Set Of Computational Experiments Research Articles

A joint sustainable order-packing vehicle routing optimisation for the cold chain e-fulfilment

AbstractDue to the new normal caused by the pandemic, consumer behaviour has now shifted to online shopping not only for general commodities but also for food and other perishable products. Therefore, e-commerce fulfilment is now integrated with cold chain capabilities to satisfy stringent requirements on time-criticality and product quality, leading to the concept of cold chain e-fulfilment. In the cold chain e-fulfilment process, perishable orders are packed in thermal packaging solutions and delivered to consumers before the quality preservation time window. To secure a sufficient time buffer during last mile delivery, excessive use of thermal packaging materials is applied, which creates an adverse environmental impact on our eco-system. Aligning with low-carbon business practices, this study proposes a novel joint optimization model, namely the Joint Optimization of Sustainable Order Packing and Multi-Temperature Delivery Problem (JOSOPMDP), for order packing and vehicle routing decisions, where the sustainable use of thermal packaging materials is promoted without negatively influencing product quality and customer satisfaction. To evaluate its viability and performance, three sets of computational experiments are subsequently conducted. It is found that the proposed model is feasible to strike a balance between order packing and vehicle routing decisions. Compared with the traditional strategy, the average total cost and satisfaction level are improved by 3.26% and 47.88%, respectively. Consequently, this research fosters sustainable thinking in the cold chain e-fulfilment process, minimizing environmental impact.

Solving the uncapacitated facility location problem under uncertainty: a hybrid tabu search with path-relinking simheuristic approach

The uncapacitated facility location problem (UFLP) is a well-known combinatorial optimization problem that finds practical applications in several fields, such as logistics and telecommunication networks. While the existing literature primarily focuses on the deterministic version of the problem, real-life scenarios often involve uncertainties like fluctuating customer demands or service costs. This paper presents a novel algorithm for addressing the UFLP under uncertainty. Our approach combines a tabu search metaheuristic with path-relinking to obtain near-optimal solutions in short computational times for the determinisitic version of the problem. The algorithm is further enhanced by integrating it with simulation techniques to solve the UFLP with random service costs. A set of computational experiments is run to illustrate the effectiveness of the solving method.

Using Clustering to Strengthen Decision Diagram Bounds for Discrete Optimization

Offering a generic approach to obtaining both upper and lower bounds, decision diagrams (DDs) are becoming an increasingly important tool for solving discrete optimization problems. In particular, they provide a powerful and often complementary alternative to other well-known generic bounding mechanisms such as the LP relaxation. A standard approach to employ DDs for discrete optimization is to formulate the problem as a Dynamic Program and use that formulation to compile a DD top-down in a layer-by-layer fashion. To limit the size of the resulting DD and to obtain bounds, one typically imposes a maximum width for each layer which is then enforced by either merging nodes (resulting in a so-called relaxed DD that provides a dual bound) or by dropping nodes (resulting in a so-called restricted DD that provides a primal bound). The quality of the DD bounds obtained from this top-down compilation process heavily depends on the heuristics used for the selection of the nodes to merge or drop. While it is sometimes possible to engineer problem-specific heuristics for this selection problem, the most generic approach relies on sorting the layer’s nodes based on objective function information. In this paper, we propose a generic and problem-agnostic approach that relies on clustering nodes based on the state information associated with each node. In a set of computational experiments with different knapsack and scheduling problems, we show that our approach generally outperforms the classical generic approach, and often achieves drastically better bounds both with respect to the size of the DD and the time used for compiling the DD.

Hub location with congestion and time-sensitive demand

This work studies the effect of hub congestion and time-sensitive demand on a hub-and-spoke location/allocation system. The Hub Location with Congestion and Time-sensitive Demand Problem is introduced, which combines these two main characteristics. On the one hand, hubs can be activated at several service levels, each of them characterized by a maximum capacity, expressed as the amount of flow that may circulate through the hub, which is associated with a hub transit time. On the other hand, alternative levels are available for served commodities, where each demand level is characterized by its amount of demand, unit revenue, and maximum service time. In this problem the efficiency of a hub-and-spoke system is given by the maximum net profit it may produce. To the best of our knowledge this is the first work where hub congestion and time-sensitive demand are jointly considered.Two alternative mixed-integer linear programming formulations are proposed. They include a new set of constraints, which are necessary to guarantee the consistency of the obtained solutions under the presence of the capacity-type constraints derived from hub service levels and served demand levels. The efficiency of the formulations is analyzed through a set of computational experiments. The results of the computational experiments allow to study the structure of the obtained solutions and to analyze how the different parameters affect them.

A scalable multi-objective maintenance optimization model for systems with multiple heterogeneous components and a finite lifespan

Delivering after-sales maintenance services is a challenging task for original equipment manufacturers who must tailor their offers to customers’ needs. To accommodate this challenge, we propose a multi-objective optimization model to derive optimal maintenance policies for systems with a large number of heterogeneous components over a finite lifespan. Based on the practical assumption of a fixed time interval between two consecutive scheduled downs, we develop a decomposition approach that enables the fast computation of the optimal policy per component and the optimal time interval between two consecutive scheduled visits. We also analyze the structural properties of the optimal policies for both age-based and condition-based maintenance and prove that they have a non-static control-limit structure. Using a set of computational experiments, we first investigate the computational tractability of our model for systems with an increasing number of components. Then, we apply our model to a real case study to demonstrate how it can be used to derive optimal maintenance policies tailored to different customer needs.

Two is better than one? Order aggregation in a meal delivery scheduling problem

We address a single-machine scheduling problem motivated by a last-mile-delivery setting for a food company. Customers place orders, each characterized by a delivery point (customer location) and an ideal delivery time. An order is considered on time if it is delivered to the customer within a time window given by the ideal delivery time ±δ2, where δ is the same for all orders. A single courier (machine) is in charge of delivery to all customers. Orders are either delivered individually, or two orders can be aggregated in a single courier trip. All trips start and end at the restaurant, so no routing decisions are needed. The problem is to schedule courier trips so that the number of late orders is minimum. We show that the problem with order aggregation is NP-hard and propose a combinatorial branch and bound algorithm for its solution. The algorithm performance is assessed through a computational study on instances derived by a real-life application and on randomly generated instances. The behavior of the combinatorial algorithm is compared with that of the best ILP formulation known for the problem. Through another set of computational experiments, we also show that an appropriate choice of design parameters allows to apply the algorithm to a dynamic context, with orders arriving over time.

An Adaptive Large Neighbourhood Search algorithm for a real-world Home Care Scheduling Problem with time windows and dynamic breaks

This paper presents a Home Care Scheduling Problem (from now on HCSP) based on a real case of a care company for elderly and dependent people located in the North of Spain. The problem incorporates many of the common features addressed in the HCSP literature, such as soft and hard time windows for the services, available working time of the caregivers or affinity levels between users and caregivers. However, it also includes other novel characteristics that increase the difficulty of the problem significantly, since the breaks between services will play a key role in the quality of the solutions. To evaluate the solutions, the users welfare will be prioritized over the cost associated with the schedule.The problem has been formulated as a Mixed Integer Linear Programming (MILP) one but, due to the complexity of the model, it is not possible to solve it for real size instances. Therefore, we have designed a method that combines the Adaptive Large Neighbourhood Search (ALNS) methodology with a heuristic approach necessary to evaluate the objective functions. To analyse the behaviour of the algorithm, a set of computational experiments are carried out under different configurations. First, the MILP formulation and the algorithm have been compared over some standard instances from the literature. Finally, the performance of the algorithm is evaluated over a real case study based on the timetables of the company during some weeks from 2016 to 2017.

Portfolio optimization through a network approach: Network assortative mixing and portfolio diversification

The paper deals with the classical problem of selecting a portfolio in the financial market and follows a risk-return optimization approach. The main issue in portfolio selection is capturing the dependency structure of the returns of the different assets. In the well-known Markowitz models this is measured by the variance/covariance matrix of the assets’ returns. Recent works have focused on a new way of modeling the dependency between returns of different assets by means of the so called “market graph” or “correlation graph”.Basing on this graph, the paper introduces new mixed integer linear formulations for the portfolio selection problem in which the portfolio expected return is maximized, while controlling the worst case loss. There are two innovative aspects related to the market graph. One is the introduction of a set of constraints over the neighborhood of each node. These constraints force the model to include in the portfolio a subset of assets which correspond to nodes poorly connected in the correlation graph. The second is the use of a measure from the area of complex network analysis called ‘assortativity’. A local assortativity coefficient is computed for each node, and it is used to formulate linear objective functions in the optimization models. We propose two Mixed Integer Linear Programs for finding the most ‘disassortative’ portfolios by using either the ‘local degree’ or the ‘local strength’ assortativity coefficients.A set of computational experiments is performed over real-world data sets to test the performance of the proposed models. The experimental results show that combining the assortativity criterion and the neighborhood constraints leads to an effective strategy to obtain portfolios with a good out-of-sample performance under the risk-return viewpoint.

Система управления колёсного привода подлёдного робота для мониторинга подводных объектов

The aim of the study is to develop a design and to study the control system of a wheeled underwater robot with adjustable buoyancy for under-ice monitoring of underwater objects.As part of the study, the task is to generate a mathematical model and its computer implementation for the controlled movement of a wheeled robot on the inner surface of ice, as well as to set up computational experiments demonstrating the operability of the proposed automatic control system for an anti-slip device.The work uses both classical methods for constructing and studying mathematical models and control systems for mobile robots, as well as original methods for numerically integrating systems of nonlinear differential equations that describe the effects of slipping the robot wheels relative to the supporting ice surface.The novelty of the work lies in using an original way of moving a wheeled robot at the interface of media with regulating the normal reaction by controlling the volume of wheeled air cylinders and controlling slippage using an automatic control system that improves the drive energy efficiency while accelerating.In the course of the study, the authors developed: an original design and a method of moving a robot for monitoring underwater objects, a design diagram of the device and a schematic design of the robot drive control system. A mathematical model is created that describes the object controlled motion and a set of computational experiments is performed to prove the applicability of the proposed methods for implementing movement without slipping the driving wheels of a mobile robot.The method of moving proposed in the paper has a number of key advantages in monitoring underwater objects; however, implementing the advantages in practice is associated with the necessity to use a system for controlling slippage of the robot wheels with a supporting surface. The paper proposes the structure and algorithms of the control system to ensure movement with minimal slippage, and computational experiments on the mathematical model of the device prove its applicability and effectiveness.

A New Visualization and Analysis Method for a Convolved Representation of Mass Computational Experiments with Biological Models

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics.

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

Event-triggered model predictive control for the cascade filling process of a hydrogen fuelling station

Efficient filling strategies for hydrogen fuel cell vehicles are critical for hydrogen utilization efficiency at hydrogen fuelling stations. A novel event-triggered model predictive control framework is proposed in this article for the filling process of a hydrogen fuelling station, which involves multiple compressors, cascade storage tanks, and multiple dispensers. The filling process is formulated as a Mixed-Integer NonLinear Programming (MINLP) problem with the objective of minimizing the vehicle filling times and maximizing the hydrogen utilization efficiency. A solution approach that combines the mixed-integer linear programming and genetic algorithm is designed for solving the resulting MINLP problem. In addition, an event-triggered mechanism is proposed to increase the computational efficiency and to update the control inputs only when needed. Different sets of computational experiments are carried out to demonstrate the effectiveness of the mathematical formulation and the solution approach.

Area Coverage Optimization using Networked Mobile Robots with State Estimation

In this paper, we present a solution to the area coverage problem using a team of mobile robots with state estimation. A group of autonomous mobile robots is deployed in a two-dimensional area of interest, for example, where communication among robots is limited or noisy as expected in a real life scenario. Each robot estimates its own state (position and orientation) using noisy range and bearing information received from other robots in its operating range. The area of interest is then divided into multiple sub-area using a voronoi tessellation. Using the classical Lloyd's algorithm, each robot employs distributed action command to move towards the centroid of the voronoi cell that it belongs yielding the maximum coverage of the area. Here we emphasize that the network of autonomous robots deployed in the environment is unknown a priori. A set of computer experiments is conducted to validate the fact that the area coverage is still possible under noisy communication among robots deployed in a two-dimensional area.

Alphabet Flatting as a variant of n-gram feature extraction method in ensemble classification of fake news

The detection of disinformation becomes a significant challenge in the modern world. Most of our communication media and most of the sources of information about reality are located on the distributed network services, where the published content is usually not a subject to any initial verification. One of the few tools that seem to be able to process such large volumes of data efficiently are pattern recognition methods employing extraction of features obtained through the Natural Language Processing models and procedures. The following paper is proposing an Alphabet Flatting – a modification of the preprocessing method for the feature extraction from large language corpora – allowing the construction of diverse classifier ensembles integrated by the support accumulation, the generalization power of which may compete with quality of the state-of-the-art models in environments with strict time constraints. The proposed method has been thoroughly evaluated with the set of computer experiments, the results of which allow us to conclude its potential usefulness in the solutions of the automatic systems for preventing the spread of fake news.

On the Value of Dynamism in Transit Networks

The rise of on-demand mobility technologies over the past decade has sparked interest in the integration of traditional transit and on-demand systems. One of the main reasons behind this is the potential to address a fundamental trade-off in transit: the ridership versus coverage dilemma. However, unlike purely fixed systems or purely on-demand systems, integrated systems are not well understood; their planning and operational problems are significantly more challenging, and their broader implications are the source of a heated debate. Motivated by this debate, we introduce the dynamicity gap, a general concept that quantifies the attainable benefit of allowing (but not requiring) dynamic components in the response strategy to a multistage optimization problem. Although computing the dynamicity gap exactly may be intractable, we develop an analytical framework with which to approximate it as a function of problem input parameters. The framework allows us to certify the value of dynamism (i.e., a dynamicity gap greater than one) for certain combinations of problem input parameters. We showcase our approach with two sets of computational experiments, from which we gain both qualitative and quantitative insights about the settings in which the integration of transit and on-demand systems may certifiably be a worthwhile investment.Funding: This work was partially supported by the National Science Foundation [Grants DMS-1839346 and CNS-1952011]. Part of this research was performed while the authors were visiting the Institute for Pure and Applied Mathematics, which is supported by the National Science Foundation [Grant DMS-1925919].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1193 .

Formulations and valid inequalities for the capacitated dispersion problem

AbstractThis work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable‐fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances.

Combining hybrid genetic search with ruin-and-recreate for solving the capacitated vehicle routing problem

The Capacitated Vehicle Routing Problem (CVRP) has been subject to intense research efforts for more than sixty years. Yet, significant algorithmic improvements are still being made. The most competitive heuristic solution algorithms of today utilize, and often combine, strategies and elements from evolutionary algorithms, local search, and ruin-and-recreate based large neighborhood search. In this paper we propose a new hybrid metaheuristic for the CVRP, where the education phase of the hybrid genetic search (HGS) algorithm proposed by (Vidal Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood 2020) is extended by applying large neighborhood search (LNS). By performing a series of computational experiments, we attempt to answer the following research questions: 1) Is it possible to gain performance by adding LNS as a component in the education phase of HGS? 2) How does the addition of LNS change the relative importance of the local search neighborhoods of HGS? 3) What is the effect of devoting computational efforts to the creation of an elite solution in the initial population of HGS? Through a set of computational experiments we answer these research questions, while at the same time obtaining a good configuration of global parameter settings for the proposed heuristic. Testing the heuristic on benchmark instances from the literature with limited computing time, it outperforms existing algorithms, both in terms of the final gap and the primal integral.

A clustering metaheuristic for large orienteering problems.

The Orienteering Problem is a routing problem that commonly appears in mapping, transportation, distribution, and scheduling scenarios. The Orienteering Problem is a challenging NP-hard problem, such that obtaining optimal or near optimal solutions usually requires a significant amount of computation for large and even moderately large instances. As a result, existing algorithms cannot effectively be utilized for solving large Orienteering Problems in an online setting, which is often required in real-world applications where a plan has to be iteratively computed. For instance, a planner might need to adapt to changes in the scenario or in the environment (e.g., this is common in goods delivery, as well as in mobile robotic scenarios for coverage, monitoring, and surveillance). Motivated by these limitations, we propose a multi-stage clustering-based metaheuristic for tackling large Orienteering Problems in an effective, strategically controlled amount of computation time. The metaheuristic starts by decomposing the problem into smaller, independent sub-problems that are efficiently solved using an algorithm of choice, sequentially or in parallel. The obtained solutions are then merged to form a solution for the original problem, and then further optimized and processed to ensure feasibility. The metaheuristic aims to dramatically improve the computation time of a given Orienteering Problem algorithm without a significant decrease in the solution quality of that algorithm, especially for large Orienteering Problems. We have validated the effectiveness of the proposed metaheuristic design through a set of computational experiments. In particular, using a state-of-the-art heuristic and an exact algorithm, we have shown that it is significantly beneficial to use the Orienteering Problem algorithm plugged into our metaheuristic, as opposed to using it as a standalone algorithm. This was found to be especially true for large problems. As a result, large instances of Orienteering Problems can be effectively tackled within reasonable time bounds even for online application scenarios.

Hyperbolic regression: a new regression model with applications to the binary classification problem

This paper proposes a new regression model in which the outcome variables are restricted to values in the interval [0,1] or also to values measured on a binary scale, when the model can be used for the binary classification problem. The name hyperbolic regression was given because the model originated from the hyperbolic penalty method. More precisely, a parameterization of the derivative of the hyperbolic penalty function is proposed for the construction of the regression model. The coefficients of the hyperbolic regression model can be obtained by either the least squares or the maximum likelihood methods. The hyperbolic regression belongs to the class of generalized linear models and has similarities with the logistic regression. Thus, a comparison of the logistic and hyperbolic regression models is presented. To illustrate the efficiency of the method, a set of computational experiments is performed, making use of the traditional instances described in the literature. In almost all experiments, the hyperbolic regression had lower residues as well as greater accuracy and F1 score than the logistic regression. Thus, the proposed model can be very promising for regressions and binary classification tasks.

Risk-averse hub location: Formulation and solution approach

In this study, we present risk-neutral and risk-averse two-stage stochastic formulations for the uncapacitated multiple allocation p-hub median problem and discuss the impact of risk-aversion on the optimal solution. Although stochastic models are useful to tackle the uncertainty in problem parameters, the solution of these models requires higher computational effort than their deterministic counterparts. Therefore, we present a scenario decomposition algorithm for the stochastic formulations. To evaluate the performance of the proposed solution algorithm, a set of computational experiments is conducted on real data sets. The results show that the proposed algorithm is very effective in finding optimal or near-optimal solutions in significantly shorter computation time than that of deterministic equivalent problems.