Deterministic Version Research Articles

A simheuristic for project portfolio optimization combining individual project risk, scheduling effects, interruptions, and project risk correlations

This paper introduces a simheuristic method to the Project Portfolio Selection Problem, designed to maximize the net present value of the portfolio while considering uncertain costs, schedules, interruptions, and inter-project risk correlations. The novel approach combines techniques from Monte Carlo simulation, critical path analysis, queuing theory, and optimization, integrating baseline schedules, project-level uncertainties, budgetary constraints, and risk correlations in a single model. A computational experiment is conducted on a realistic set of ten candidate projects and validated respect to the deterministic version of the problem, demonstrating its ability to select near optimal portfolio proposals with varying combinations of risk and net present value. The findings highlight the significant impact of factors such as contingency reserve allocation policies, operational interruptions, and project risk correlations on portfolio decisions, constituting a helpful framework for the decision-makers at portfolio level.

Better Apprenticeship Learning with LLM Explanations

As the population ages, care robots will play an increasing role in assisting caregiving by taking on repetitive or physically cumbersome activities. To effectively provide care, robotic agents must be able to meet the needs and preferences of care receivers. However, these needs and preferences may change over time, making it intractable to pre-define the way the care robot should act before deployment. Instead, the care robot should be able to learn directly from non-expert end-user demonstrations. However, prior work investigating the feasibility of learning a policy from older adult demonstrations finds that older adult demonstrators desire a better understanding of what the robot needs them to do, and how. To help demonstrators understand how to improve on suboptimal or heterogeneous demonstrations, we propose to utilize a Large Language Model to provide human-interpretable explanations of Shapley values of a policy. These explanations enable the demonstrator to understand how the policy is performing, and what changes are needed, informing their corrective demonstrations. We showcase our framework's performance in deterministic and stochastic versions of Wumpus World.

Exact pretransition effects in kinetically constrained circuits: Dynamical fluctuations in the Floquet-East model.

We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical "Floquet-East" model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the "energy-entropy" crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of "hydrophobic collapse."

Scaling laws and exact results in turbulence *

In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity 13 249–55) and Eyink (2003 Nonlinearity 16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s 45 , 43 , 415 laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.

Pricing heterogeneous products to heterogeneous customers who buy sequentially

This paper considers optimal pricing in a system with limited substitutable resources, such as certain goods or services. Prices for the different resources have to be set and then customers with heterogeneous preferences show up sequentially. Customers, of n types, select an item from the m available resources, depending on their valuations of the resources and the prices. The goal is to analyze this optimization problem, characterize a set of candidates to optimal solutions and provide methods for solving it. We prove that this problem is NP-hard to approximate within a factor O(n1-ε)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^{1-\\varepsilon })$$\\end{document} for any fixed ε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon >0$$\\end{document}. Another important contribution is to prove that, the space of prices (which in principle is a continuous domain in Rm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^m$$\\end{document}), can be reduced to a finite set of vectors of cardinality mm-2nm2m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m^{m-2}n^m2^m$$\\end{document}. For a deterministic version of the problem, where the customer types are known to the firm, we provide a mathematical program that chooses the best set of prices. We report extensive computational results showing the usefulness of our exact approach to solve medium size problems with up to 200 customers and different assortments of products and customer types. We then show how to approximate the stochastic model by a small number of solutions of deterministic scenarios solved using a mixed-integer linear program.

Impacts of Stochastic Coalescence Variability on Warm Rain Initiation Using Lagrangian Microphysics in Box and Large-Eddy Simulations

Abstract Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing (AON) superdroplet method (SDM) and a deterministic version of SDM (dSDM) that applies a fractional approach similar to the average impact method. In LES, variabilities driven by microphysics and by flow realizations are separated using the “piggybacking” technique. Rain initiation averaged over many realizations of the box model is delayed, and rain variability increases as the number of superdrops per collision volume NSD is decreased using SDM. In contrast, rain initiation time using SDM in LES is insensitive to NSD for 32 ≤ NSD ≤ 512. This is explained through the interaction between LES grid boxes, each acting as a separate collision volume. Variability across the ensemble of LES collision volumes using SDM results in rain quickly initiating in some of the LES grid cells at low NSD and leading to a similar overall timing of rain initiation from the cloud compared to simulations with high NSD. There is a ∼20% decrease in the total rain mass and mean rain flux as NSD is increased from 32 to 256, with little additional change as NSD is increased from 256 to 512. The fractional coalescence approach in dSDM leads to reduced microphysical variability and a 15–18-min delay in rain initiation compared to SDM. An additional LES ensemble with microphysical variability feeding back to the dynamics shows that flow variability dominates the impact of microphysical variability on rain properties. Thus, flow variability must be constrained to isolate impacts of microphysical variability. Significance Statement An emerging tool in cloud microphysics modeling represents drops by computational particles called “superdroplets” that evolve in the modeled flow. Recent studies have documented that different superdroplet models produce widely varying predictions of rain. Understanding these differences is an important step in the wider adoption of these models by the community. Here, we examine different methods for representing droplet collision-coalescence in a superdroplet model and sensitivity to the number of superdroplets employed. The timing of rain initiation is insensitive to the superdroplet number in 3D cloud simulations, but rain is substantially delayed using a coalescence method that limits random variability in droplet collisions. We also show that flow variability must be constrained to isolate impacts of microphysical variability on rain properties.

Onsager's ‘ideal turbulence’ theory

In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for individual turbulent flow realisations modelled by incompressible Navier–Stokes equations, motivated by experimental observations that dissipation of kinetic energy does not vanish. I review here developments spurred by his key idea that such flows are well described by distributional or ‘weak’ solutions of ideal Euler equations. 1/3 Hölder singularities of the velocity field were predicted by Onsager and since observed. His theory describes turbulent energy cascade without probabilistic assumptions and yields a local, deterministic version of the Kolmogorov $4/5$ th law. The approach is closely related to renormalisation group methods in physics and envisages ‘conservation-law anomalies’, as discovered later in quantum field theory. There are also deep connections with large-eddy simulation modelling. More recently, dissipative Euler solutions of the type conjectured by Onsager have been constructed and his $1/3$ Hölder singularity proved to be the sharp threshold for anomalous dissipation. This progress has been achieved by an unexpected connection with work of John Nash on isometric embeddings of low regularity or ‘convex integration’ techniques. The dissipative Euler solutions yielded by this method are wildly non-unique for fixed initial data, suggesting ‘spontaneously stochastic’ behaviour of high-Reynolds-number solutions. I focus in particular on applications to wall-bounded turbulence, leading to novel concepts of spatial cascades of momentum, energy and vorticity to or from the wall as deterministic, space–time local phenomena. This theory thus makes testable predictions and offers new perspectives on large-eddy simulation in the presence of solid walls.

Odyssean forward guidance in normal times

We present a systematic treatment of dynamic effects of Odyssean forward guidance – explicit announcements about future policy rates. We focus on normal times unlike the mainstream of the literature that focuses on episodes of an effective (zero) lower bound on nominal interest rates. We present novel closed-form solutions to both deterministic and stochastic versions of a stylized new Keynesian model with fully anticipated future shocks. We establish a theorem that delineates the parameter space into real and complex-root regions characterized by different characteristic roots. We formulate a simple recipe for testing the effectiveness of forward guidance: the size of the smallest root is a single sufficient statistics that determines whether or not forward guidance generates significant contemporaneous effects.

A Sim-Learnheuristic for the Team Orienteering Problem: Applications to Unmanned Aerial Vehicles

In this paper, we introduce a novel sim-learnheuristic method designed to address the team orienteering problem (TOP) with a particular focus on its application in the context of unmanned aerial vehicles (UAVs). Unlike most prior research, which primarily focuses on the deterministic and stochastic versions of the TOP, our approach considers a hybrid scenario, which combines deterministic, stochastic, and dynamic characteristics. The TOP involves visiting a set of customers using a team of vehicles to maximize the total collected reward. However, this hybrid version becomes notably complex due to the presence of uncertain travel times with dynamically changing factors. Some travel times are stochastic, while others are subject to dynamic factors such as weather conditions and traffic congestion. Our novel approach combines a savings-based heuristic algorithm, Monte Carlo simulations, and a multiple regression model. This integration incorporates the stochastic and dynamic nature of travel times, considering various dynamic conditions, and generates high-quality solutions in short computational times for the presented problem.

Comparison of stochastic and deterministic models for gambiense sleeping sickness at different spatial scales: A health area analysis in the DRC.

The intensification of intervention activities against the fatal vector-borne disease gambiense human African trypanosomiasis (gHAT, sleeping sickness) in the last two decades has led to a large decline in the number of annually reported cases. However, while we move closer to achieving the ambitious target of elimination of transmission (EoT) to humans, pockets of infection remain, and it becomes increasingly important to quantitatively assess if different regions are on track for elimination, and where intervention efforts should be focused. We present a previously developed stochastic mathematical model for gHAT in the Democratic Republic of Congo (DRC) and show that this same formulation is able to capture the dynamics of gHAT observed at the health area level (approximately 10,000 people). This analysis was the first time any stochastic gHAT model has been fitted directly to case data and allows us to better quantify the uncertainty in our results. The analysis focuses on utilising a particle filter Markov chain Monte Carlo (MCMC) methodology to fit the model to the data from 16 health areas of Mosango health zone in Kwilu province as a case study. The spatial heterogeneity in cases is reflected in modelling results, where we predict that under the current intervention strategies, the health area of Kinzamba II, which has approximately one third of the health zone's cases, will have the latest expected year for EoT. We find that fitting the analogous deterministic version of the gHAT model using MCMC has substantially faster computation times than fitting the stochastic model using pMCMC, but produces virtually indistinguishable posterior parameterisation. This suggests that expanding health area fitting, to cover more of the DRC, should be done with deterministic fits for efficiency, but with stochastic projections used to capture both the parameter and stochastic variation in case reporting and elimination year estimations.

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.

A stochastic simulation-based chance-constrained programming model for optimizing watershed best management practices for nonpoint source pollution control under uncertainty

In this study, a stochastic simulation-based chance-constrained programming (SSCP) model is developed by integrating soil and water assessment tool (SWAT), generalized likelihood uncertainty estimation (GLUE), chance-constrained programming (CCP) and genetic algorithm (GA) for managing non-point source (NPS) pollution under uncertainty. The SSCP model improves upon conventional simulation-based optimization methods by effectively (i) reflecting the propagation of stochastic uncertainties from the SWAT to the optimization framework by the joint GLUE and CCP (GLUE-CCP) approach, and (ii) identifying the optimal implementation levels of best management practices (BMPs) under different constraint-violation risk levels. The SSCP is solved using a GA with parallel sampling technique after conversion into the corresponding deterministic version. The model is applied to determine the optimal types, sizes and locations of BMPs for NPS pollution control in the Hanjiang River basin, China. The results indicate that, under low-risk conditions, grassed waterways and filter strips should be implemented in the northern part of the basin and larger detention ponds of about 637.8 ∼ 850.4 ha should be installed in the northern and eastern parts of the basin; whereas under high-risk conditions, filter strips should be installed in the northeastern part of the basin and larger detention ponds of about 562.1 ∼ 749.5 ha should be installed in the northern and southwestern parts of the basin. Moreover, as the risk level decreases, stricter control of constraint violations leads to higher BMP implementation costs in order to mitigate the risk of excessive NPS pollution loads. Thus, the proposed model provides valuable insights into the selection of BMP placement schemes at various risk levels, facilitating the reduction of NPS pollution at the outlet of the Hanjiang River basin to acceptable levels while considering the tradeoff between system cost and risk.

Disposition effect and its outcome on endogenous price fluctuations

AbstractWe have developed a financial market model that incorporates the Disposition Effect, which refers to traders’ tendency to avoid realizing losses. Specifically, our model replicates several stylized facts commonly observed in financial markets, such as fat tails and volatility clustering. These market characteristics can be attributed to the Disposition Effect, especially when the trading behavior of agents aligns with the findings of Ben-David and Hirshleifer (Rev Financ Stud 25(8):2485–2532, 2012). To demonstrate this, we examine two versions of the model: one where a class of agents exhibits a high degree of Disposition Effect and another where traders are not influenced by it. By comparing the simulated time series generated by both versions, we find that the one with agents affected by the Disposition Effect better replicates the features observed in real financial markets. This holds true for both the deterministic and stochastic versions of the model.

Scalable High-Quality Hypergraph Partitioning

Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality. This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar . Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening – which are used in a multilevel scheme with log (n) levels. As additional components, we parallelize the n -level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs. We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar , while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x (log (n) -level), and 25.9x ( n -level).

Optimization models for the installation planning of offshore wind farms

Challenges posed by global warming motivate the increasing interest in green energy sources, such as wind energy. To make wind energy attractive from an economic viewpoint, the decision-making problems faced in designing, installing, and maintaining wind farms have to be optimized. In this paper, we focus on the problem of optimally planning the installation process of offshore wind farms, as faced by Vattenfall, a leading European energy company. We first formulate the deterministic version of this Installation Planning of Offshore Wind Farms (IPOWF) problem as a Mixed Integer Linear Programming (MILP) model. From this model, we then derive other MILPs that can provide lower and upper bounds to the optimal installation cost. To cope with weather uncertainty, we also provide a light-robust MILP. These models are tested on real-life instances corresponding to two wind farms that Vattenfall has recently built in Denmark and Germany. Computational results show that tight primal and dual solutions can be computed for the deterministic case with the proposed models and that the light-robust model yields solutions that are robust to weather uncertainty.

Erasure Codes with a Hierarchical Bundle Structure

This paper presents a proof of the existence of computationally fast probabilistic erasure codes at distance ∈ from being MDS, namely the decoding algorithm is able with high probability to reconstruct the n letter message from any set of (1+∈)n letters. It can either be fixed rate or a rateless LT code [10] in that any number of code letters can be produced and each is produced independently of the others. We also decrease the minimum packet size from many to one letter. The key ingredient is a scheme Hierarchical Bun- dle/Bin (HB) which splits the message into a hierarchy of disjoint bundles and produces coded packets about each bundle. We show a correspondence of this to a particular game having to do with randomly throwing balls into a hierarchy of bins. The “information” that does not over flow from a smaller bin, contributes to the next larger bin that it is contained in. We prove matching upper and lower bounds on the cost of this game and provide the implementation details. This analysis is somewhat analogous to the evolution of the “ripple” in the LT decoding analysis [10]. The bundle size corresponds to the degree of the packet, therefore, smaller bundles tend to reduce encoding/decoding complexity, but packets coming from larger bundles ensure the approximately-MDS constraint, by ensuring more coverage. Our HB scheme with largest block size b requires encoding and decoding time O(∈b2) rather than the O(b2) needed for Reed-Solomon codes. This scheme HB (together with Spielman’s expanders) gives a probabilistic code with running time O(∈-1 ln(∈-1)n). Alon and Luby [5, 6] simultaneously developed a deterministic version but their running time is O(∈-4n). Both our and Alon’s results have since been completely subsumed by the latest generation of Shokrollahi and Luby’s Raptor codes [13, 14, 11].

Pre-auction optimization for the selection of shared customers in the last-mile delivery

AbstractCompanies are constantly looking for new strategies to improve their logistics performance and ensure their competitiveness in the global market. This article provides a new scheme for managing the selection of shared customers for a logistics company. The new mechanism proposes the use of the auction as a tool to manage the selection of shared clients through the coalition pool. Thus, all unprofitable shared customers will be pushed to the pool for outsourcing by the other collaborating carriers. Then, some profitable auctioned ones will be selected. The selection system is designed based on solving a vehicle routing problem that aims to maximize the carrier's profit in a decentralized context. At first, a mixed integer linear programing model is derived to solve the deterministic version of the problem. Then in order to efficiently address the stochastic version of the problem, a simulation-based optimization model is developed. This model is employed to solve a real case study of a parcel delivery company, considering the travel times as a bimodal distribution. A comparative study is conducted to demonstrate the effectiveness of the auction approach in managing shared customers. The results of our study reveal that the proposed auction approach efficiently manages the shared customers which leads to the substantial increase of 22.65% in profits for the delivery company. These findings have significant implications for logistics companies seeking to improve their performance and competitiveness in the global market.

Dynamic routing for the Electric Vehicle Shortest Path Problem with charging station occupancy information

We study the problem of an Electric Vehicle (EV) having to travel from an origin to a destination in the shortest amount of time. We focus on long-distance settings, where the shortest path between the origin and the destination has energy requirements exceeding the EV autonomy. The EV may charge its battery at public Charging Stations (CSs), which are subject to unknown arrivals of exogenous vehicles requiring uncertain charging times. Thus, the waiting times at CSs are uncertain. Similar to other contributions in the literature, we model CSs using appropriately defined queues, whose status is revealed upon the EV arrival. However, following recent technological advances, we also consider that the status of each CS is updated in real-time via binary Occupancy Indicator (OI) information signaling if a CS is busy or not. Therefore, we assume that the EV continuously receives OI updates on all CSs. At each update, we determine the sequence of CSs to visit along with associated charging quantities. We name the resulting problem as the Electric Vehicle Shortest Path Problem with charging station Occupancy Indicator information (EVSPP-OI). In this problem, we consider that the EV is allowed to partially charge its battery, and we model charging times via piecewise linear charging functions that depend on the CS technology.We propose a Markov Decision Process formulation for the EVSPP-OI, which aims at optimizing the EV routing and charging policy. To solve the problem, we develop a reoptimization algorithm that establishes the sequence of CS visits and charging amounts based on system updates. Specifically, we propose a simulation-based approach to estimate the waiting time of the EV at a CS as a function of its arrival time. As the path to a CS may consist of multiple intermediate CS stops, estimating the arrival times at each CS is fairly intricate. To this end, we propose an efficient heuristic that yields approximate lower bounds on the arrival time of the EV at each CS, which are used to derive an estimation of the waiting time at each CS. We use these estimations to define a compatible deterministic version of the EVSPP, which we solve with an existing algorithm. We conduct a comprehensive computational study and compare the performance of our methodology with a benchmark that observes the status of CSs only upon arrival (i.e., with no OI information). Results show that our method reduces waiting times and total trip duration by an average of 23.7%–95.4% and 1.4%–18.5%, respectively.

Minimal Determinization Algorithm for Fuzzy Automata

The determinization of fuzzy automata is a well-studied problem in theoretical computer science celebrated for its practical applications. Indeed, in the fields of fuzzy discrete event systems, fault diagnosis, clinical monitoring, decision-making systems, and model checking, when a suitable model of a fuzzy automaton is employed, it is desirable to find its language-equivalent deterministic version because of its computational efficiency. Although many methods have been developed to convert a fuzzy automaton to its language equivalent fuzzy deterministic finite automaton (FDfA), they can be applied only for fuzzy automata defined over specific underlying sets of truth values. For example, recently developed determinization methods employ the concept of maximal factorization, which can be defined only on non-locally finite lattices or the Boolean lattice. In addition, not all such determinization methods result in a minimal FDfA. On the other hand, even though such determinization methods have been developed for fuzzy automata over specific underlying structures, these methods cannot be generalized for fuzzy automata over locally finite lattices. This article focuses on filling this gap and develops a novel method for computing a minimal FDfA for a fuzzy automaton defined over a locally finite and divisible residuated lattice. Our method uses the new concept of a reduction graph that emerges from the strict order relation on the resulting fuzzy states, according to which we can construct all minimal FDfAs equivalent to a given fuzzy automaton.

An advanced hyperheuristic approach for the home health care scheduling problem with time window in deterministic and uncertain environments

In the last two decades, Home Health Care (HHC) services have garnered substantial attention from global researchers and practitioners. These services face significant challenges related to strategic, tactical, and operational decisions that must be solved for enhancing their efficiency and quality. Notably, researchers have focused significantly on the scheduling and routing aspects, recognizing their potential to enhance patient satisfaction, safety, and cost-effectiveness for both patients and HHC companies. Recent studies have highlighted the stochastic nature of these services, including random service and travel times, that may affect the scheduling and routing components. Nonetheless, a significant portion of recent research predominantly focuses on the deterministic version of the problem, disregarding its fundamental stochastic nature as emphasized by feedback from HHC companies. Within this context, we propose a two-stage mixed integer mathematical formulation to address the Home Health Care Scheduling and Routing Problem (HHCSRP), encompassing stochastic demand, service, and travel times. Given the inherent Nondeterministic Polynomial (NP)-hardness of these scheduling and routing problems, we introduce a hyperheuristic approach based on a TS metaheuristic and Variable Neighborhood Search (VNS) heuristic. Extensive experiments validate the effectiveness of our proposed modeling and solving approaches, outperforming similar methods across various metrics. Notably, our stochastic model exhibits superior performance in terms of parameters like the number of patients served within time windows and computational time required to achieve optimal solutions. This study thus contributes a valuable decision support system for Home Health Care companies, empowering them to make informed decisions and construct robust schedules for their caregivers.