noise and subjective factors in labels. Meanwhile, an asymmetric hash learning scheme is proposed to efficiently perform hash learning. In addition, a discrete optimization algorithm is proposed to fast solve the hash code directly and discretely. During the optimization process, the hash code learning and the hash function learning interact, i.e., the learned hash codes can guide the learning process of the hash function and the hash function can also guide the hash code generation simultaneously. Extensive experiments performed on two benchmark datasets highlight the superiority of DSAH over several state-of-the-art methods.

A new multi-material topology optimization algorithm and selection of candidate materials

With the availability of multi-material additive manufacturing, topology optimization of a multi-material structure and the selection of candidate materials become increasingly important. This paper aims to develop a new multi-material topology optimization algorithm and propose the guidelines for the selection of candidate materials from the database. The multi-material design variables and their inequality relationship are built on volume fractions of multiple materials within each element. The multi-material design variables are relaxed and multiple floating projection constraints simulate their discrete constraints by pushing design variables towards 0 or 1. Meanwhile, their inequality relationship is enforced by their variation limits. The proposed multi-material topology optimization algorithm can be applied to the compliance minimization problem constrained by a single mass or multiple volumes, as demonstrated in numerical examples. This paper mainly focuses on a single mass constraint, and 2D and 3D numerical examples systematically demonstrate that an optimized design under a mass constraint achieves a lower compliance when more materials appear in the final design simultaneously. Furthermore, we establish an approach to predict the inclusion or exclusion of a material from the final design, and propose the conditions for the co-existence of candidate materials, which guide users to select candidate materials from the database.

Graph matching based on fast normalized cut and multiplicative update mapping

Point correspondence is a fundamental problem in pattern recognition and computer vision, which can be tackled by graph matching. Since graph matching is basically an NP-complete problem, some approximate methods are proposed to solve it. Continuous relaxation offers an effective approximate method for graph matching problem. However, the discrete constraint is not taken into consideration in the optimization step. In this paper, a fast normalized cut based graph matching method is proposed, where the discrete constraint is introduced into the optimization step. Specifically, first a semidefinite positive affinity matrix based form objective function is constructed by introducing a regularization term which is related to the discrete constraint. Then the fast normalized cut algorithm is utilized to find the continuous solution. Last, the discrete solution of graph matching is obtained by a multiplicative update algorithm. Experiments on both synthetic points and real-world images validate the effectiveness of the proposed method by comparing it with the state-of-the-art methods.

Generic stacks and application of composite rules for the detailed sizing of laminated structures

Two-stage approaches are commonly applied to optimise the stacking sequence of large-scale composite structures. The two stages consist of a gradient and non-gradient based optimisation addressing the mixed nature of continuous and discrete constraints and design variables of the detailed sizing of laminated structures. For the two-stage process to be successful, all constraints from both stages should be fulfilled eventually. This study employs generic stacks to model the thickness and stiffness distribution of the structure. A generic stack is comprised of a collection of layers whose orientations are fixed a priori, but thicknesses can vary independently enabling exploration of the design space. To achieve a ‘right first time’ implementation and avoid burdensome iterations over both stages, a maximum amount of discrete design and manufacturing constraints should be considered in the gradient-based optimisation stage. A special attention is paid to the continuity or blending constraint which can be formulated precisely using generic stacks. The results for a benchmark case show that the introduced two-stage approach can, not only satisfy all imposed constraints in a single iteration of the overall two-stage process but also yield a lower structural mass when compared to equivalent previously proposed approaches.

Optimum design of sewer networks with pump station using Genetic Algorithms

The main aim of the current study is to develop a new model for the minimum cost of optimum design for a sewer network with pumping stations. The difficulty and relatively large number of nonlinear and discrete constraints in a sewer network with pump station design problems make their handling of extreme importance. For this purpose, an adaptive genetic algorithm (GA) model is proposed for the effective and efficient optimal design with a fixed layout so that each chromosome, consists of diameters, slopes of the pipes and pump indicators. In the present model, the pump locations are decided preliminary, then for each GA chromosome, the network characteristics including the diameters of pipes and slope for those pipes are determined. MATLAB code was used to perform the optimization model. Then a sewer network from previous literature was used to be designed as a benchmark example for the proposed method. It’s concluded that the proposed model has reached the optimal solution at the lowest cost and the fewest number of generations compared with previous methods in the literature.

Integrating stochastic discrete constraints in MPC. Application to Home Energy Management System

In this paper, in a Model Predictive Control problem, we tackle the integration of uncertain constraints that belong to a discrete set. We propose a controller that offers a solution to reformulate the discrete stochastic constraints to avoid the exponential growth of scenario tree experienced by existing controllers. The proposed controller’s efficiency is shown by benchmarking and comparing it with the Multistage Stochastic Programming algorithm in a context of Home Energy Management System. The comparison is made based on simulations using real-life data to manage the energy flow within a building connected to the electricity feeder, which random character involves its availability and nonavailability.

Learning to hash based on angularly discriminative embedding

Hashing, a widely-studied tool to the approximate nearest neighbor search, aims to embed samples as compact binary representations. Current approaches to this issue generally seek a low-dimensional Hamming Space where representations are discrete and have smaller intra-class distance and larger inter-class distance. As a result, the performance is often limited by the discrete constraint. In this work, we propose to seek an angularly discriminative Embedding Space where representations are continuous and have smaller intra-class angular margin and larger inter-class angular margin. For our goal is to learn continuous representations rather than discrete hash codes, the problems caused by discrete constraint can be avoided. Besides, in order to further reduce the gap between Embedding Space and Hamming Space, we introduce an additional coordinate-constraint for representations. Our method is simple yet effective. Extensive experiments on the image retrieval task show that it achieves encouraging results on four benchmark datasets. Furthermore, the success of our proposed method demonstrates that leveraging the progress made in representation learning to improve hashing is promising in future.

Transmit beampattern synthesis for MIMO radar with one-bit digital-to-analog converters

This paper considers the problem of transmit beampattern synthesis (i.e., transmit beamforming) in multiple-input multiple-output (MIMO) radar which deploys one-bit digital-to-analog converts (DACs). By appropriately designing the transmitted signal waveforms quantized by one-bit DACs, the majority of radiated energy can be focused into the mainlobe(s) region to enhance the intensity of backscattered signals from targets. Meanwhile, the amount of energy inevitably leaked into the sidelobe region is minimized to suppress the interferences. More specifically, the essence of the proposed design can be regarded as optimizing the one-bit signal waveforms such that the synthesized transmit beampattern has a minimum integrated-sidelobe-to-mainlobe ratio (ISMR). In order to tackle the nonconvex discrete constraint in the resulting optimization problem, we propose to introduce auxiliary variables to reformulate the discrete constraint into continuous constraints. On this basis, the alternating direction multiplier method (ADMM) framework is applied to deal with the reformulated problem. The proposed method can approximately solve the sub-problems with closed-form solutions in each iteration, and hence, it is computationally efficient. Simulation results indicate that the proposed method is able to provide promising performance.

Efficient inversion of 2.5D electrical resistivity data using the discrete adjoint method

We have developed a memory and operation-count efficient 2.5D inversion algorithm of electrical resistivity (ER) data that can handle fine discretization domains imposed by other geophysical (e.g, ground penetrating radar or seismic) data. Due to numerical stability criteria and available computational memory, joint inversion of different types of geophysical data can impose different grid discretization constraints on the model parameters. Our algorithm enables the ER data sensitivities to be directly joined with other geophysical data without the need of interpolating or coarsening the discretization. We have used the adjoint method directly in the discretized Maxwell’s steady state equation to compute the data sensitivity to the conductivity. In doing so, we make no finite-difference approximation on the Jacobian of the data and avoid the need to store large and dense matrices. Rather, we exploit matrix-vector multiplication of sparse matrices and find successful convergence using gradient descent for our inversion routine without having to resort to the Hessian of the objective function. By assuming a 2.5D subsurface, we are able to linearly reduce memory requirements when compared to a 3D gradient descent inversion, and by a power of two when compared to storing a 2D Hessian. Moreover, our method linearly outperforms operation counts when compared with 3D Gauss-Newton conjugate-gradient schemes, which scales cubically in our favor with respect to the thickness of the 3D domain. We physically appraise the domain of the recovered conductivity using a cutoff of the electric current density present in our survey. We evaluate two case studies to assess the validity of our algorithm. First, on a 2.5D synthetic example, and then on field data acquired in a controlled alluvial aquifer, where we were able to match the recovered conductivity to borehole observations.

Adaptive sampling point planning for free-form surface inspection under multi-geometric constraints

Free-form surfaces have been widely used in aerospace, automotive and other fields. Due to its complex geometry, free-form surface inspection is generally conducted by touch-trigger or measuring probe-based Coordinate Measurement Machines or On-machine Measurement. Sampling strategy plays a decisive role in improving both measurement accuracy and efficiency, which is determined by sample size and distribution of sample points. However, it is difficult to simultaneously take the surface curvature, sampling density and approximation error into account, considering the complexity of surface geometry. In this paper, triangle mesh simplification is innovatively adopted in sampling planning to achieve multi-geometric constraints. As triangle mesh has outstanding advantages in representing the surface features, strong stability and is easy to modify its structure, free-form surface is converted to a dense triangle mesh. Triangle mesh simplification is implemented by iteratively contracting triangle edges. An improved quadric error metric is established to decide contraction order and optimal target vertices under discrete curvature constraint. Sampling density is controlled by limiting the triangle edge length. Detailed adaptive sampling algorithm under multi-geometric constraints is then developed. Both simulation and experiment are conducted to validate feasibility and robustness of the proposed method. The results are compared with uniform sampling and existing adaptive sampling strategy to show that the proposed method can prominently reduce sampling error when sample size is small.

A Two-Stage Offline-to-Online Multiobjective Optimization Strategy for Ship Integrated Energy System Economical/ Environmental Scheduling Problem

The economical/environmental scheduling problem (EESP) of the ship integrated energy system (SIES) has high computational complexity, which includes more than one optimization objective, various types of constraints, and frequently fluctuated load demand. Therefore, the intelligent scheduling strategies cannot be applied to the ship energy management system (SEMS) online, which has limited computing power and storage space. Aiming at realizing green computing on SEMS, in this paper a typical SIES-EESP optimization model is built, considering the form of decision vectors, the economical/environmental optimization objectives, and various types of real-world constraints of the SIES. Based on the complexity of SIES-EESPs, a two-stage offline-to-online multiobjective optimization strategy for SIES-EESP is proposed, which transfers part of the energy dispatch online computing task to the offline high-performance computer systems. The specific constraints handling methods are designed to reduce both continuous and discrete constraints violations of SIES-EESPs. Then, an establishment method of energy scheduling scheme-base is proposed. By using the big data offline, the economical/environmental scheduling solutions of a typical year can be obtained and stored with more computing resources and operation time on land. Thereafter, a short-term multiobjective offline-to-online optimization approach by SEMS is considered, with the application of multiobjective evolutionary algorithm (MOEA) and typical schemes corresponding to the actual SIES-EESPs. Simulation results show that the proposed strategy can obtain enough feasible Pareto solutions in a shorter time and get well-distributed Pareto sets with better convergence performance, which can well adapt to the features of real-world SIES-EESPs and save plenty of operation time and storage space for the SEMS.

Beamforming Optimization for Intelligent Reflecting Surface Assisted MISO: A Deep Transfer Learning Approach

This article studies the beamforming optimization for intelligent reflecting surface (IRS) assisted multiple-input single-output (MISO) wireless communication system. We establish a deep transfer learning (DTL)-based framework to learn how to optimize the phase shifts at the IRS side. Based on it, we also design a loss function to implement unsupervised training without a large number of labeled data samples. Finally, we extend the optimization problem to discrete phase shift constraint to solve the hardware limitation. The simulation verifies that the proposed DTL-based approach can achieve similar performance compared with upper bound while substantially reducing the computational complexity.

Learning Modulo Theories for constructive preference elicitation

This paper introduces CLEO, a novel preference elicitation algorithm capable of recommending complex configurable objects characterized by both discrete and continuous attributes and constraints defined over them. While existing preference elicitation techniques focus on searching for the best instance in a database of candidates, CLEO takes a constructive approach to recommendation through interactive optimization in a space of feasible configurations. The algorithm assumes minimal initial information, i.e., a set of catalog attributes, and defines decisional features as logic formulae combining Boolean and algebraic constraints over the attributes. The (unknown) utility of the decision maker is modeled as a weighted combination of features. CLEO iteratively alternates a preference elicitation step, where pairs of candidate configurations are selected based on the current utility model, and a refinement step where the utility is refined by incorporating the feedback received. The elicitation step leverages a Max-SMT solver to return optimal configurations according to the current utility model. The refinement step is implemented as learning to rank, and a sparsifying norm is used to favor the selection of few informative features in the combinatorial space of candidate decisional features.A major feature of CLEO is that it can recommend optimal configurations in hybrid domains (i.e., including both Boolean and numeric attributes), thanks to the use of Max-SMT technology, while retaining uncertainty in the decision-maker's utility and noisy feedback. In so doing, it adapts the recently introduced learning modulo theory framework to the preference elicitation setting. The combinatorial formulation of the utility function coupled with the feature selection capabilities of 1-norm regularization allow to effectively deal with the uncertainty in the DM utility while retaining high expressiveness. Experimental results on complex recommendation tasks show the ability of CLEO to quickly identify optimal configurations, as well as its capacity to recover from suboptimal initial choices. Our empirical evaluation highlights how CLEO outperforms a state-of-the-art Bayesian preference elicitation algorithm when applied to a purely discrete task

Analysis of Regional Economic Development Differences Based on Intelligent Hybrid Algorithm

The diversities in the natural, social, and human environment of various regions often lead to the differences in their regional economic development level and industrial structure and layout; moderate regional differences can mobilize economic vitality and improve development efficiency, but excessive differences may lead to social instability or even turbulence. Intelligent algorithms or their improved and hybrid algorithms can recently achieve more suitable solutions to practical problems of nonlinear, discrete, nondifferentiable, and multiple constraints. Therefore, this paper's main point is on the analysis of regional economic development differences based on intelligent hybrid algorithms. On the basis of summarizing and analyzing previous research works, this paper expounded the research status and significance of regional economic development differences analysis, elaborated the development background, current status, and future challenges of intelligent hybrid algorithms, introduced the methods and principles of principal component distance weighting algorithm and sequential quadratic programming algorithm, constructed a basic model for regional economic development differences based on intelligent hybrid algorithm, conducted the construction of analysis index system and the hybrid of intelligence algorithm, analyzed the regional economic development differences based on intelligent hybrid algorithm, performed the principal component analysis and time-space change analysis of regional economic development, and finally carried out a simulation experiment and its result analysis. The study results show that the intelligent hybrid algorithm can simulate the intelligent behavior of certain groups in nature when analyzing the differences in regional economic development, so that it has essentially parallelism, high accuracy, and convergence speed. The study results of this paper provide a reference for further researches on the regional economic development differences analysis based on intelligent hybrid algorithm.

Finite-Alphabet Symbol-Level Multiuser Precoding for Massive MU-MIMO Downlink

We propose a finite-alphabet symbol-level precoding technique for massive multiuser multiple-input multiple-output (MU-MIMO) downlink systems which are equipped with finite-resolution digital-to-analog converters (DACs) of any precision. Using the idea of constructive interference (CI), we adopt a max-min fair design criterion which aims to maximize the minimum instantaneous received signal-to-noise ratio (SNR) among the user equipments (UEs) while ensuring a CI constraint for each UE under the restriction that the output of the precoder is a vector with finite-alphabet discrete elements. Due to this latter constraint, the design problem is an NP-hard quadratic program with discrete variables, and hence, is difficult to solve. In this paper, we tackle this difficulty by reformulating the problem in several steps into an equivalent continuous-domain biconvex form, including equivalent representations for discrete and binary constraints. Our final biconvex reformulation is obtained via an exact penalty approach and can efficiently be solved using a standard cyclic block coordinate descent algorithm. We evaluate the performance of the proposed finite-alphabet precoding design for DACs with different resolutions, where it is shown that employing low-resolution DACs can lead to higher power efficiencies. In particular, we focus on a setup with one-bit DACs and show through simulation results that compared to the existing schemes, the proposed design can achieve SNR gains of up to 2 dB. We further provide analytic and numerical analyses of complexity and show that our proposed algorithm is computationally efficient as it typically needs only a few tens of iterations to converge.

One-Step Robust Low-Rank Subspace Segmentation for Tumor Sample Clustering.

Clustering of tumor samples can help identify cancer types and discover new cancer subtypes, which is essential for effective cancer treatment. Although many traditional clustering methods have been proposed for tumor sample clustering, advanced algorithms with better performance are still needed. Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample. For a gene expression data set, we seek its lowest rank representation matrix and the noise matrix. By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one step. To improve the robustness of the method, capped norm is adopted to remove the extreme data outliers in the noise matrix. Furthermore, we conduct an efficient solution to solve the problem of ORLRS. Experiments on several tumor gene expression data demonstrate the effectiveness of ORLRS.