Discrete Optimization Algorithm Research Articles

Recent Developments in Data-Driven Algorithms for Discrete Optimization

Recent Developments in Data-Driven Algorithms for Discrete Optimization

Discrete Student Psychology Optimization Algorithm for the Word Sense Disambiguation Problem

Discrete Student Psychology Optimization Algorithm for the Word Sense Disambiguation Problem

Topology Optimization of Continuum Structures Based on Binary Hunter-Prey Optimization Algorithm

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used to solve the problems that the BESO method of topology optimization has, such as easily falling into the local optimal value and being unable to obtain the optimal topology configuration; the metaheuristic algorithm was able to solve the topology optimization model’s low computational efficiency and could easily produce intermediate elements and unclear boundaries. Firstly, the BHPO algorithm was constructed by discrete binary processing using the s-shape transformation function. Secondly, BHPO-BESO topology optimization theory was established by combining the BHPO algorithm with BESO topology optimization. Using the sensitivity information of the objective function and the updated principle of the meta-heuristic of the BHPO algorithm, a semi-random search for the optimal topology configuration was carried out. Finally, numerical simulation experiments were conducted by using the three typical examples of the cantilever beam, simply supported beam, and clamping beam as optimization objects and the results were compared with the solution results of BESO topology optimization. The experimental results showed that compared with BESO, BHPO-BESO could find the optimal topology configuration with lower compliance and maximum stiffness, and it has higher computational efficiency, which can solve the above problems.

Sleep-wakeup scheduling algorithm for lifespan maximization of directional sensor networks: a discrete cuckoo search optimization algorithm

Directional sensor networks (DSNs) are ad-hoc networks which are utilized in different industrial applications. Their usual engagements are to monitor and to perform the coverage of all specific targets in the observing fields permanently. These kinds of networks include numerous configurable directional sensors in which they can be utilized in one of the possible directions along with the one of their adjustable ranges. Although the energy harvesting methodology is being applied for these battery-hungry applications, the battery management and network lifetime maximization are still prominent challenges. In this paper, the network lifetime extension is formulated to a discrete optimization problem which is a famous non-deterministic polynomial time hardness (NP-Hard) problem. To solve this combinatorial problem, a discrete cuckoo search algorithm (D-CSA) is designed and is called in several rounds. A cover is a sub set of configured sensors capable of monitoring all targets in the observing field. In each round, the most efficient cover is constituted along with its activation time. In the determined activation time, the sensors in the cover are scheduled in wakeup mode whereas others are set in sleep mode to save energy. Despite other meta-heuristic algorithms, this proposed algorithm utilizes the novel defined discrete walking around procedures that makes to reach a good balance between exploration and exploitation in this complex search space. The proposed algorithm has been tested in different scenarios to be evaluated. The simulation results in the variety circumstances prove the superiority of the proposed algorithm is about 20.29%, 19.55%, 14.40%, 14.51%, 7.70% and 8.03% in term of average lifespan improvement against H-MNLAR, Hm-LifMax-BC, GA, ACOSC, H-GATS, and HDPSO algorithms, respectively. The results also show the high potential scalability of the proposed algorithm.

Approaches Used In Adapting Metaheuristic Optimization Algorithms Developed For Continuous Problems to Discrete Problems

Many real-world problems such as determining the type and number of wind turbines, facility placement problems, job scheduling problems, are in the category of combinatorial optimization problems in terms of the type of decision variables. However, since many of the evolutionary optimization algorithms are developed for solving continuous optimization problems, they cannot be directly applied to optimization problems with discrete decision variables. Therefore, the continuous decision variable values generated by these metaheuristics need to be converted to binary values using some techniques. In other words, to apply such algorithms to discrete optimization problems, it is necessary to adapt the candidate solution vectors of the algorithms to discrete values and make changes in their working structures. In this study, firstly, adaptation methods that are frequently used in previous studies in transforming metaheuristic optimization algorithms designed for the solution of continuous optimization problems into discrete optimization algorithms are explained. Then, the popular location update strategies used in solving discrete optimization problems are explained. The presented work summarizes the process of adapting continuous optimization algorithms to solve combinatorial problems step by step.

An effective fruit fly optimization algorithm for the distributed permutation flowshop scheduling problem with total flowtime

Distributed permutation flowshop scheduling problem (DPFSP) has always been a hot issue. The optimization goal of minimizing the total flowtime is of great significance to the environment of multi-factory. In this paper, a discrete fruit fly optimization algorithm (DFFO) is proposed to solve the DPFSP with the total flowtime criterion. In the proposed DFFO, an initialization method considering the population quality and diversity is adopted. In the smell-based search stage, three perturbation operators, the Shift-based operator, the Exchange-based operator and the Hybrid operator are designed respectively, and each fruit fly improves its state through a specific neighborhood strategy. In addition, we propose an improved reference local search (MRLS) method to enhance the exploitation ability of fruit flies. In the vision-based search stage, fruit flies use a well-designed combination update mechanism to lead fruit flies to more potential areas. In order to enhance the exploration ability, we use random reinforcement method for the population. The parameters are evaluated using an orthogonal experimental design to determine the appropriate values of the key parameters. In addition, we test the DFFO and the state-of-art algorithms from the literature on 720 large-scale instances. The experimental results show that DFFO is a very effective metaheuristic.

Discrete Whale Optimization Algorithm for Disassembly Line Balancing With Carbon Emission Constraint

With the advancement of science and technology in recent years, the rate of product upgrading by end users has increased, resulting in a high number of End-Of-Life (EOL) products. For environmental protection and economic benefits, disassembly lines are set up to recycle them. A disassembly line balancing problem arises and has attracted widespread attention. In this paper, we design a model to address a class of disassembly line balancing problems in which the main optimization objective is to maximize profits, while keeping carbon emission in a tolerable range. A discrete whale optimization algorithm is proposed to search their high-quality solutions. Its efficiency is verified by comparing its solutions with their analytic solutions obtained from a commercial optimization solver and other swarm intelligence algorithms. Experimental results show that it is significantly faster than CPLEX and other swarm intelligence algorithms in solving large-scale optimization problems while guaranteeing its solutions quality.

A Novel Maximum Distance Separable Coded OFDM-RIS for 6G Wireless Communications

The vision of the sixth generation mobile communication (6G) calls for extremely reliable data transmission over complex and diverse wireless channels. By combining the maximum distance separable (MDS) codes with the classic orthogonal frequency division multiplexing (OFDM), we present a new paradigm with the assistance of the reconfigurable intelligent surfaces (RIS). In our design, the RIS with limited phase shifts are adopted and the pairwise error probability (PEP) of the proposed system is first derived. Then, in order to further minimize the bit error rate (BER), we provide a novel method based on phase alignment to obtain the optimal solution for the discrete phase shifts. Our simulation results show that the proposed scheme provides considerable BER performance improvements compared to conventional OFDM systems. Moreover, the proposed discrete phase optimization algorithm is capable of achieving performance similar to that of the system with continuous phase shifts.

Multiresolution discrete optimization registration method of ultrasound and magnetic resonance images based on key points

The registration of preoperative magnetic resonance (MR) images and intraoperative ultrasound (US) images is very important in the planning of brain tumor surgery and during surgery. Considering that the two-modality images have different intensity range and resolution, and the US images are degraded by lots of speckle noises, a self-similarity context (SSC) descriptor based on local neighborhood information was adopted to define the similarity measure. The ultrasound images were considered as the reference, the corners were extracted as the key points using three-dimensional differential operators, and the dense displacement sampling discrete optimization algorithm was adopted for registration. The whole registration process was divided into two stages including the affine registration and the elastic registration. In the affine registration stage, the image was decomposed using multi-resolution scheme, and in the elastic registration stage, the displacement vectors of key points were regularized using the minimum convolution and mean field reasoning strategies. The registration experiment was performed on the preoperative MR images and intraoperative US images of 22 patients. The overall error after affine registration was (1.57 ± 0.30) mm, and the average computation time of each pair of images was only 1.36 s; while the overall error after elastic registration was further reduced to (1.40 ± 0.28) mm, and the average registration time was 1.53 s. The experimental results show that the proposed method has prominent registration accuracy and high computational efficiency.

Optimum design and techno-socio-economic analysis of a PV/biomass based hybrid energy system for a remote hilly area using discrete grey wolf optimization algorithm

Un-economical grid extension in remote locations has motivated to the creation of stand-alone systems that are inexpensive and reasonably efficient. Renewable sources such as solar energy and biomass are easily available in remote and rural areas which can be utilized to fulfil the energy demands. In the present paper, a PV/Biomass/Battery based hybrid system is considered for an un-electrified village located in Indian state of West Bengal. A novel design of hybrid energy system has been investigated under the technical, social and economic constraints. Further, two distinct resource scenarios have been considered and compared based on system cost. Further, 12 combinations of batteries and PV panels available in market are considered. The Discrete Grey Wolf Optimization (DGWO) algorithm has been used to investigate the optimal sizes and the system net present cost (NPC). Based on the findings, it is found that Scenario-2 (Biomass-solar-battery-based hybrid system) yields the lowest NPC of $159,648.70 at the levelized cost of energy of $0.0712/kWh.

Efficient routing optimization with discrete penguins search algorithm for MTSP

The Travelling Salesman Problem (TSP) is a well-known combinatorial optimization problem that belongs to a class of problems known as NP-hard, which is an exceptional case of travelling salesman problem (TSP), which determines a set of routes enabling multiple salesmen to start at and return to home cities (depots). The penguins search optimization algorithm (PeSOA) is a new metaheuristic optimization algorithm. In this paper, we present a discrete penguins search optimization algorithm (PeSOA) for solving the multiple travelling salesman problem (MTSP). The PeSOA evaluated by a set of benchmarks of TSP instance from TSPLIB library. The experimental results show that PeSOA is very efficient in finding the right solutions in a reasonable time

Dynamic sub-route-based self-adaptive beam search Q-learning algorithm for traveling salesman problem.

In this paper, a dynamic sub-route-based self-adaptive beam search Q-learning (DSRABSQL) algorithm is proposed that provides a reinforcement learning (RL) framework combined with local search to solve the traveling salesman problem (TSP). DSRABSQL builds upon the Q-learning (QL) algorithm. Considering its problems of slow convergence and low accuracy, four strategies within the QL framework are designed first: the weighting function-based reward matrix, the power function-based initial Q-table, a self-adaptive ε-beam search strategy, and a new Q-value update formula. Then, a self-adaptive beam search Q-learning (ABSQL) algorithm is designed. To solve the problem that the sub-route is not fully optimized in the ABSQL algorithm, a dynamic sub-route optimization strategy is introduced outside the QL framework, and then the DSRABSQL algorithm is designed. Experiments are conducted to compare QL, ABSQL, DSRABSQL, our previously proposed variable neighborhood discrete whale optimization algorithm, and two advanced reinforcement learning algorithms. The experimental results show that DSRABSQL significantly outperforms the other algorithms. In addition, two groups of algorithms are designed based on the QL and DSRABSQL algorithms to test the effectiveness of the five strategies. From the experimental results, it can be found that the dynamic sub-route optimization strategy and self-adaptive ε-beam search strategy contribute the most for small-, medium-, and large-scale instances. At the same time, collaboration exists between the four strategies within the QL framework, which increases with the expansion of the instance scale.

Multi-Objective Evolutionary Algorithm With Machine Learning and Local Search for an Energy-Efficient Disassembly Line Balancing Problem in Remanufacturing

Abstract Product disassembly is a vital element of recycling and remanufacturing processes. The disassembly line balancing problem (DLBP), i.e., how to assign a set of tasks to a disassembly workstation, is crucial for a product disassembly process. Based on the importance of energy efficiency in product disassembly and the trend toward green remanufacturing, this study proposes an optimization model for a multi-objective disassembly line balancing problem that aims to minimize the idle rate, smoothness, cost, and energy consumption during the disassembly operation. Due to the complex nature of the optimization problem, a discrete whale optimization algorithm is proposed in this study, which is developed as an extension of the whale optimization algorithm. To enable the algorithm to solve discrete optimization problems, we propose coding and decoding methods that combine the features of DLBP. First of all, the initial disassembly solution is obtained by using K-means clustering to speed up the exchange of individual information. After that, new methods for updating disassembly sequences are developed, in which a local search strategy is introduced to increase the accuracy of the algorithm. Finally, the algorithm is used to solve the disassembly problem of a worm reducer and the first 12 feasible task allocation options in the Pareto frontier are shown. A comparison with typically existing algorithms confirms the high performance of the proposed whale optimization algorithm, which has a good balance of solution quality and efficiency.

Architecture Optimization of a Non-Linear Autoregressive Neural Networks for Mackey-Glass Time Series Prediction Using Discrete Mycorrhiza Optimization Algorithm.

Recurrent Neural Networks (RNN) are basically used for applications with time series and sequential data and are currently being used in embedded devices. However, one of their drawbacks is that RNNs have a high computational cost and require the use of a significant amount of memory space. Therefore, computer equipment with a large processing capacity and memory is required. In this article, we experiment with Nonlinear Autoregressive Neural Networks (NARNN), which are a type of RNN, and we use the Discrete Mycorrhizal Optimization Algorithm (DMOA) in the optimization of the NARNN architecture. We used the Mackey-Glass chaotic time series (MG) to test the proposed approach, and very good results were obtained. In addition, some comparisons were made with other methods that used the MG and other types of Neural Networks such as Backpropagation and ANFIS, also obtaining good results. The proposed algorithm can be applied to robots, microsystems, sensors, devices, MEMS, microfluidics, piezoelectricity, motors, biosensors, 3D printing, etc.

Joint optimization of production and maintenance scheduling for unrelated parallel machine using hybrid discrete spider monkey optimization algorithm

This paper considers an unrelated parallel machine scheduling problem with variable maintenance based on machine reliability to minimize the maximum completion time. To obtain the optimal solution of small-scale problems, we firstly establish a mixed integer programming model. To solve the medium and large-scale problems efficiently and effectively, we develop a hybrid discrete spider monkey optimization algorithm (HDSMO), which combines discrete spider monkey optimization (DSMO) with genetic algorithm (GA). A few additional features are embedded in the HDSMO: a three-phase constructive heuristic is proposed to generate better initial solution, and an individual updating method considering the inertia weight is used to balance the exploration and exploitation capabilities. Moreover, a problem-oriented neighborhood search method is designed to improve the search efficiency. Experiments are conducted on a set of randomly generated instances. The performance of the proposed HDSMO algorithm is investigated and compared with that of other existing algorithms. The detailed results show that the proposed HDSMO algorithm can obtain significantly better solutions than the DSMO and GA algorithms.

Multi-Patch Black-White Topology Optimization in Isogeometric Analysis

Topological optimization plays a guiding role in the conceptual design process. This paper conducts research on structural topology optimization algorithm within the framework of isogeometric analysis. For multi-component structures, the Nitsche’s method is used to glue different meshes to perform isogeometric multi-patch analysis. The discrete variable topology optimization algorithm based on integer programming is adopted in order to obtain clear boundaries for topology optimization. The sensitivity filtering method based on the Helmholtz equation is employed for averaging of curved elements' sensitivities. In addition, a simple averaging method along coupling interfaces is proposed in order to ensure the material distribution across coupling areas is reasonably smooth. Finally, the performance of the algorithm is demonstrated by numerical examples, and the effectiveness of the algorithm is verified by comparing it with the results obtained by single-patch and ABAQUS cases.

A Knowledge-Based Adaptive Discrete Water Wave Optimization for Solving Cloud Workflow Scheduling

Workflow scheduling in cloud environments has become a significant topic in both commercial and industrial applications. However, it is still an extraordinarily challenge to generate effective and economical scheduling schemes under the deadline constraint especially for the large scale workflow applications. To address the issue, this paper investigates the cloud workflow scheduling problem with the aim of minimizing the whole cost of workflow execution whereas maintaining its execution time under a predetermined deadline. A novel knowledge-based adaptive discrete water wave optimization (KADWWO) algorithm is developed based on the problem-specific knowledge of cloud workflow scheduling. In the proposed KADWWO, a discrete propagation operator is designed based on the idle time knowledge of hourly-based cost model to adaptively explore the huge search space. The adaptive refraction operator is employed to avoid stagnation and expand the available resource pool. Meanwhile, the dynamic grouping based breaking operator is designed to exploit the excellent block structure knowledge of task allocation scheme and corresponding resource to intensify the local region and accelerate convergence. Extensive simulation experiments on the well-known scientific workflow demonstrate that the KADWWO approach outperforms several recent state-of-the-art algorithms.

Summation of the Enumerators in the Discrete Optimization Problems

The publication presents an approach to the use of discrete optimization algorithms, in particular, the search for suboptimal solutions. The theory of enumerators, proposed by the famous Leningrad mathematician I.V. Romanovsky, and the operation of their summation, which is proposed to be used to create multi-domain suboptimal algorithms,are considered. The paper presents an efficient algorithm to sum enumerators based on the recalculation of the Pareto boundary. Motivations for using the proposed algorithm within the framework of a well–known task in the field of Master Data Management are given.

Maximizing the Influence Spread in Social Networks: A Learning-Automata-Driven Discrete Butterfly Optimization Algorithm

Influence maximization aims at the identification of a small group of individuals that may result in the most wide information transmission in social networks. Although greedy-based algorithms can yield reliable solutions, the computational cost is extreme expensive, especially in large-scale networks. Additionally, centrality-based heuristics tend to suffer from the problem of low accuracy. To solve the influence maximization problem in an efficient way, a learning-automata-driven discrete butterfly optimization algorithm (LA-DBOA) mapped into the network topology is proposed in this paper. According to the LA-DBOA framework, a novel encoding mechanism and discrete evolution rules adapted to network topology are presented. By exploiting the asymmetry of social connections, a modified learning automata is adopted to guide the butterfly population toward promising areas. Based on the topological features of the discrete networks, a new local search strategy is conceived to enhance the search performance of the butterflies. Extensive experiments are conducted on six real networks under the independent cascade model; the results demonstrate that the proposed algorithm achieves comparable influence spread to that of CELF and outperforms other classical methods, which proves that the meta-heuristics based on swarm intelligence are effective in solving the influence maximization problem.

A discrete teaching–learning based optimization algorithm with local search for rescue task allocation and scheduling

The allocation and scheduling of the emergency rescue forces is a fundamental task in emergency management. This paper aims to address the allocation and scheduling problem to minimize the average completion time of all rescue teams by using a discrete teaching–learning based optimization algorithm with local search (DTOLS). First, an improved k-means clustering algorithm with constraints is proposed to assign tasks to rescue teams based on the location of rescue tasks. Second, a hybrid discrete optimization algorithm based on a teaching–learning mechanism is designed to generate the task scheduling sequence for each rescue team as an initial solution. Next, an efficient two-phase local search strategy is presented to improve the current solution. For three neighborhood task moves based on problem characteristics, which contains insert task within a team, swap tasks within a team, insert task between teams, the speed-up techniques are introduced to reduce the computational complexity of calculating completion time of a rescue team. Finally, the parameters of DTOLS are calibrated by Taguchi method to determine appropriate values. DTOLS is compared with the state-of-the-art algorithms, and the experimental results demonstrate the effectiveness of DTOLS in solving a set of test instances.