Side Constraints Research Articles

Sliding-Window Matrix Pencil Method for Design Optimization with Limit-Cycle Oscillation Constraints

This paper introduces a novel approach to constrain limit-cycle oscillations in design optimization. The approach builds upon a limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, circumventing the need for bifurcation diagrams. Previous work demonstrated the constraint using approximate recovery rates obtained by evaluating the system state velocity for prescribed states. This work proposes a fully nonlinear matrix pencil method that accurately evaluates the recovery rate based on transient simulations. The proposed method captures the amplitude variation in the recovery rate using a short time window that slides along the time history of a quantity of interest. This sliding-window matrix pencil method is first verified for a typical section model. Sensitivity analyses identify guidelines to obtain accurate recovery rates efficiently. The system is then optimized subject to limit-cycle oscillation, flutter, and side constraints, and the results are compared with the ones based on approximate recovery rates. The sliding-window matrix pencil method allows the optimizer to produce a less conservative design while preventing limit-cycle oscillations at desired operating conditions and amplitudes. The approach introduced in this paper can facilitate the inclusion of limit-cycle oscillation considerations in the design phase of a broad class of nonlinear systems.

Deep learning algorithms for predicting routes of snowplows in European cities

Most cities are faced with annual snowfall but are finding it difficult to deal with their snow plowing activities. Even though winter road maintenance has been studied for many decades, most of the papers do not present models that can be scaled up to allow for incorporation of side constraints that are often met in practical applications. Subject of the paper: Comparison of deep learning algorithms for forecasting snowplow routes in European cities in terms of spatial analysis, routing and traffic flow. The study focuses on extending neural networks including Recurrent Neural Network (RNN), Convolutional Neural Network (CNN) and Graph Neural Network (GNN) to overcome the problematics of snowplow in urban setting. Temporal and spatial data are incorporated using sophisticated models such as Spatio-Temporal Graph Convolutional Networks (STGCNs) using examples that capture the capacity to control the changes in the snowplow routes in reaction to the real-time traffic flow and weather information. The report also looks at how transformer models among other emerging technologies could be harnessed to improve predictive accuracy as well as efficiency. Comparisons made to these other methods evaluating deep learning methods’ benefits and drawbacks and their application to urban infrastructure and traffic flow. The results, therefore, point out that integrating these complicated formulas can go a long way in enhancing the efficiency and safety of snowplowing in the European cities to create better lit and safer transport networks

Simultaneous optimization of capacity and topology of seismic isolation systems in multi-story buildings using a fuzzy reinforced differential evolution method

Inter-story isolation systems, as an alternative earthquake protection system, reduce in-building movement compared to base isolation systems. In this context, the current study focuses on simultaneously optimizing the topology and capacity of base and inter-story isolation systems for a multi-story building exposed to multiple earthquake scenarios. In addressing this challenge, an optimization model is developed that simultaneously considers both the topology (vertical arrangement) and capacity (required stiffness) of the seismic isolators as the decision variables of the model. To attain more practical and feasible solutions, the side constraints of the problem involve the inter-story drift and the total cost of seismic isolation systems. A gradient-free and self-adaptive search method, Fuzzy Differential Evolution incorporated Virtual Mutant (FDEVM), is employed to solve the optimization problem. The FDEVM approach applies a fuzzy mechanism to adopt its search behavior with governing condition(s) of the current problem. The selected method's performance is implicitly compared with its standard version. The obtained results indicate that optimally placing inter-story isolators with an optimal configuration and capacity not only improves the seismic performance of the systems but also its more cost-efficient approach compared with conventional based isolation systems. Also, the comparative outcomes indicate that the FDEVM method exhibits a high search capability for this class of problems.

Connected k-Center and k-Diameter Clustering

Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. The former problem has been introduced by Ge et al. (ACM Trans Knowl Discov Data 2(2):1–35, 2008. https://doi.org/10.1145/1376815.1376816) to model clustering of data sets with both attribute and relationship data. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graphG on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an O(log2k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log ^2k)$$\\end{document}-approximation algorithm for the disjoint connected k-center and k-diameter problem. For Euclidean spaces of constant dimension and for metrics with constant doubling dimension, the approximation factor improves to O(1). Our algorithm works by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.

A GRASP algorithm for the concrete delivery problem

This paper addresses a novel variant of the Concrete Delivery Problem (CDP), which involves the efficient scheduling of ready-mixed concrete deliveries to construction sites while balancing the conflicting goals of minimizing transportation costs and maximizing customer satisfaction. In this study, we propose an exact formulation and a heuristic approach based on the Greedy Randomized Adaptive Search Procedure (GRASP) to tackle this challenging CDP variant. This variant introduces realistic side constraints, including driver working shifts, a minimum driver working time, and overtime penalties. Additionally, it considers the case where customers may request multiple types of concrete delivered within the same time window. We assess the performance of our heuristic using new instances generated for this problem and provide a comparative analysis with another CDP variant from the literature to demonstrate its effectiveness.

Inverse optimization in semi-definite programs to impute unknown constraint matrices

In a typical (forward) optimization problem, a decision-maker uses given values of model parameters to compute the values of decision variables. The goal in inverse optimization (IO) is instead to infer parameters that render given values of decision variables optimal. Most papers on IO utilize duality to impute objective function parameters. A corresponding literature for imputing constraint parameters is essentially non-existent, even for linear programs. The difficulty is that these IO problems include nonconvex bilinear constraints and/or objectives. We study inverse semi-definite programs (SDPs) where matrices on the left-hand-sides of constraints are unknown. These unknown matrices must satisfy some side constraints. We consider two types of such problems, depending on which SDP decision variable values are given: primal or dual. In each situation, we study three sub-cases based on whether both the right-hand-side coefficients and the objective function matrix are known or only one of these two is known. This creates six variants of the inverse problem. For each variant, we first look for sufficient conditions, either on the side constraints or on problem structure, under which the nonconvex bilinear inverse problem can be simplified substantially. In particular, it either has a trivial solution or can be reformulated as a (set of) convex program(s). When such conditions are not evident, we propose three tailored heuristics called the Convex–Concave Procedure, Sequential Semi-definite Programming, and Alternate Convex Search. We perform computational experiments to gain insights into the performance of these three methods.

Paths, Proofs, and Perfection: Developing a Human-Interpretable Proof System for Constrained Shortest Paths

People want to rely on optimization algorithms for complex decisions but verifying the optimality of the solutions can then become a valid concern, particularly for critical decisions taken by non-experts in optimization. One example is the shortest-path problem on a network, occurring in many contexts from transportation to logistics to telecommunications. While the standard shortest-path problem is both solvable in polynomial time and certifiable by duality, introducing side constraints makes solving and certifying the solutions much harder. We propose a proof system for constrained shortest-path problems, which gives a set of logical rules to derive new facts about feasible solutions. The key trait of the proposed proof system is that it specifically includes high-level graph concepts within its reasoning steps (such as connectivity or path structure), in contrast to, e.g., using linear combinations of model constraints. Thus, using our proof system, we can provide a step-by-step, human-auditable explanation showing that the path given by an external solver cannot be improved. Additionally, to maximize the advantages of this setup, we propose a proof search procedure that specifically aims to find small proofs of this form using a procedure similar to A* search. We evaluate our proof system on constrained shortest path instances generated from real-world road networks and experimentally show that we may indeed derive more interpretable proofs compared to an integer programming approach, in some cases leading to much smaller proofs.

A Lagrangian bounding and heuristic principle for bi-objective discrete optimization

Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems with complicating side constraints. Its aim is often twofold; first, it provides bounds for the optimal value, and, second, it can be used to heuristically find near-optimal feasible solutions, the quality of which can be assessed by the bounds. We consider bi-objective discrete optimization problems with complicating side constraints and extend this Lagrangian bounding and heuristic principle to such problems. The Lagrangian heuristic here produces non-dominated candidates for points on the Pareto frontier, while the bounding forms a polyhedral outer approximation of the Pareto frontier, which can be used to assess the quality of the candidate points. As an illustration example we consider a facility location problem in which both CO2 emission and cost should be minimized. The computational results are very encouraging, both with respect to bounding and the heuristically found non-dominated solutions. In particular, the Lagrangian bounding is much stronger than the outer approximation given by the Pareto frontier of the problem’s linear programming relaxation.

Constrained Reweighting of Distributions: An Optimal Transport Approach.

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task-namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms.

Enhanced methods for the weight constrained shortest path problem

AbstractThe classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

Tensorial multi-view subspace clustering with side constraints for elevator security warning

Tensorial multi-view subspace clustering with side constraints for elevator security warning

Side-constrained graph fusion for semi-supervised multi-view clustering

In these years, semi-supervised learning arouses ongoing attentions due to its appealing avail and economic expenditure of guiding model training. Semi-supervised multi-view clustering takes advantages of heterogeneous features and a small number of side constraints (i.e., must-link constraints and cannot-link constraints) to partition data points. However, most of existing approaches are very limited in absorbing available side constraints since it is difficult to optimize cannot-link constraints in a provable way, and thus greatly waste the value of prior information. To address it, we innovatively pose a side-constrained multi-view graph clustering method, where the pairwise constraints are flexibly incorporated into the multiple graph fusion framework. The technique definitely formulates the pairwise constraints in the graph clustering model by designing a semi-supervised graph regularization term. In this way, the structured optimal graph that satisfies multiple perspectives and specified pairwise relations is obtained. By virtue of graph fusion, the self-adaptive weight of each single-view is optimally determined without partiality. We demonstrate theoretical feasibility of the proposed method. Extensive experimental results in four multi-view data sets witness our superiority compared to the state-of-the-art approaches.

Range-constrained traffic assignment for electric vehicles under heterogeneous range anxiety

This paper studied the range-constrained traffic assignment problem (RTAP), where heterogeneous range anxiety is considered among the driving population by electric vehicles (EVs). In order not to get stranded en-route, each EV driver is assumed to have his/her own driving range limit for being able to complete the trip. As a result, two types of multi-class RTAP can be defined through discrete or continuous distributed range anxiety. Given path-based side constraint structures, we proposed two variational inequality (VI) formulations for modeling discrete and continuous RTAPs, where the former is finite-dimensional according to a discrete number of user classes and the latter is infinite-dimensional accounting for an infinite number of user classes. We reformulate the continuous RTAP into finite-dimensional by merging adjacent EV drivers into one group. A unified path-based solution framework is developed to solve the two RTAPs, built upon the gradient projection algorithm. We design column generation and dropping schemes to adaptively maintain compact path sets and an inner equilibration strategy to accelerate convergence. Finally, a small network is used to examine the correctness and effectiveness of proposed models, and a large Winnipeg network is adopted to evaluate the impacts of stochastic driving range on network flows and computation costs. Numerical results provide compelling evidence of the outstanding superiority of the proposed algorithm, and show that EV drivers with heightened sensitivity towards range anxiety may contribute to the emergence of critical links experiencing severe congestion.

An integrated model with a solution algorithm for improving an existing public bicycle sharing system

This study uses a time–space network flow technique combined with a mathematical programming method to construct a holistic model for improving an existing bicycle sharing system. The model considers bicycle rental station site selection, expansion of station capacity, expansion of bicycle fleet size, and bicycle deployment and relocation issues in the same integrated framework. The model can be formulated as an integer network flow problem with side constraints. Since the problem is NP-hard, we design a heuristic algorithm to solve the problem efficiently and effectively. Finally, numerical tests are conducted in order to perform a preliminary evaluation of the model and heuristic algorithm with data from an existing public bicycle sharing system. The results indicate that the model and heuristic algorithm could be helpful to planners to improve their bike-sharing system operations.

EVALUASI KINERJA SIMPANG TAK BERSINYAL TIPE 422 DAN TIPE 424M (STUDI KASUS : SIMPANG EMPAT TAK BERSINYAL JALAN TGH IBRAHIM KHOLIDI, KECAMATAN KEDIRI, KABUPATEN LOMBOK BARAT)

The unsignalized four-way intersection in Kediri is located in the Kediri Subdistrict of West Lombok Regency and is one of the unsignalized intersections situated very close to the center of community activities. Additionally, there is an educational center in the vicinity, and the traffic conditions at this intersection are quite congested on a daily basis. The mobility level of both individuals and goods, using both light and heavy vehicles, is visibly high at this intersection. A median strip is the central part of the road that physically separates opposing traffic flows. Therefore, the use of a median strip on the road significantly impacts traffic flow efficiency, by reducing delays, queue probabilities, side hindrances, decreasing accident rates, and providing comfort for road users, thereby making road users feel safe and organized. Thus, the government is planning to construct a road median.This study analyzes the performance of an unsignalized intersection before and after the installation of a median, covering aspects such as volume, side constraints, queue probabilities, delays, and saturation levels, using the 1997 Indonesian Highway Capacity Manual (MKJI) methodology.The analysis results for the unsignalized intersection before median installation show a capacity of 3061.5 vehicles per hour, a saturation level of 0.970 (Service Level D), a delay of 14.885 seconds per vehicle, a queue probability of 36.361%, and side constraints amounting to 881.9 incidents per hour. On the other hand, for the unsignalized intersection tipe after median installation, it exhibits a capacity of 3330.5 vehicles per hour, a saturation level of 0.729 (Service Level C), a delay of 12.654 seconds per vehicle, a queue probability of 21.942%, and side constraints amounting to 629.2 incidents per hour.The performance of the four-way intersection in Kediri on TGH Ibrahim Kholidi Road, in the Kediri Subdistrict of West Lombok Regency, was lower before the median installation compared to the tipe of intersection after median installation.

Split-demand multi-trip vehicle routing problem with simultaneous pickup and delivery in airport baggage transit

In this study, we focus on the routing and scheduling of multi-carriage transit trains for airport baggage transit. It is modeled as a vehicle routing problem with cross-route dependencies caused by side constraints, including split demand, multiple trips per vehicle, and simultaneous pickup and delivery. Besides, some other practical constraints such as time windows, baggage release time, baggage waiting time, and priority of unloading are taken into account in the implementation. The joint consideration of these characteristics brings a unique challenge to determine the start time of each service for aircraft due to the interdependencies across vehicle routes. Thus, we adopt topological sort to construct the directed acyclic graph and then derive the flight service time. Based on that, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm. Moreover, in order to examine the moves quickly, a two-stage solution evaluation method is proposed, where the single tour is checked based on the segment-based evaluation method in the first stage, and the complete solution is checked using the topological sort in the second stage. The results demonstrate the superiority of our algorithm in computational time and solution quality. In addition, some insightful conclusions are drawn through detailed analyses.

Block-based state-expanded network models for multi-activity shift scheduling

This paper presents new mixed-integer linear programming formulations for multi-activity shift scheduling problems (MASSP). In these formulations, the rules governing shift feasibility are encoded in block-based state-expanded networks in which nodes are associated with states and arcs represent assignments of blocks of work or break periods inducing state transitions. A key advantage of these formulations is that for the anonymous MASSP in which all employees are considered as equal only a single network with integer flow variables is needed as long as the network encodes all shift composition rules. A challenging aspect is that the networks can become very large, yielding huge models that are hard to solve for large problem instances. To address this challenge, this paper proposes two exact modeling techniques that substantially reduce the size of the model instances: First, it introduces a set of aggregate side constraints enforcing that an integer flow solution can be decomposed into paths representing feasible shifts. Second, it proposes to decouple the shift composition from the assignment of concrete activities to blocks of work periods, thereby removing a large amount of symmetry from the original model. In a computational study with two MASSP instance sets from the literature dealing with shift scheduling problems, we demonstrate the effectiveness of these techniques for reducing the both size of the model instances and the solution time: We are able to solve all instances, including more than 70 previously open instances, to optimality–the vast majority of them in less than 30 min on a notebook computer.

Optimization of multi-directional functionally graded plates in thermal environment based on 3D isogeometric analysis and adaptive-hybrid evolutionary firefly algorithm

In this study, a numerical model based on three-dimensional isogeometric analysis and adaptive hybrid evolutionary firefly algorithm is developed to concurrently optimize the shape and material distribution of multi-directional functionally graded plates. The optimization problems focus on maximizing the fundamental frequency of the plates subjected to thermal effects, while the volume fraction of ceramic constituent material and volume of the plates are considered as side constraints. Isogeometric multi-mesh design approach is employed to generate design and analysis domain. The free vibration analysis of multi-directional functionally graded plates with variable thickness is conducted within the framework of three-dimensional elasticity theory and isogeometric analysis. The generalized numerical framework developed in this study could accurately capture the thermal effects on the behavior of nonhomogeneous plates with variable thickness. Various numerical examples are conducted to illustrate the optimal shapes and material distributions within square, rectangular, and circular plates. Influences of temperature field, boundary conditions, and geometries of the plates on the optimal results are also addressed.

A new MILP formulation for the flying sidekick traveling salesman problem

AbstractNowadays, truck‐and‐drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem (FS‐TSP) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck‐and‐drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc‐based integer linear programming formulation for the FS‐TSP. The solution of such formulation required the development of a branch‐and‐cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state‐of‐the‐art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.

A two-stage approach to aircraft recovery under uncertainty

The paper presents a two-stage approach for minimizing the impact of daily disruptions on an airline’s published flight schedule. The problem is characterized by uncertainty in the duration of the disruption and the point in time when its length becomes known. Both a single-commodity network model and multi-commodity network model with side constraints are developed to first determine the flights that are most likely to be affected, and then to adjust their schedules to achieve system-wide optimality. The overall objective is to minimize the weighted sum of total passenger delay costs, cancellation costs, curfew violation costs, and variation from the original schedule. The two types of uncertainty are addressed by examining a range of scenarios that reflect the most likely outcomes. The results provide guidance and a measure of robustness for the flight director as the disruption unfolds. A rolling horizon approach that closely mimics current procedures used by several airlines is also presented to provide a benchmark for comparisons with the two-stage solutions.