Approaches to discrete optimization problems with interval objective function

В работе дается обзор подходов к решению задач дискретной оптимизации с интервальной целевой функцией. Эти подходы рассматриваются в общем контексте исследований оптимизационных задач с неопределенностями в постановках. Приводятся варианты концепций оптимальности решений для задач дискретной оптимизации с интервальной целевой функцией - робастные решения, множества решений, оптимальных по Парето, слабые и сильные оптимальные решения, объединенные множества решений и др. Оценивается предпочтительность выбора той или иной концепции оптимальности при решении задач и отмечаются ограничения для применения использующих их подходов Optimization problems with uncertainties in their input data have been investigated by many researchers in different directions. There are a lot of sources of the uncertainties in the input data for applied problems. Inaccurate measurements and variability of the parameters with time are some of such sources. The interval of possible values of uncertain parameter is the natural and the only possible way to represent the uncertainty for a wide share of applied problems. We consider discrete optimization problems with interval uncertainties in their objective functions. The purpose of the paper is to provide an overview of the investigations in this field. The overview is given in the overall context of the researches of optimization problems with uncertainties. We review the interval approaches for the discrete optimization problem with interval objective function. The approaches we consider operate with the interval values and are focused on obtaining possible solutions or certain sets of the solutions that are optimal according to some concepts of optimality that are used by the approaches. We consider the different concepts of optimality: robust solutions, the Pareto sets, weak and strong solutions, the united solution sets, the sets of possible approximate solutions that correspond to possible values of uncertain parameters. All the approaches we consider allow absence of information on probabilistic distribution on intervals of possible values of parameters, though some of them may use the information to evaluate the probabilities of possible solutions, the distribution on the interval of possible objective function values for the solutions, etc. We assess the possibilities and limitations of the considered approaches

Application Analysis on PSO Algorithm in the Discrete Optimization Problems

Particle Swarm Optimization (PSO) is kind of algorithm that can be used to solve optimization problems. In practice, many optimization problems are discrete but PSO algorithm was initially designed to meet the requirements of continuous problems. A lot of researches had made efforts to handle this case and varieties of discrete PSO algorithms were proposed. However, these algorithms just focus on the specific problem, and the performance of it significantly degrades when extending the algorithm to other problems. For now, there is no reasonable unified principle or method for analyzing the application of PSO algorithm in discrete optimization problem, which limits the development of discrete PSO algorithm. To address the challenge, we first give an investigation of PSO algorithm from the perspective of spatial search, then, try to give a novel analysis of the key feature changes when PSO algorithm is applied to discrete optimization, and propose a classification method to summary existing discrete PSO algorithms.

On the problem and algorithms for coordinated optimal management of production and material flows of an enterprise

At present, any unified approach that would allow solving the problems of coordinated optimal control of input and output material flows and production has not been implemented in the theory and practice of managing technological and organizational systems. The works published in this area are often aimed at solving specific problems. When attempting a complex solution the declared systemicity is either indicated only in words, or is implemented heuristically by gluing the constituent components without discussing and analyzing the effectiveness and, moreover, proof. This article, based on the earlier works of the authors, develops an apparatus of coordinated optimal control of all logically related subsystems. A formal setting created for this purpose is a discrete optimization problem and it takes into account all the main factors of production and movement of material flows. A special algorithm for an approximate solution is constructed, which transfers the created problem from the category of NP-hard problems to the category of polynomially solvable ones. The formal setting contains logical conditions for choosing from a variety of parameters, including sources and directions of flows, conditions of supply, volumes and dynamics of production, and determination of optimal prices at the output. Thus, the restrictions systematically take into account both production components and restrictions on resources and the logic of movement of input and output material flows. A maximum net profit at the end of the planning period was used as a criterion for the effectiveness of all processes. The considered model and control problems are investigated using a unified approach that allows working with logical conditions of any complexity and setting appropriate formal optimization problems. The results of testing the algorithm on test data close to real dimensions are also given.

Sleep-wakeup Scheduling Algorithm for Lifespan Maximization of Directional Sensor Networks: An Advanced Discrete Cuckoo Search Optimization Algorithm

Directional sensor networks are ad hoc networks which are utilized in different applications to monitor and coverage all of the specific targets in the observing fields permanently. These kinds of networks include several configurable directional sensors in which they can be adjusted in one the possible directions along with one of its adjustable ranges. Although the energy harvesting methodology is being applied for these battery-hungry applications, the battery management and network lifetime maximization is still a challenge. This paper formulates the expansion of directional sensor network lifespan to a discrete optimization problem. Several proposals were presented in literature to solve the stated problem, but majority of them are threatened to get stuck in local optimum and led low efficiency. To solve this combinatorial problem, an advanced discrete cuckoo search algorithm is designed and is called several times until the remaining battery associated to alive sensors do not let observe all targets. In each time, algorithm returns an efficient cover along with its activation time. A cover is a sub set of available sensors capable of monitoring all targets in the observing field. 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. Designing miscellaneous discrete walking around procedures makes to reach a good balance between exploration and exploitation in search space. The proposed algorithm has been tested in different scenarios to be evaluated. The simulation results in variety circumstances proves the superiority of the proposed algorithm is about 19.33%, 14.83%, 13.50%, and 5.33% in term of average lifespan improvement against H-MNLAR, ACOSC, GA, and HDPSO algorithms respectively.

Joint Power Allocation and Bit-Loading for Multicarrier Systems with Discrete Modulation

In this paper, we propose two algorithms for joint power allocation and bit-loading in multicarrier systems using discrete modulations. The objective is to maximize the data rate under the constraint of a suitable Bit Error Rate per subcarrier. The first algorithm is based on the Lagrangian Relaxation of the discrete optimization problem in order to find an initial solution. A discrete solution is found by bit truncation followed by an iterative modulation adjustment. The second algorithm is based on Discrete Coordinate Ascent framework with iterative modulation increment of one selected subcarrier at each iteration. A simple cost function related to the power increment per bit is used for subcarrier selection. A sub-optimal low complexity Discrete Coordinate Ascent algorithm is proposed that overcome the limitations of the Hughes-Hartogs algorithm. The Lagrangian Relaxation algorithm provides a suboptimal solution for non-coded system using M-QAM modulations, whereas the low complexity Discrete Coordinate Ascent algorithm provides a near optimal solution for coded as well as for non-coded system using an arbitrary modulation set. Numerical results show the efficiency of the proposed algorithms in comparison with traditional methods.

Discrete Social Spider Algorithm for Solving Traveling Salesman Problem

The Social Spider Algorithm (SSA) was introduced based on the information-sharing foraging strategy of spiders to solve the continuous optimization problems. SSA was shown to have better performance than the other state-of-the-art meta-heuristic algorithms in terms of best-achieved fitness values, scalability, reliability, and convergence speed. By preserving all strengths and outstanding performance of SSA, we propose a novel algorithm named Discrete Social Spider Algorithm (DSSA), for solving discrete optimization problems by making some modifications to the calculation of distance function, construction of follow position, the movement method, and the fitness function of the original SSA. DSSA is employed to solve the symmetric and asymmetric traveling salesman problems. To prove the effectiveness of DSSA, TSPLIB benchmarks are used, and the results have been compared to the results obtained by six different optimization methods: discrete bat algorithm (IBA), genetic algorithm (GA), an island-based distributed genetic algorithm (IDGA), evolutionary simulated annealing (ESA), discrete imperialist competitive algorithm (DICA) and a discrete firefly algorithm (DFA). The simulation results demonstrate that DSSA outperforms the other techniques. The experimental results show that our method is better than other evolutionary algorithms for solving the TSP problems. DSSA can also be used for any other discrete optimization problem, such as routing problems.

Optimal national prioritization policies for hospital care during the SARS-CoV-2 pandemic

In response to unprecedented surges in the demand for hospital care during the SARS-CoV-2 pandemic, health systems have prioritized patients with COVID-19 to life-saving hospital care to the detriment of other patients. In contrast to these ad hoc policies, we develop a linear programming framework to optimally schedule elective procedures and allocate hospital beds among all planned and emergency patients to minimize years of life lost. Leveraging a large dataset of administrative patient medical records, we apply our framework to the National Health Service in England and show that an extra 50,750–5,891,608 years of life can be gained compared with prioritization policies that reflect those implemented during the pandemic. Notable health gains are observed for neoplasms, diseases of the digestive system, and injuries and poisoning. Our open-source framework provides a computationally efficient approximation of a large-scale discrete optimization problem that can be applied globally to support national-level care prioritization policies.

Computation of optimal transport with finite volumes

We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these type of discretizations are prone to form instabilities in their more natural implementation, and we propose a variation based on nested meshes in order to overcome these issues. Despite the lack of strict convexity of the problem, we also derive quantitative estimates on the convergence of the method, at least for the discrete potential and the discrete cost. Finally, we introduce a strategy based on the barrier method to solve the discrete optimization problem.

Two-stage improved Grey Wolf optimization algorithm for feature selection on high-dimensional classification

In recent years, evolutionary algorithms have shown great advantages in the field of feature selection because of their simplicity and potential global search capability. However, most of the existing feature selection algorithms based on evolutionary computation are wrapper methods, which are computationally expensive, especially for high-dimensional biomedical data. To significantly reduce the computational cost, it is essential to study an effective evaluation method. In this paper, a two-stage improved gray wolf optimization (IGWO) algorithm for feature selection on high-dimensional data is proposed. In the first stage, a multilayer perceptron (MLP) network with group lasso regularization terms is first trained to construct an integer optimization problem using the proposed algorithm for pre-selection of features and optimization of the hidden layer structure. The dataset is compressed using the feature subset obtained in the first stage. In the second stage, a multilayer perceptron network with group lasso regularization terms is retrained using the compressed dataset, and the proposed algorithm is employed to construct the discrete optimization problem for feature selection. Meanwhile, a rapid evaluation strategy is constructed to mitigate the evaluation cost and improve the evaluation efficiency in the feature selection process. The effectiveness of the algorithm was analyzed on ten gene expression datasets. The experimental results show that the proposed algorithm not only removes almost more than 95.7% of the features in all datasets, but also has better classification accuracy on the test set. In addition, the advantages of the proposed algorithm in terms of time consumption, classification accuracy and feature subset size become more and more prominent as the dimensionality of the feature selection problem increases. This indicates that the proposed algorithm is particularly suitable for solving high-dimensional feature selection problems.

IPDCA: Intelligent Proficient Data Collection Approach for IoT-Enabled Wireless Sensor Networks in Smart Environments

The Internet of Things (IoT) enables the interrelation of physical things and devices that can be accessed through the internet and it simply forms a single integrated network of various things. An IoT-facilitated smart city scenario spans several sectors, such as industrial applications, public transportation, smart grid, emergency services, health care, etc. In this paper, we propose an Intelligent Proficient Data Collection Approach (IPDCA) to deliver public data in a large-scale smart city set-up. IPDCA utilizes public vehicles as the mobile data collectors (D-collectors) that read (or collect) data from multiple Access Points (APs) and send them back to the central Base Station (BS). Moreover, IPDCA adopts a modified Bat algorithm for path finding of D-collectors, where we extend the Bat algorithm to solve our discrete optimization problem. Besides, for selecting D-collectors in smart city settings, we use a multi-objective fitness function that considers the count, travelled distance, and storage of D-collectors to ensure optimal use of resources. Efficiency of the proposed mechanism is proved through simulations.