Discrete Optimization Research Articles

OPTIMAL SINGLE-STORY STEEL BUILDINGS UNDER HIGH LOADS

This paper presents the parametric optimization of single-story steel buildings subjected to high loads. In the parametric study, high loads of snow and wind are determined for different altitudes up to 3000 meters above sea level. The Alpine region and the Eurocode 1 standard are considered. The discrete mixed-integer non-linear programming optimization is performed for different altitude alternatives. The optimization model for the steel structure is developed and used. The mass objective function of the structure is subjected to dimensioning and deflection constraints defined by the Eurocode standards. The modified outer-approximation and equality-relaxation algorithm is applied. The optimal results obtained include the minimal possible mass of the structure, the optimal topology, the steel sections and the steel grade. In the case of a medium-sized single-story steel building, it was found that the structural mass increases by 2.7 times and the number of main portal frames increases by 80 % when the altitude of the building site is increased from 500 to 3000 meters above sea level. The optimal results clearly show how the structural mass and cross-sections increase with increasing load.

Discrete Choquet Integral Optimization With Positive and Negative Interactions

Discrete Choquet Integral Optimization With Positive and Negative Interactions

A comparative study of maximum matching algorithms

One of the central problems of discrete optimization is the problem of determining the maximal matching, which can be solved in various ways, depending on the structure of the initial data. In this article, a comparative study of the efficiency of maximal flow algorithms (Ford-Fulkerson) and the direct algorithm for determining maximal matching (Even & Kariv) on unweighted bipartite graphs is conducted. The analysis is based on a set of high-difficulty computing competition problems. Therefore, the results will be useful not only to those interested in the maximal matching problem but also to all those who are preparing to participate in various programming competitions.

BinDMO: a new Binary Dwarf Mongoose Optimization algorithm on based Z-shaped, U-shaped, and taper-shaped transfer functions for CEC-2017 benchmarks

Intelligent swarm optimization algorithms have become increasingly common due to their success in solving real-world problems. Dwarf Mongoose Optimization (DMO) algorithm is a newly proposed intelligent swarm optimization algorithm in recent years. It was developed for continuous optimization problem solutions in its original paper. But real-world problems are not always problems that take continuously variable values. Real-world problems are often problems with discrete variables. Therefore, heuristic algorithms proposed for continuous optimization problems need to be updated to solve discrete optimization problems. In this study, DMO has been updated for binary optimization problems and the Binary DMO (BinDMO) algorithm has been proposed. In binary optimization, the search space consists of binary variable values. Transfer functions are often used in the conversion of continuous variable values to binary variable values. In this study, twelve different transfer functions were used (four Z-shaped, four U-shaped, and four Taper-shaped). Thus, twelve different BinDMO variations were obtained (BinDMO1, BinDMO2, …, BinDMO12). The achievements of BinDMO variations were tested on thirteen different unimodal and multimodal classical benchmark functions. The effectiveness of population sizes on the effectiveness of BinDMO was also investigated. When the results were examined, it was determined that the most successful BinDMO variation was BinDMO1 (with Z1-shaped transfer function). The most successful BinDMO variation was compared with three different binary heuristic algorithms selected from the literature (SO, PDO, and AFT) on CEC-2017 benchmark functions. According to the average results, BinDMO was the most successful binary heuristic algorithm. This has proven that BinDMO can be chosen as an alternative algorithm for binary optimization problems.

Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection

The branch-and-bound algorithm based on decision diagrams is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on pruning inequalities given by rough upper bounds and local bounds — two additional filtering techniques recently introduced. Computational experiments show that the pruning brought by this caching mechanism allows for significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0340 ), as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0340 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Parameters optimization for chatter-free milling tool path based on spindle speed variation method

Existing methods orienting for optimizing cutting parameters in milling process with spindle speed variation (SSV) only optimally selected the axial depth of cut and only considered the acceleration constraint of spindle. This article proposes a systematic optimization method to obtain the best combination of multiple machining parameters (axial and radial depths of cut) and SSV’s parameters (the ratio of variation amplitude and the ratio of variation frequency) so that the chatter-free milling tool path can be shortened. Both acceleration and jerk constraints of spindle are considered. A C3 continuous variable feedrate scheduling algorithm is used to eliminate the influence of spindle speed variation on feed per tooth, which is thus not required to treat as an optimization variable. The machining parameters of each iterative step are updated by following that the number of axial and radial cutting layers could be decreased. Discrete optimization method is combined with chatter stability analysis to solve the problem. A series of milling experiments verify that the proposed method can achieve the shortest tool path with chatter-free condition.

Discrete Artificial Fish Swarm Algorithm-Based One-Off Optimization Method for Multiple Co-Existing Application Layer Multicast Routing Trees

As an effective multicast application mechanism, the application layer multicast (ALM) determines the path of data transmission through a routing tree. In practical applications, multiple multicast sessions often occur simultaneously; however, few studies have considered this situation. A feasible solution is to sequentially optimize each co-existing ALM routing tree. However, this approach can lead to node congestion, and, even if the node out-degree reservation strategy is adopted, an optimal solution may not be obtained. In this study, to solve the problem of routing tree construction for multiple co-existing application layer multicast sessions, an optimization model that minimizes the overall delay and instability is constructed, and a one-off optimization method based on the discrete artificial fish swarm algorithm (DAFSA) is proposed. First, Steiner node sets corresponding to the multicast sessions are selected. Then, the routing trees for each multicast session are obtained through the improved spanning tree algorithm based on the complete graph composed of Steiner node sets. The experimental results show that the proposed method can simultaneously obtain multiple co-existing ALM routing trees with a low total delay and low instability. Even if the input is a single multicast session, it can lead to ALM routing trees with a lower delay and less instability than other algorithms, and the introduction of a penalty function can effectively avoid the problem of excessive replication and forwarding loads on some end-hosts. In addition, the proposed algorithm is insensitive to parameter changes and exhibits good stability and convergence properties for networks of different sizes.

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

Advancements in Unsupervised Learning: Mode-Assisted Quantum Restricted Boltzmann Machines Leveraging Neuromorphic Computing on the Dynex Platform

The integration of neuromorphic computing into the Dynex platform signifies a transformative step in computational technology, particularly in the realms of machine learning and optimization. This advanced platform leverages the unique attributes of neuromorphic dynamics, utilizing neuromorphic annealing - a technique divergent from conventional computing methods - to adeptly address intricate problems in discrete optimization, sampling, and machine learning. Our research concentrates on enhancing the training process of Restricted Boltzmann Machines (RBMs), a category of generative models traditionally challenged by the intricacy of computing their gradient. Our proposed methodology, termed “quantum mode training”, blends standard gradient updates with an off-gradient direction derived from RBM ground state samples. This approach significantly improves the training efficacy of RBMs, outperforming traditional gradient methods in terms of speed, stability, and minimized converged relative entropy (KL divergence). This study not only highlights the capabilities of the Dynex platform in progressing unsupervised learning techniques but also contributes substantially to the broader comprehension and utilization of neuromorphic computing in complex computational tasks.

Quantum annealing-driven branch and bound for the single machine total weighted number of tardy jobs scheduling problem

In the paper we present a new approach to solving NP-hard problems of discrete optimization adapted to the architecture of quantum processors (QPU, Quantum Processor Unit) implementing hardware quantum annealing. This approach is based on the use of the quantum annealing metaheuristic in the exact branch and bound algorithm to compute the lower and upper bounds of the objective function. To determine the lower bound, a new method of defining the Lagrange function for the dual problem (the generalized discrete knapsack problem) was used, the value of which is calculated on the QPU of a quantum machine. In turn, to determine the upper bound, we formulate an appropriate task in the form of binary quadratic programming with constraints.Despite the fact that the results generated by the quantum machine are probabilistic, the hybrid method of algorithm construction proposed in the paper, using alternately a CPU and QPU, guarantees the optimal solution. As a case study we consider the NP-hard single machine scheduling problem with minimizing the weighted number of tardy jobs. The performed computational experiments showed that optimal solutions were already obtained in the root of the solution tree, and the values of the lower and upper bounds differ by only a few percent.

Discrete Approximations and Optimality Conditions for Controlled Free-Time Sweeping Processes

Discrete Approximations and Optimality Conditions for Controlled Free-Time Sweeping Processes

Handling Imbalance and Limited Data in Thyroid Ultrasound and Diabetic Retinopathy Datasets Using Discrete Levy Flights Grey Wolf Optimizer Based Random Forest for Robust Medical Data Classification

In the field of disease diagnosis, medical image classification faces an inherent challenge due to various factors involving data imbalance, image quality variability, annotation variability, and limited data availability and data representativeness. Such challenges affect the algorithm's classification ability on the medical images in an adverse way, which leads to biased model outcomes and inaccurate interpretations. In this paper, a novel Discrete Levy Flight Grey Wolf Optimizer (DLFGWO) is combined with the Random Forest (RF) classifier to address the above limitations on the biomedical datasets and to achieve better classification rate. The DLFGWO-RF resolves the image quality variability in ultrasound images and limits the inaccuracies on classification using RF by handling the incomplete and noisy data. The sheer focus on the majority class may lead to unequal distribution of classes and thus leads to data imbalance. The DLFGWO balances such distribution by leveraging grey wolves and its exploration and exploitation capabilities are improved using Discrete Levy Flight (DLF). It further optimizes the classifier's performance to achieve balanced classification rate. DLFGWO-RF is designed to perform classification even on limited datasets, thereby the requirement of numerous expert annotations can thus be reduced. In diabetic retinopathy grading, the DLFGWO-RF reduces disagreements in annotation variability using subjective interpretations. However, the representativeness of the diabetic retinopathy dataset fails to capture the entire population diversity, which limits the generalization ability of the proposed DLFGWO-RF. Thus, fine-tuning of RF can robustly adapt to the subgroups in the dataset, enhancing its overall performance. The experiments are conducted on two widely used medical image datasets to test the efficacy of the model. The experimental results show that the DLFGWO-RF classifier achieves improved classification accuracy between 90-95%, which outperforms the existing techniques for various imbalanced datasets.

Multi-Objective Dynamic Reconstruction of Distributed Energy Distribution Networks Based on Stochastic Probability Models and Optimized Beetle Antennae Search

In the dynamic optimization problem of the distribution network, a dynamic reconstruction method based on a stochastic probability model and optimized beetle antennae search is proposed. By implementing dynamic reconstruction of distributed energy distribution networks, the dynamic regulation and optimization capabilities of the distribution network can be improved. In this study, a random probability model is used to describe the uncertainty in the power grid. The beetle antennae search is used for dynamic multi-objective optimization. The performance of the beetle antennae search is improved by combining it with the simulated annealing algorithm. According to the results, the optimization success rate of the model was 98.7%. Compared with the discrete binary particle swarm optimization algorithm and bacterial foraging optimization algorithm, it was 9.3% and 26.1% faster, respectively. For practical applications, this model could effectively reduce power grid transmission losses, with a reduction range of 16.7–18.6%. Meanwhile, the charging and discharging loads were effectively reduced, with a reduction range of 16.2–19.7%. Therefore, this method has significant optimization effects on actual power grid operation. This research achievement contributes to the further development of dynamic reconstruction technology for distribution networks, improving the operational efficiency and stability of the power grid. This has important practical significance for achieving green and intelligent operation of the power system.

A New Approach Based on Collective Intelligence to Solve Traveling Salesman Problems.

This paper presents a novel approach based on the ant system algorithm for solving discrete optimization problems. The proposed method is based on path construction, path improvement techniques, and the footprint mechanism. Some information about the optimization problem and collective intelligence is used in order to create solutions in the path construction phase. In the path improvement phase, neighborhood operations are applied to the solution, which is the best of the population and is obtained from the path construction phase. The collective intelligence in the path construction phase is based on a footprint mechanism, and more footprints on the arc improve the selection chance of this arc. A selection probability is also balanced by using information about the problem (e.g., the distance between nodes for a traveling salesman problem). The performance of the proposed method has been investigated on 25 traveling salesman problems and compared with state-of-the-art algorithms. The experimental comparisons show that the proposed method produced comparable results for the problems dealt with in this study.

Multi-day tourism recommendations for urban tourists considering hotel selection: A heuristic optimization approach

With the development of tourism, digital technology is increasingly being applied in the design of tourist routes. This study takes into account that tourists are experience-driven in tourism activities and hotel selections. In this study, the tourist trip design problem with hotel selection is formulated based on bi-objective optimization with total utility of the points of interest maximization and the average utility of the hotels maximization, and a three-step hybrid algorithm combined with discrete particle swarm optimization, an adaptive differential evolution with an optional external archive, and a local search is designed to identify the optimal route. To examine the performance of the designed algorithm, a numerical experiment was conducted. The results of Wilcoxon rank sum tests verified that the proposed algorithm performed distinctly better than extant approaches. Moreover, the results also indicate that the two main innovative mechanisms about initialization and hybrid evolution play a critical role in improving the algorithm's efficiency for the tourist trip design problem with hotel selection.

Discrete variable topology optimization for maximizing single/multiple natural frequencies and frequency gaps considering the topological constraint

AbstractFinding optimized structural topology design for maximizing natural frequencies and frequency gaps of continuum structures is crucial for engineering applications. However, two significant numerical issues must be addressed: non‐smoothness caused by multiple frequencies and Artificial Localized Rigid Motion (ALRM) modes due to the violation of the topological constraint related to isolated islands and point‐connections. The above two issues are solved by employing the discrete variable topology optimization method based on Sequential Approximate Integer Programming (SAIP). First, the directional differentiability and multiple frequencies preservation constraints are formulated as the linear integer constraints. And then, the integer programming with these linear integer constraints is established and solved by the discrete variable linear or quadratic programming solver with multi‐constraint Canonical Relaxation Algorithm (CRA). We also prove that the popular Average Modal Frequencies (AMF) strategy, like the Kreisselmeier‐Steinhauser (KS) function, cannot rigorously tackle this non‐smoothness caused by multiple frequencies. Furthermore, to eliminate the ALRM modes and concentrate on the real structural global modes, the burning method is employed to impose the topological constraint of the first Betti number that represents the number of isolated islands and point‐connections. Numerical examples, including 2D and 3D, two‐fold and three‐fold multiple frequencies, natural frequencies and frequency gaps, are presented to show the effectiveness of the proposed method.

A Hybrid Initialization and Effective Reproduction-Based Evolutionary Algorithm for Tackling Bi-Objective Large-Scale Feature Selection in Classification

Evolutionary algorithms have been widely used for tackling multi-objective optimization problems, while feature selection in classification can also be seen as a discrete bi-objective optimization problem that pursues minimizing both the classification error and the number of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) can encounter setbacks when the dimensionality of features explodes to a large scale, i.e., the curse of dimensionality. Thus, in this paper, we focus on designing an adaptive MOEA framework for solving bi-objective feature selection, especially on large-scale datasets, by adopting hybrid initialization and effective reproduction (called HIER). The former attempts to improve the starting state of evolution by composing a hybrid initial population, while the latter tries to generate more effective offspring by modifying the whole reproduction process. Moreover, the statistical experiment results suggest that HIER generally performs the best on most of the 20 test datasets, compared with six state-of-the-art MOEAs, in terms of multiple metrics covering both optimization and classification performances. Then, the component contribution of HIER is also studied, suggesting that each of its essential components has a positive effect. Finally, the computational time complexity of HIER is also analyzed, suggesting that HIER is not time-consuming at all and shows promising computational efficiency.

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. The approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.

Global exact optimisations for chloroplast structural haplotype scaffolding

BackgroundScaffolding is an intermediate stage of fragment assembly. It consists in orienting and ordering the contigs obtained by the assembly of the sequencing reads. In the general case, the problem has been largely studied with the use of distances data between the contigs. Here we focus on a dedicated scaffolding for the chloroplast genomes. As these genomes are small, circular and with few specific repeats, numerous approaches have been proposed to assemble them. However, their specificities have not been sufficiently exploited.ResultsWe give a new formulation for the scaffolding in the case of chloroplast genomes as a discrete optimisation problem, that we prove the decision version to be NP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{NP}$$\\end{document}-Complete. We take advantage of the knowledge of chloroplast genomes and succeed in expressing the relationships between a few specific genomic repeats in mathematical constraints. Our approach is independent of the distances and adopts a genomic regions view, with the priority on scaffolding the repeats first. In this way, we encode the structural haplotype issue in order to retrieve several genome forms that coexist in the same chloroplast cell. To solve exactly the optimisation problem, we develop an integer linear program that we implement in Python3 package khloraascaf. We test it on synthetic data to investigate its performance behaviour and its robustness against several chosen difficulties.ConclusionsWe succeed to model biological knowledge on genomic structures to scaffold chloroplast genomes. Our results suggest that modelling genomic regions is sufficient for scaffolding repeats and is suitable for finding several solutions corresponding to several genome forms.

Optimized topology design of finned ducts for internal flow thermal performance by discrete variable eigenvalue-related optimization

Optimized topology design of finned ducts for internal flow thermal performance by discrete variable eigenvalue-related optimization