Discrete Optimization Research Articles

A novel discrete adjoint-based level set topology optimization method in B-spline space

A novel discrete adjoint-based level set topology optimization method in B-spline space

A dual-horizon peridynamic model for Reissner–Mindlin plates with arbitrary horizon sizes and shapes

A dual-horizon peridynamic (DHPD) model with arbitrary horizon sizes and shapes is proposed for predicting structural responses of thin-walled structures subjected to out-of-plane loadings. The proposed DHPD method can diminish the influence arising from ghost forces in irregular particle distributions and lessen the computational consumption with optimal refinement discretizations. Meanwhile, the variable PD parameters of each discrete particle that derive based on its own current horizon domain are adopted to mitigate the PD surface effect. Several static and dynamic structural responses with different geometric and boundary conditions are compared between the reference and DHPD approaches. It is concluded that the proposed DHPD method can effectively reproduce structural behaviors in fracture mechanics problems with less computational effort.

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.

Stochastic Localization Methods for Convex Discrete Optimization via Simulation

Solving Convex Discrete Optimization via Simulation via Stochastic Localization Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems. For a number of applications, the objective function exhibits convexity in the discrete decision variables or the problem can be transformed into a convex one. In “Stochastic Localization Methods for Convex Discrete Optimization via Simulation,” Zhang, Zheng, and Lavaei propose provably efficient simulation-optimization algorithms for general large-scale convex discrete optimization via simulation problems. By utilizing the convex structure and the idea of localization and cutting-plane methods, the developed stochastic localization algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, the simulation cost is upper bounded by a value that is independent of the objective function. The stochastic localization methods also exhibit a superior numerical performance compared with existing algorithms.

Reliability constrained dynamic generation expansion planning using honey badger algorithm

Generation expansion planning (GEP) is a complex, highly constrained, non-linear, discrete and dynamic optimization task aimed at determining the optimum generation technology mix of the best expansion alternative for long-term planning horizon. This paper presents a new framework to study the GEP in a multi-stage horizon with reliability constrained. GEP problem is presented to minimize the capital investment costs, salvage value cost, operation and maintenance, and outage cost under several constraints over planning horizon. Added to that, the spinning reserve, fuel mix ratio and reliability in terms of Loss of Load Probability are maintained. Moreover, to decrease the GEP problem search space and reduce the computational time, some modifications are proposed such as the Virtual mapping procedure, penalty factor approach, and the modified of intelligent initial population generation. For solving the proposed reliability constrained GEP problem, a novel honey badger algorithm (HBA) is developed. It is a meta-heuristic search algorithm inspired from the intelligent foraging behavior of honey badger to reach its prey. In HBA, the dynamic search behavior of honey badger with digging and honey finding approaches is formulated into exploration and exploitation phases. Added to that, several modern meta-heuristic optimization algorithms are employed which are crow search algorithm, aquila optimizer, bald eagle search and particle swarm optimization. These algorithms are applied, in a comparative manner, for three test case studies for 6-year, 12-year, and 24-year of short- and long-term planning horizon having five types of candidate units. The obtained results by all these proposed algorithms are compared and validated the effectiveness and superiority of the HBA over the other applied algorithms.

Dys-R Questionnaire: A Novel Screening Tool for Dysbiosis Linked to Impaired Gut Microbiota Richness.

Practical and affordable tools to screen intestinal dysbiosis are needed to support clinical decision making. Our study aimed to design a new subjective screening tool for the risk of intestinal dysbiosis from a previously described nonvalidated questionnaire (DYS/FQM) and based on subjective and objective data. A total of 219 individuals comprised the chronic diseases (CD; n = 167) and healthy control (HC; 52 subjects) groups. Sociodemographic, anthropometric, body composition, lifestyle, past history, intestinal health, and dietary data were collected. The gut microbiota (GM) profile was assessed from fecal samples using the 16S rRNA sequencing. Scores for the new tool (Dys-R Questionnaire) were assigned using discrete optimization techniques. The association between Dys-R scores and dysbiosis risk was assessed through correlation, simple linear models, sensitivity, specificity, as well as positive and negative predictive values. We found significant differences in the Chao1 Index between CD and HC groups (adjusted p-value = 0.029), highlighting lower GM richness as the primary marker for intestinal dysbiosis. DYS/FQM showed poor performance in identifying poor GM richness. Dys-R exhibited a 42% sensitivity, 82% specificity, 79% positive predictive value (PPV), and 55% negative predictive value (NPV) to identify poor GM richness. The new Dys-R questionnaire showed good performance in ruling out dysbiosis.

Optimised sizing of a hybrid renewable water pumping system based on recent metaheuristic algorithms: a case study in Algeria

This paper proposes a new design model for techno-economic analysis and optimization of water pumping systems. The model incorporates the Levelised Cost of Water Pumped (LCOWP) as the objective function to capture the economic criterion, while the technical criterion is represented by the Loss of Water Supply Probability (LWSP). The model integrates three decision variables: the number of PV modules, wind turbines and water tanks, which is a unique combination that has been rarely explored in previous studies.. To address the complexity of this non-linear discrete optimization problem, the Equilibrium Optimiser (EO), a recent metaheuristic algorithm, is employed. Comparative analysis conducted against four other algorithms demonstrates the superior accuracy and convergence time of EO, establishing its effectiveness. To showcase the practicality of the model, it is utilised to optimise a water pumping system for irrigation in Adrar, Algeria, considering four different pumping heads and exploring various reliability levels (represented by LWSP). The sizing results demonstrate how the LCOWP is influenced by the pumping heads and the desired LWSP. For instance, at a pumping head of 45 m, the cost decreases from 1.181$/m3 with 0% LWSP to 0.991$/m3 when accepting 1% LWSP.

Application of clustering cooperative differential privacy in spatial crowdsourcing task allocation

A framework for spatial crowdsourcing task allocation based on centralized differential privacy is proposed for addressing the problem of worker’s location privacy leakage. Firstly, by combining two stages of differential privacy noise addition and clustering matching, a spatial crowdsourcing worker dataset with high differential privacy protection can be obtained; Secondly, the dynamic problem of spatial crowdsourcing task allocation is transformed into a static combinatorial optimization problem by dividing the spatiotemporal units and the “delay matching” strategy; Finally, the improved discrete glowworm swarm optimization algorithm is used to calculate the results of spatial crowdsourcing task allocation. It has been demonstrated that, compared to the direct differential privacy noise-adding assignment method and the discrete glowworm swarm optimization assignment method, the proposed method achieves better task assignment results, with the total travel distance reduced by 12.42% and 3.56%, respectively, and the task assignment success rate increased by 11.75% and 3.34%, respectively.

Discrete spider monkey optimization algorithm for latency‐sensitive VNF deployment and resource allocation

SummaryThe next‐generation networks are expected to support diverse latency‐sensitive services, that is, auto‐driving, telemedicine, and so on. Deploying these services in current hardware‐based networks faces significant challenges. The emergence of network function virtualization (NFV) and software defined network (SDN) makes network deployment flexible and agile. In order to meet the strict latency constraints, joint VNF deployment and resource allocation problems are needed. In this paper, we consider the resource‐delay interpendency and formulate the joint VNF deployment and resource allocation problems as linear programming (LP) problems. Discrete spider monkey optimization (DSMO) algorithm is proposed to solve this problem, which imitates spider monkeys' fission and fusion social behavior during foraging. The two‐phase decision update mechanism greatly increases the diversity of the spider monkey decision population and promotes the algorithm to perform a global search of the solution space. Evaluation results show that the proposed solutions achieve superior performance in terms of latency, CPU utilization and service acceptance rate.

Multi-material isogeometric topology optimization in multiple NURBS patches

In design optimization of structures, design domains are often described by multiple non-uniform rational B-spline (NURBS) patches. To perform multi-material topological design in such design domains, an effective Nitsche-based multi-material isogeometric topology optimization (ITO) method is proposed in this paper. Specifically, the Nitsche's method is utilized to effectively couple the interfaces between adjacent NURBS patches. In order to preserve the coercivity of the bilinear form, the stabilization parameters are estimated locally according to the element size. Meanwhile, the discrete material optimization (DMO) approach is employed to describe the mixing of candidate materials. Analytical computation of sensitivities for coupled elements is developed as well. The effectiveness of the proposed method is demonstrated via several 2D and 3D numerical examples, where the design domains are constituted by conforming and non-conforming NURBS patches, respectively.

A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization

We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global techniques from discrete optimization. We assume that the region defined by the convex constraints can be written as the intersection of a finite collection of convex sets, such that it is easy and inexpensive to project onto each one of them (e.g., boxes, hyper-planes, or half-spaces). Taking advantage of a recently developed continuous reformulation that relaxes the cardinality constraint, we propose a specialized penalty gradient projection scheme combined with alternating projection ideas to compute a solution candidate for these problems, i.e., a local (possibly non-global) solution. To illustrate the proposed algorithm, we focus on the standard mean-variance portfolio optimization problem for which we can only invest in a preestablished limited number of assets. For these portfolio problems with cardinality constraints, we present a numerical study on a variety of data sets involving real-world capital market indices from major stock markets. In many cases, we observe that the proposed scheme converges to the global solution. On those data sets, we illustrate the practical performance of the proposed scheme to produce the effective frontiers for different values of the limited number of allowed assets.

Deep reinforcement learning based model-free optimization for unit commitment against wind power uncertainty

Solving the unit commitment (UC) problem in a computationally efficient manner has become increasingly crucial, especially in the context of high renewable energy penetration. This paper tackles this challenge by employing the offline training of a model-free deep reinforcement learning (DRL) framework, thereby enhancing the optimization efficiency of the UC problem. The complex modeling of random variables is avoided by reformulating the UC problem as a Markov decision process, where the DRL-based method extracts knowledge regarding wind output forecasting errors from historical data. Finally, a discrete proximal policy optimization (PPO-D) algorithm is developed to generate UC solutions under the discrete action spaces necessitated by unit start-up/shut-down variables. Simulation results on the 5-unit system demonstrate that the proposed DRL-based UC model can yield an optimal solution with higher computational efficiency compared to the conventional mathematical optimization methods, while hedging against the wind power uncertainty. In addition, the case study on the IEEE 118-bus system involving 31 testing days further validates the generalization ability of the proposed DRL-based UC model.

Scalable Transfer Evolutionary Optimization: Coping With Big Task Instances.

In today's digital world, we are faced with an explosion of data and models produced and manipulated by numerous large-scale cloud-based applications. Under such settings, existing transfer evolutionary optimization (TrEO) frameworks grapple with simultaneously satisfying two important quality attributes, namely: 1) scalability against a growing number of source tasks and 2) online learning agility against sparsity of relevant sources to the target task of interest. Satisfying these attributes shall facilitate practical deployment of transfer optimization to scenarios with big task instances, while curbing the threat of negative transfer. While applications of existing algorithms are limited to tens of source tasks, in this article, we take a quantum leap forward in enabling more than two orders of magnitude scale-up in the number of tasks; that is, we efficiently handle scenarios beyond 1000 source task instances. We devise a novel TrEO framework comprising two co-evolving species for joint evolutions in the space of source knowledge and in the search space of solutions to the target problem. In particular, co-evolution enables the learned knowledge to be orchestrated on the fly, expediting convergence in the target optimization task. We have conducted an extensive series of experiments across a set of practically motivated discrete and continuous optimization examples comprising a large number of source task instances, of which only a small fraction indicate source-target relatedness. The experimental results show that not only does our proposed framework scale efficiently with a growing number of source tasks but is also effective in capturing relevant knowledge against sparsity of related sources, fulfilling the two salient features of scalability and online learning agility.

RIS-Aided MIMO Systems With Hardware Impairments: Robust Beamforming Design and Analysis

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

Intuitionistic fuzzy multi-objective transportation model during pandemic COVID-19

The given paper discusses an intuitionistic fuzzy discrete time-space optimization model while taking into account the COVID-19 pandemic. The novelty of this study is characterized by the proposal of a distinctive multi-objective intuitionistic fuzzy transportation model in which the demand function varies with time as the number of infected, exposed and susceptible persons increase. Forecasting of demand is executed using the epidemic diffusion model. Also, a new approach to defuzzify triangular intuitionistic fuzzy numbers, depending upon the concept of the golden ratio, is presented. Intuitionistic fuzzy programming approach is used to obtain the pareto-optimal solution. A real-life numerical illustration is explained using the proposed methodology to examine its practical suitability. Outperforming the existing traditional method of solving a transportation problem verifies its proficiency.

Joint IRS Location and Size Optimization in Multi-IRS Aided Two-Way Full-Duplex Communication Systems

Intelligent reflecting surfaces (IRSs) have emerged as a promising wireless technology for the dynamic configuration and control of electromagnetic waves, thus creating a smart (programmable) radio environment. In this context, we study a multi-IRS assisted two-way communication system consisting of two users that employ full-duplex (FD) technology. More specifically, we deal with the joint IRS location and size (i.e., the number of reflecting elements) optimization in order to minimize an upper bound of system outage probability under various constraints: minimum and maximum number of reflecting elements per IRS, maximum number of installed IRSs, maximum total number of reflecting elements (implicit bound on the signaling overhead) as well as maximum total IRS installation cost. First, the problem is formulated as a discrete optimization problem and, then, a theoretical proof of its NP-hardness is given. Moreover, we provide a lower bound on the optimum value by solving a linear-programming relaxation (LPR) problem. Subsequently, we design two polynomial-time algorithms, a deterministic greedy algorithm and a randomized approximation algorithm, based on the LPR solution. The former is a heuristic method that always computes a feasible solution for which (a posteriori) performance guarantee can be provided. The latter achieves an approximate solution, using randomized rounding, with provable (a priori) probabilistic guarantees on the performance. Furthermore, extensive numerical simulations demonstrate the superiority of the proposed algorithms compared to the baseline schemes. Finally, useful conclusions regarding the comparison between FD and conventional half-duplex (HD) systems are also drawn.

Discrete artificial ecosystem-based optimization for spherical capacitated vehicle routing problem

Discrete artificial ecosystem-based optimization for spherical capacitated vehicle routing problem

Discrete sizing optimization method based on dividing rectangles algorithm and local response surface for steel frame structures

It has always been the goal of structural engineers to construct safe and stable buildings using the least amount of materials. Utilizing a quick and effective way to optimize the cross-section size is crucial because conventional building design methods are impacted by the designers' knowledge, and it is challenging to prevent material waste. Due to its implicit optimization function, discrete design variables, and expensive individual evaluation, sizing optimization of high-rise buildings is very challenging to achieve. In order to effectively handle this optimization problem, a two-stage discrete sizing optimization method for high-rise buildings based on the DIviding RECTangles (DIRECT) algorithm and local response surface is proposed in this paper. The optimization method suggested in this research consists of two key stages: the global search stage and the local search stage. In the global search stage, the entire design domain is divided using a modified DIRECT algorithm to swiftly identify potentially optimal subregions that may contain the best points. In the local search stage, the local response surface model is constructed to approximate the objective and constraint functions using the sampling points from the previous stage, and the discrete optimal solution is rapidly found through mathematical iterative solving. A sizing optimization calculation program for high-rise buildings was developed in Microsoft Visual Studio 2015 on the basis of C++ to achieve automatic optimization. The new method was applied to optimize three high-rise steel frame buildings with different heights and plan shapes. The results showed that the material cost could be successfully saved compared with the conventional design, and the over-limit constraints could be adjusted automatically, which demonstrated the viability and efficacy of the two-stage optimization method.

Variables selection using [formula omitted] penalty

The determination of a tuning parameter by the generalized information criterion (GIC) is considered an important issue in variable selection. It is shown that the GIC and the L0 penalized objective functions are equivalent, leading to a new L0 penalized maximum likelihood method for high-dimensional generalized linear models in this article. Based on the technique of the well-known discrete optimization problem in theoretical computer science, a two-step algorithm for local solutions is proposed. The first step optimizes the L0 penalized objective function under a given model size, where only a maximum likelihood algorithm is needed. The second step optimizes the L0 penalized objective function under a candidate set of model sizes, where only the GIC is needed. As the tuning parameter can be fixed, the selection of the tuning parameter can be ignored in the proposed method. The theoretical study shows that the algorithm is polynomial and any resulting local solution is consistent. Thus, it is not necessary to use the global solution in practice. The numerical studies show that the proposed method outperforms its competitors in general.

Influence maximization in social networks based on discrete harris hawks optimization algorithm

Influence maximization in social networks based on discrete harris hawks optimization algorithm