Discrete Optimization Algorithm Research Articles

Projected Gaussian Markov Improvement Algorithm for High-Dimensional Discrete Optimization via Simulation

This article considers a discrete optimization via simulation (DOvS) problem defined on a graph embedded in the high-dimensional integer grid. Several DOvS algorithms that model the responses at the solutions as a realization of a Gaussian Markov random field (GMRF) have been proposed exploiting its inferential power and computational benefits. However, the computational cost of inference increases exponentially in dimension. We propose the projected Gaussian Markov improvement algorithm (pGMIA), which projects the solution space onto a lower-dimensional space creating the region-layer graph to reduce the cost of inference. Each node on the region-layer graph can be mapped to a set of solutions projected to the node; these solutions form a lower-dimensional solution-layer graph. We define the response at each region-layer node to be the average of the responses within the corresponding solution-layer graph. From this relation, we derive the region-layer GMRF to model the region-layer responses. The pGMIA alternates between the two layers to make a sampling decision at each iteration. It first selects a region-layer node based on the lower-resolution inference provided by the region-layer GMRF, then makes a sampling decision among the solutions within the solution-layer graph of the node based on the higher-resolution inference from the solution-layer GMRF. To solve even higher-dimensional problems (e.g., 100 dimensions), we also propose the pGMIA+: a multi-layer extension of the pGMIA. We show that both pGMIA and pGMIA+ converge to the optimum almost surely asymptotically and empirically demonstrate their competitiveness against state-of-the-art high-dimensional Bayesian optimization algorithms.

Loading pattern optimization of VVER-1000 reactor core based on the discrete golden eagle optimization algorithm

The main features of the loading pattern optimization (LPO) problem, such as high-dimensionality, multi-modality, and non-linearity, make it difficult to achieve a truly optimal configuration. In recent years, metaheuristic methods have been successfully used to solve this problem. In this research, a discrete golden eagle optimization (DGEO) algorithm has been developed to solve the LPO problem in the first cycle of VVER-1000 reactor core. To evaluate the proposed algorithm, a linear multi-purpose fitness function has been used to improve the safety parameters of the reactor core by obtaining a flatter power distribution during the first cycle, and also to enhance the economic parameters by increasing the cycle length and reducing the cost of fuel recycling. For this purpose, a FORTRAN program has been written to map the DGEO algorithm for the LPO problem using the PMAX and PARCS core calculation code to compute the fitness function in each iteration. To speed up the calculations, parallel computing has been applied in the written program. The results demonstrated that the loading pattern, which is suggested by the DGEO algorithm, enhances all the safety and economic parameters in the fitness function. Thus, the DGEO algorithm is highly reliable for the LPO problems in the VVER 1000 reactor core.

Optimal scheduling and demand response implementation for home energy management

The optimal scheduling of the loads based on dynamic tariffs and implementation of a direct load control (DLC) based demand response program for the domestic consumer is proposed in this work. The load scheduling is carried out using binary particle swarm optimization and a newly prefaced nature-inspired discrete elephant herd optimization technique, and their effectiveness in minimization of cost and the peak-to-average ratio is analyzed. The discrete elephant herd optimization algorithm has acceptable characteristics compared to the conventional algorithms and has determined better exploring properties for multi-objective problems. A prototype hardware model for a home energy management system is developed to demonstrate and analyze the optimal load scheduling and DLC-based demand response program. The controller effectively schedules and implements DLC on consumer devices. The load scheduling optimization helps to improve PAR by a value of 2.504 and results in energy cost savings of ₹ 12.05 on the scheduled day. Implementation of DLC by 15% results in monthly savings of ₹ 204.18. The novelty of the work is the implementation of discrete elephant herd optimization for load scheduling and the development of the prototype hardware model to show effects of both optimal load scheduling and the DLC-based demand response program implementation.

Manipulation order optimization in industrial pick-and-place operations: application to textile and leather industry

AbstractThis work addresses the problem of the development of a robotic system for the picking of parts cut by a CNC machine and the optimization of the sequencing of this picking process. An automated parts collection system is optimized to reduce the time required to perform the task of both picking and the subsequent classification by the type of part. The automated picking system, which is located at the end of a cutting machine, uses a robot equipped with an additional axis to expand its working space. Therefore, in this proposal, the industrial equipment necessary to automate this process is designed and the process to be optimized is computationally modeled. In particular, three discrete optimization algorithms are analyzed, with different evolution strategies and operators, but all of them are free of specific configuration parameters. The whole process is shown in this research, from the design of the procedure to the design of the tool, the algorithm selection, and elements validation. Finally, the first steps towards its industrial implementation are presented, and the hypothesis behind this project is validated.

A Discrete Adaptive Lion Optimization Algorithm for QoS-Driven IoT Service Composition with Global Constraints

A Discrete Adaptive Lion Optimization Algorithm for QoS-Driven IoT Service Composition with Global Constraints

Time-discrete momentum consensus-based optimization algorithm and its application to Lyapunov function approximation

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques.

A study on the application of discrete curvature feature extraction and optimization algorithms to battery health estimation

A study on the application of discrete curvature feature extraction and optimization algorithms to battery health estimation

A discrete dwarf mongoose optimization algorithm to solve task assignment problems on smart farms

A discrete dwarf mongoose optimization algorithm to solve task assignment problems on smart farms

Design of a novel multimodal optimization algorithm and its application in logistics optimization

<abstract> <p>This study was purposed to design a multimodal continuous optimization algorithm based on a scheme agent to address the multidimensional complexity of optimization. An evolutionary sampling method of subarea exploration and multiple exploitations was developed by employing the scheme with variable population size so as to obtain higher optimization speed and accuracy. Second, the distribution plan was quantified into high-dimensional variable parameters based on the characteristics of logistics distribution optimization problems, and a high-dimensional discrete optimization model was constructed. Then, we identified and addressed the prominent issues and malignant virtual changes in the application of continuous algorithms to discrete problems. We have introduced a reasonable mutation mechanism during the optimization sampling process to mitigate this issue. Continuous real coordinate points were transformed across the neighborhood to standard discrete integer coordinate points by normalizing and logicizing the optimization sampling coordinates; also, the discretization of the continuous algorithm was realized. This approach could effectively prevent the algorithm from searching for targets in continuous optimization space, thereby fully reducing the complexity of the objective function distribution after conversion. The experiments showed that the transformed multimodal discrete optimization algorithm effectively addressed the optimization design problem of logistics distribution.</p> </abstract>

NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices.

A data-driven discrete simulation-based optimization algorithm for car-sharing service design

This paper formulates a discrete simulation-based optimization (SO) algorithm for a family of large-scale car-sharing service design problems. We focus on the profit-optimal assignment of vehicle fleet across a network of two-way (i.e., round-trip) car-sharing stations. The proposed approach is a metamodel SO approach. A novel metamodel based on a mixed-integer program (MIP) is formulated. The metamodel is embedded within a general-purpose discrete SO algorithm. The proposed algorithm is validated with synthetic toy network experiments. The algorithm is then applied to a high-dimensional Boston case study using reservation data from a major US car-sharing operator. The method is benchmarked versus several algorithms, including stochastic programming. The experiments indicate that the analytical network model information, provided by the MIP to the SO algorithm, is useful both at the first iteration of the algorithm and across subsequent iterations. The solutions derived by the proposed method are benchmarked versus the solution deployed in the field by the car-sharing operator. Via simulation, the proposed solutions improve those deployed with an average improvement of profit of 6% and of vehicle utilization of 3%.The combination of the problem-specific analytical MIP with a general-purpose SO algorithm enables the discrete SO algorithm to: (i) address high-dimensional problems, (ii) become computationally efficient (i.e., it can identify good quality solutions within few simulation observations), (iii) become robust to the quality of the initial points and of the stochasticity of the simulator. More generally, the information provided by the MIP to the SO algorithm enables it to exploit problem-specific structural information. This leads to an algorithm with both asymptotic convergence guarantees as well as good short term performance (i.e., performance given few simulation observations). We view this general idea of combining analytical MIP formulations with general-purpose SO algorithms, or more broadly with general-purpose sampling strategies of high-resolution data, as an innovative and promising area of future research.

Joint scheduling of AGVs and parallel machines in an automated electrode foil production factory

In recent years, the automated guided vehicle (AGV) scheduling problem and parallel machine scheduling problem (PMSP) in workshops have become two hot topics in the field of operational research. In practical production, the two problems are closely related and coupled, and both play important roles in manufacturing systems. However, in the literature, the two problems are often addressed separately, which decreases the efficiency of manufacturing systems to a great degree. Therefore, this paper studies the joint scheduling problem of AGV and parallel machines in a production process of automatic electrode foil. Taking makespan as the optimization objective, a mixed-integer linear programming model is established and verified by the GUROBI solver. A discrete gray wolf optimization algorithm is proposed to solve the AGV-PMSP. An improved NEH heuristic is used to propose the quality of the initial solution. Six neighborhood operators are used to improve the exploration capabilities of the proposed algorithm. A theorem is proved to improve computational efficiency. The performance of the proposed algorithm is verified using comprehensive simulation experiments.

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.

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.

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.

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.

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

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

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

Efficient Supervised Graph Embedding Hashing for large-scale cross-media retrieval

Recently, graph based hashing has gained much attention due to its effectiveness in multi-media retrieval. Although several graph embedding based works have been designed and achieved promising performance, there are still some issues that need to be further studied, including, (1) one significant drawback of graph embedding is its expensive memory and computation cost caused by the graph Laplacian matrix; (2) most pioneer works fail to fully explore the available class labels in training procedure, which generally makes them suffer from unsatisfactory retrieval performance. To overcome these drawbacks, we propose a simple yet effective supervised cross-media hashing scheme, termed Efficient Supervised Graph Embedding Hashing (ESGEH), which can simultaneously learn hash functions and discrete binary codes efficiently. Specifically, ESGEH leverages both class label based semantic embedding and graph embedding to generate a sharing semantic subspace, and class labels are also incorporated to minimize the quantization error for better approximating the generated binary codes. In order to reduce the computational sources, a well-designed intermediate terms decomposition is proposed to avoid explicitly computing the graph Laplacian matrix. Finally, an iterative discrete optimal algorithm is derived to solve above problem, and each subproblem can yield a closed-form solution. Extensive experimental results on four public datasets demonstrate the superiority of the proposed approach over several existing cross-media hashing methods in terms of both accuracy and efficiency.

Improved Metropolis–Hastings algorithms via landscape modification with applications to simulated annealing and the Curie–Weiss model

AbstractIn this paper, we propose new Metropolis–Hastings and simulated annealing algorithms on a finite state space via modifying the energy landscape. The core idea of landscape modification rests on introducing a parameter c, such that the landscape is modified once the algorithm is above this threshold parameter to encourage exploration, while the original landscape is utilized when the algorithm is below the threshold for exploitation purposes. We illustrate the power and benefits of landscape modification by investigating its effect on the classical Curie–Weiss model with Glauber dynamics and external magnetic field in the subcritical regime. This leads to a landscape-modified mean-field equation, and with appropriate choice of c the free energy landscape can be transformed from a double-well into a single-well landscape, while the location of the global minimum is preserved on the modified landscape. Consequently, running algorithms on the modified landscape can improve the convergence to the ground state in the Curie–Weiss model. In the setting of simulated annealing, we demonstrate that landscape modification can yield improved or even subexponential mean tunnelling time between global minima in the low-temperature regime by appropriate choice of c, and we give a convergence guarantee using an improved logarithmic cooling schedule with reduced critical height. We also discuss connections between landscape modification and other acceleration techniques, such as Catoni’s energy transformation algorithm, preconditioning, importance sampling, and quantum annealing. The technique developed in this paper is not limited to simulated annealing, but is broadly applicable to any difference-based discrete optimization algorithm by a change of landscape.