Solution Algorithm Research Articles

Due date-oriented picker routing, an efficient exact solution algorithm, and its application to pick-from-store omnichannel retailing

The advent of e-commerce and omnichannel retailing has sparked renewed interest in picker routing in warehouses. This paper presents two significant methodological advances in this well-established field. First, it is a well-known fact that the parallel-aisle layout of warehouses, as opposed to general graphs, allows for polynomial-time solutions of the Traveling Salesman Problem. We show that the parallel-aisle structure can also be exploited when pickers are tasked with visiting storage positions associated with specific due dates. We establish that picker routing in warehouses, subject to soft due date constraints, is a binary NP-hard problem. We also present an exact branch-and-bound algorithm with pseudo-polynomial time complexity. This algorithm effectively solves instances with up to 60 picking positions and five cross aisles within a few seconds while guaranteeing optimality. Second, for even larger pick lists, we demonstrate the successful integration of our algorithm into a real-time framework. This approach allows us to avoid extended solution times that would otherwise delay the picker’s departure, without compromising the quality of the solution. To illustrate the practical relevance of these two methodological innovations, we apply our routing algorithm to the context of pick-from-store omnichannel retailing. By assigning due dates to critical products, we significantly reduce stockout occurrences for online customers. These stockouts occur when the stock level, initially deemed sufficient to confirm an online order, is depleted by walk-in customers before the picker reaches the relevant shelf.

Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control

AbstractIt is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint variables. High accuracy with moderate computing time can be achieved by such time integration methods that satisfy a sufficiently large number of adjoint order conditions and supply gradients with higher orders of consistency. In this paper, we upgrade our former implicit two-step Peer triplets constructed in [Algorithms, 15:310, 2022] to meet those new requirements. Since Peer methods use several stages of the same high stage order, a decisive advantage is their lack of order reduction as for semi-discretized PDE problems with boundary control. Additional order conditions for the control and certain positivity requirements now intensify the demands on the Peer triplet. We discuss the construction of 4-stage methods with order pairs (3, 3) and (4, 3) in detail and provide three Peer triplets of practical interest. We prove convergence of order $$s-1$$ s - 1 , at least, for s-stage methods if state, adjoint and control satisfy the corresponding order conditions. Numerical tests show the expected order of convergence for the new Peer triplets.

Stochastic optimal allocation of grid-side independent energy storage considering energy storage participating in multi-market trading operation

The integration of large-scale intermittent renewable energy generation into the power grid imposes challenges to the secure and economic operation of the system, and energy storage (ES) can effectively mitigate this problem as a flexible resource. However, the conventional ES allocation is mostly planned to meet the regulation demands of individual entities, which is likely to result in low utilization of ES and difficult to recover the investment cost. Therefore, a two-stage stochastic optimal allocation model for grid-side independent ES (IES) considering ES participating in the operation of multi-market trading, such as peak-valley arbitrage, frequency regulation, and leasing, is proposed in this paper to improve the comprehensive benefits and utilization rate of ES. The first stage aims to allocate IES and develop a systematic scheduling plan based on the forecast of wind power output and load demand, while the second stage responds to the uncertainty of wind power output by re-dispatching generating units and invoking ES power leased by wind farms. Then, a two-layer loop iterative solution algorithm based on the Benders decomposition is formed to effectively solve the proposed model. Finally, the approach developed in this paper is applied to a modified IEEE RTS-79 test system, and the results verify that it is both feasible and effective.

Secure and covert communication strategy of UAV based on hybrid RF/FSO system

The hybrid radio frequency (RF)/free-space optical (FSO) system can improve communication security by using complimentary characteristics and mitigating the risks of RF links being susceptible to co-channel interference (CCI) and malicious eavesdropping. We investigate the secure and covert communication performance of unmanned aerial vehicles (UAVs) equipped with a hybrid RF/FSO system. In terms of secure communication, UAVs employ the strategy of transmitting private data concurrently through RF and FSO links, considering two modes based on active eavesdropping by a malicious user. Closed-form expressions for the secrecy outage probability (SOP) and effective secrecy throughput (EST) are derived. With respect to covert communication, the communication strategy is to utilize the RF link to generate interfering signals, thus aiding the FSO signals in accomplishing covert communication. We formulate an optimization problem that maximizes the EST while considering transmit power and user-acceptable detection error probability. A two-stage gradient-based iterative solution algorithm is proposed. The numerical results demonstrate the effectiveness of the proposed secure and covert communication strategy based on the hybrid RF/FSO system, which is expected to enhance the communication security of UAVs in the RF-challenged environment.

From human explanations to explainable AI: Insights from constrained optimization

Many complex decision-making scenarios encountered in the real-world, including energy systems and infrastructure planning, can be formulated as constrained optimization problems. Solutions for these problems are often obtained using white-box solvers based on linear program representations. Even though these algorithms are well understood and the optimality of the solution is guaranteed, explanations for the solutions are still necessary to build trust and ensure the implementation of policies. Solution algorithms represent the problem in a high-dimensional abstract space, which does not translate well to intuitive explanations for lay people. Here, we report three studies in which we pose constrained optimization problems in the form of a computer game to participants. In the game, called Furniture Factory, participants manage a company that produces furniture. In two qualitative studies, we first elicit representations and heuristics with concurrent explanations and validate their use in post-hoc explanations. We analyze the complexity of the explanations given by participants to gain a deeper understanding of how complex cognitively adequate explanations should be. Based on insights from the analysis of the two qualitative studies, we formalize strategies that in combination can act as descriptors for participants’ behavior and optimal solutions. We match the strategies to decisions in a large behavioral dataset (>150 participants) gathered in a third study, and compare the complexity of strategy combinations to the complexity featured in participants’ explanations. Based on the analyses from these three studies, we discuss how these insights can inform the automatic generation of cognitively adequate explanations in future AI systems.

A shaping two-stage anomaly data recovery method based on multi-norm joint optimization under energy internet

With the deep integration of energy networks and information communication technology, the involvement of hardware and environmental factors intensifies the challenges to data security. Prior research focuses predominantly on interpolating random missing data under the assumption of no data damage, without providing strategies for addressing continuous data loss. To overcome, we proposes a novel two-stage data recovery method, that includes three-fold ideas: (1) it introduces the matrix shaping differentiation strategy to realize the differentiated recovery of random and continuous missing data; (2) it designs a two-stage data recovery approach, in which the first stage constructs a random missing data recovery objective function by eliminating the consecutive missing data columns, and the second stage performs temporal pre-interpolation backfilling on the eliminated columns and introduces the temporal correlation to construct the temporal smoothing objective function; and (3) it develops an alternating direction method of multipliers-based iterative solution algorithm. Experimental results on four public datasets demonstrate that our model is superior to five state-of-the-art and classical methods in terms of random missing error rate, random column missing error rate, root mean square error, and mean absolute error.

Novel Particle Swarm Optimization Algorithm to Solve the Internet Shopping Optimization Problem with Shipping Costs

In this paper, we approach the Internet Shopping Optimization Problem with Shipping Costs (IShOP), an NP-hard-relevant problem in the current e-commerce environment. To our knowledge, several solution metaheuristic algorithms have been reported in the literature. In this paper, we propose a novel Particle Swarm Optimization algorithm (PSO) to solve the problem. PSO incorporates a neighborhood diversification technique (NDT), a local search (LS) technique, and an adaptive parameter tuning (APT) method. The proposed algorithm (NDTLSAA-PSO) includes two techniques at the end of each iteration to avoid premature convergence in the search process, balancing exploration and exploitation in selecting candidate solutions. A comparison of the performance of the proposed algorithm has been made against the performance of the best state-of-the-art memetic algorithm solution of the IShOP. A total of 90 instances classified into three groups of small, medium, and large sizes were resolved. The Wilcoxon and Holm non-parametric tests were applied to validate the significance of the differences observed between these two algorithms. The results show that the proposed NDTLSAA-PSO algorithm is superior to the memetic algorithm. In addition, the proposed algorithm obtains the best results in all the in-stances evaluated in terms of quality.

Collaboration and resource sharing in the multidepot time-dependent vehicle routing problem with time windows

Concerns about energy conservation and emission reduction have highlighted the importance of environmentally sound logistics networks in urban areas. These networks are deeply intertwined with urban traffic systems, where variations in transit speeds can significantly increase the energy consumption and carbon emissions of delivery vehicles, compromising the environmental sustainability of urban deliveries. To address this, we propose a multidepot time-dependent vehicle routing problem with time windows, enhancing route planning flexibility and resource configuration. Our approach begins with a route spatiotemporal decomposition method to estimate vehicle travel times and emissions based on varying vehicle speeds. We then develop a multiobjective mixed integer linear programming model that aims to minimize total operating costs, the number of vehicles, and carbon dioxide emissions. A hybrid heuristic algorithm combining spectral clustering, multiobjective ant colony optimization, and variable neighborhood search is proposed to solve the model. This algorithm incorporates collaboration and resource sharing strategies, a pheromone initialization mechanism, a novel heuristic operator that accounts for time dependency, and a self-adaptive update mechanism, enhancing both solution quality and algorithm convergence. We compare the performance of our algorithm with that of the CPLEX solver, multiobjective ant colony optimization, non-dominated sorting genetic algorithm-Ⅲ, and multiobjective particle swarm optimization. The results demonstrate the superior convergence, uniformity, and spread of our proposed algorithm. Furthermore, we apply our model and algorithm to a real-world case in Chongqing, China, analyzing optimized results for different time intervals and vehicle speeds. This study offers robust methodologies for theoretically and practically addressing the multidepot time-dependent vehicle routing problem with time windows, contributing to the development of economical, efficient, collaborative, and sustainable urban logistics networks.

Three-dimensional simulation of cavitating flow in reciprocating positive displacement pumps with fluid-actuated valves

Abstract An in-house compressible three-dimensional (3D) finite volume Computational Fluid Dynamics (CFD) method, with statistical turbulence model and moving grid capabilities, is presented and applied to the suction stroke of a simplex plunger positive displacement pump. The approach utilizes a pressure-based implicit solution algorithm and a mass transfer cavitation model. Fluid-actuated valve dynamics are approximated using a fluid-structure interaction algorithm. The closed valve and early phase of valve opening are approximated by a permeable wall. A circular segment model is introduced, significantly reducing computing time. Experimental validation is performed by time-resolved pressure and flow rate measurements, as well as high-speed visualizations of the valve dynamics. A speed variation is conducted to investigate harmless advanced and erosive distinctive partial cavitation. The simulation reproduces the delay of cavity collapse, observed with increasing speed, and reveals distinctive void patterns related to the chamber pressure time progression. These void patterns are fundamental for understanding the cavitation dynamics and potential erosion risk in the system. Deviations from data remain in the flow phase subsequent to the collapse due to overestimated wave reflection at the inlet boundary in the suction pipe.

Analytic Approach Solution to Time-Fractional Phi-4 Equation with Two-Parameter Fractional Derivative

This paper is devoted to building a general framework for constructing a solution to fractional Phi-4 differential equations using a Caputo definition with two parameters. We briefly introduce some definitions and properties of fractional calculus in two parameters and the Phi-4 equation. By investigating the homotopy analysis method, we built the solution algorithm. The two parameters of the fractional derivative gain vary the behavior of the solution, which allows the researchers to fit their data with the proper parameter. To evaluate the effectiveness and accuracy of the proposed algorithm, we compare the results with those obtained using various numerical methods in a comprehensive comparative study.

Encoding consumer interests into product snippets with a multi-criteria genetic optimization approach

As an essential product cue in consumer information foraging, textual snippets can convey valuable scents that attract consumers to further access products, paving the way for online sellers to seize a competitive advantage. Premised on shopping goals theory, this study proposes a novel approach to designing high-quality product snippets that are particularly enhanced with consumer interests. First, snippet encoding is formulated as a multi-criteria optimization problem in which information sources are incorporated to distill consumer-appealing keywords considering both driving search and attracting selection, as well as to integrate the perspectives of sellers and consumers. Subsequently, a constrained genetic solution algorithm is developed, which copes well with the evolutionary nature of the problem to optimize snippets in an effective and efficient manner. Extensive experiments are conducted to verify the validity and superiority of the proposed approach.

Blind Deblurring Method for CASEarth Multispectral Images Based on Inter-Band Gradient Similarity Prior.

Multispectral remote sensing images contain abundant information about the distribution and reflectance of ground objects, playing a crucial role in target detection, environmental monitoring, and resource exploration. However, due to the complexity of the imaging process in multispectral remote sensing, image blur is inevitable, and the blur kernel is typically unknown. In recent years, many researchers have focused on blind image deblurring, but most of these methods are based on single-band images. When applied to CASEarth satellite multispectral images, the spectral correlation is unutilized. To address this limitation, this paper proposes a novel approach that leverages the characteristics of multispectral data more effectively. We introduce an inter-band gradient similarity prior and incorporate it into the patch-wise minimal pixel (PMP)-based deblurring model. This approach aims to utilize the spectral correlation across bands to improve deblurring performance. A solution algorithm is established by combining the half-quadratic splitting method with alternating minimization. Subjectively, the final experiments on CASEarth multispectral images demonstrate that the proposed method offers good visual effects while enhancing edge sharpness. Objectively, our method leads to an average improvement in point sharpness by a factor of 1.6, an increase in edge strength level by a factor of 1.17, and an enhancement in RMS contrast by a factor of 1.11.

A symmetric interior-penalty discontinuous Galerkin isogeometric analysis spatial discretization of the self-adjoint angular flux form of the neutron transport equation

This paper presents the first application of a symmetric interior-penalty discontinuous Galerkin isogeometric analysis (SIP-DG-IGA) spatial discretization to the self-adjoint angular flux (SAAF) form of the multi-group neutron transport equation. The penalty parameters are determined, for general element types, from a mathematically rigorous coercivity analysis of the bilinear form. The proposed scheme produces a compact spatial discretization stencil. It also yields symmetric positive-definite (SPD) matrices, which can be efficiently solved using pre-conditioned conjugate gradient (PCG) solution algorithms. The proposed discretization scheme is verified using the method of manufactured solutions (MMS) and several nuclear reactor physics benchmark verification test cases. For sufficiently smooth elliptic problems, the proposed spatial discretization can exploit higher-order continuity, or k-refinement, of the NURBS basis to consistently yield greater numerical accuracy per degree of freedom (DoF) than standard h-refinement. Since this is a discontinuous scheme, it can also accurately model significant changes in the neutron scalar flux that may occur near the material interfaces of heterogeneous problems.

A novel hybrid algorithm based on improved marine predators algorithm and equilibrium optimizer for parameter extraction of solar photovoltaic models

In the field of solar photovoltaic (PV) systems, the accurate and reliable extraction of parameters from PV models is crucial for effective simulation, evaluation, and control. Although various optimization algorithms have been widely used for parameter extraction in solar PV systems, the accuracy and reliability of the parameters extracted by these methods usually fall short of the expected standards. To address these shortcomings, a novel hybrid algorithm that combines the improved marine predators algorithm (MPA) with the equilibrium optimizer (EO), named IMPAEO, is proposed. In the IMPAEO, an elite opposition-based learning strategy is introduced to expand the exploration range of the algorithm to enhance population diversity; an adaptive weight coefficient is employed to improve the updating rule of the MPA, facilitating a balance between global exploration and local exploitation; the EO operator is integrated to enhance the performance of the MPA in the local exploitation phase to improve the solution quality and convergence speed; and the linear population size reduction (LPSR) technique is introduced to dynamically reduce the population size and improve the search performance. The effectiveness of the proposed IMPAEO is validated using the CEC2017 benchmark test suite, which is also applied to extract parameters of the single diode model, the double diode model, and three different PV modules. Comparative analysis with other algorithms demonstrates that the IMPAEO exhibits significant advantages in terms of solution quality, convergence speed, and algorithm stability. Consequently, the proposed IMPAEO not only proves to be efficient and reliable in parameter extraction for solar PV models but also offers a promising alternative in this field.

A two-stage location model covering COVID-19 sampling, transport and DNA diagnosis: design of a national scheme for infection control.

During the COVID-19 pandemic, a system was established in China that required testing of all residents for COVID-19. It consisted of sampling stations, laboratories capable of carrying out DNA investigations and vehicles carrying out immediate transfer of all samples from the former to the latter. Using Beilin District, Xi'an City, Shaanxi Province, China as example, we designed a genetic algorithm based on a two-stage location coverage model for the location of the sampling stations with regard to existing residencies as well as the transfer between the sampling stations and the laboratories. The aim was to estimate the minimum transportation costs between these units. In the first stage, the model considered demands for testing in residential areas, with the objective of minimizing the costs related to travel between residencies and sampling stations. In the second stage, this approach was extended to cover the location of the laboratories doing the DNAinvestigation, with the aim of minimizing the transportation costs between them and the sampling stations as well as the estimating the number of laboratories needed. Solutions were based on sampling stations and laboratories existing in 2022, with the results visualized by geographic information systems (GIS). The results show that the genetic algorithm designed in this paper had a better solution speed than the Gurobi algorithm. The convergence was better and the larger the network size, the more efficient the genetic algorithm solution time.

Bi-level task planning strategy for blended-wing-body underwater gliders

ABSTRACT This study focuses on the task planning problem of the blended-wing-body underwater glider (BWBUG), which must autonomously navigate through a sequence of underwater visitation points while ensuring safety and economy. Firstly, the task planning problem of the BWBUG is analysed, with attention given to operational space and task requirements. Subsequently, a bi-level planning framework that incorporates both the bottom-level and top-level planners is proposed. The bottom-level planner optimises the glide path between any two visit points by considering safety and glide angle constraints, with the objective of minimising energy usage. The top-level planner focuses on the task constraints and optimises the global visitation path of the BWBUG to achieve the objective of global energy minimisation. Simulations demonstrate the effectiveness of the bi-level based task planning strategy proposed in this study. The solution algorithms are highly competitive, capable of planning rational global visitation paths for the BWBUG.

An Improved Driving Training-Based Optimization Algorithm for the Minimum Gap Graph Connected Partition Problem

In this paper, we consider the minimum gap partition problem in an undirected connected graph with nonnegative vertex weights. This problem involves in dividing the given graph into a specified number of connected subgraphs such that the total difference between the largest and the smallest vertex weights in each subgraph is minimized. Namely, let G = (V, E, W) be a given undirected connected graph with vertex set V , edge set E, and nonnegative vertex weight function W : V → R+, and let k ≥ 2 be a given positive integer. The minimum gap partition problem consists of constructing a partition P = {V1, V2, . . . , Vk} of non-empty and pairwise disjoint subsets of V such that each vertex set Vi, i = 1, 2, . . . , k, induces a connected subgraph G[Vi] of G. The objective of the problem is to find such a partition of V that minimizes the total difference 1≤i≤k maxv∈Viw(v) − minv∈Viw(v). This problem, as many other variants of graph partition problems, is known to be NP-hard problem. We designed an efficient metaheuristic algorithm for finding approximate solution of large-scale instances of this problem. The quality of the proposed algorithm is assessed comparing with the previous algorithms proposed for the problem.

Connected and Autonomous Vehicle Scheduling Problems: Some Models and Algorithms

In this paper, we consider some problems that arise in connected and autonomous vehicle (CAV) systems. Their simplified variants can be formulated as scheduling problems. Therefore, scheduling solution algorithms can be used as a part of solution algorithms for real-world problems. For four variants of such problems, mathematical models and solution algorithms are presented. In particular, three polynomial algorithms and a branch and bound algorithm are developed. These CAV scheduling problems are considered in the literature for the first time. More complicated NP-hard scheduling problems related to CAVs can be considered in the future.

Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers in practice, that is, without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: the speed of LP iterative refinement, in particular, in the majority of cases when a double-precision floating-point solver is able to compute approximate solutions with small errors, and the robustness of precision boosting whenever extended levels of precision become necessary. We compare the practical performance of the resulting algorithm with both pure methods on a large set of LPs and mixed-integer programs (MIPs). The results show that the combined algorithm solves more instances than a pure LP iterative refinement approach while being faster than pure precision boosting. When embedded in an exact branch-and-cut framework for MIPs, the combined algorithm is able to reduce the number of failed calls to the exact LP solver to zero while maintaining the speed of the pure LP iterative refinement approach. History: Accepted by Antonio Frangioni, Area Editor for Design and Analysis of Algorithms: Continuous. Funding: The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (BMBF) [Grants 05M14ZAM and 05M20ZBM].

A relaxation‐based Voronoi diagram approach for equitable resource distribution

AbstractThis paper introduces a methodology designed to reduce cost, improve demand coverage, and ensure equitable vaccine distribution during the initial stages of the vaccination campaign when demand significantly exceeds supply. We formulate an enhanced maximum covering problem as a mixed integer linear program, aiming to minimize the total vaccine distribution cost while maximizing the allocation of vaccines to population blocks under equity constraints. Block‐level census data are employed to define demand locations, identifying gender, age, and racial groups within each block using population data. A Lagrangian relaxation technique integrated with a modified Voronoi diagram is proposed to solve the location–allocation problem efficiently. Empirical case studies in Pennsylvania, using real‐world data from the Centers for Disease Control and Prevention and health department websites, were conducted for the first 4 months of the COVID‐19 vaccination campaign. Preliminary results show that the proposed solution algorithm effectively solves the problem, achieving a 5.92% reduction in total transportation cost and a 28.15% increase in demand coverage. Moreover, our model can reduce the deviation from equity to 0.07 (∼50% improvement).