Stochastic Combinatorial Optimization Research Articles

Solving the Online On-Demand Warehousing Problem

In On-Demand Warehousing, an online platform acts as a central mechanism to match unused storage space and related services offered by suppliers to customers. Storage requests can be for small capacities and very short commitment periods if compared to traditional leasing models. The objective of the On-Demand Warehousing Problem (ODWP) is to maximize the number of successful transactions among the collected offers and requests, considering the satisfaction of both the supply and demand side to preserve future participation to the platform. The Online ODWP can be modeled as a stochastic reservation and assignment problem, where dynamically arriving requests of customers must be rapidly assigned to suppliers. Firstly, an online stochastic combinatorial optimization framework is adapted to the Online ODWP. The key idea of this approach is to generate samples of future requests by evaluating possible allocations for the current request against these samples. In addition, expectation, consensus, and regret, and two greedy algorithms are implemented. All solution methods are compared on a dataset of realistic instances of different sizes and features, demonstrating their effectiveness compared to the oracle solutions, which are based on the assumption of perfect information about future request arrivals. A newly proposed approach of risk approximation is shown to outperform alternative algorithms on large instances. Managerial insights regarding acceptance and rejection strategies for the platform are derived. It is shown how requests with large demand, long time frame, not very long spanning time, and average compatibility degree, are very likely to be rejected in the optimal solution.

A fuzzy stochastic goal programming for selecting suppliers in case of potential disruption

ABSTRACT Due to globalization and the new characteristics of the business, companies face various challenges to ensure their continuity and competitive advantages. COVID-19 pandemic can be an extreme event that will eventually force many businesses and all industries to redesign and transform their global supply chain model? Challenges concerning mainly reducing the operating cost which is based on selecting the optimal suppliers to provide a reliable product. This study contributes to solving a supplier selection problem under disruption risk due to the lack of literature reviews with a lack of multi-methodological perspective for the fuzzy stochastic notions and quantitative techniques for the quantification of risk alternatives. Prior studies are neglecting to consider the value of risk and prefer to discover chances for optimizing anticipated costs or profits. This study proposed a fuzzy stochastic goal programming approach for selecting the optimal supplier under disruption risk. The proposed model incorporates multiple criteria such as capacity, stochastic demand, and probability of disturbance. The problem of stochastic combinatorial optimization obtained is presented as a program of fuzzy random aim by integrating techniques of value at risk and conditional risk value. Numeric samples and calculation results are included. The results of the models help the decision-maker to optimize the selection of suppliers in the event of a disturbance risk problem by an estimated value at risk and by simultaneously minimizing the conditional value of the risk and demonstrate the efficacy and acceptability of the created risk-averse technique as well as the effects of risk factors on our model behavior.

Learning to schedule heuristics for the simultaneous stochastic optimization of mining complexes

The simultaneous stochastic optimization of mining complexes is a large-scale stochastic combinatorial optimization problem that simultaneously manages the extraction of materials from multiple mines and their processing through interconnected facilities to generate a set of final products, while taking into account geological (material supply) uncertainty to manage the associated risk. Existing methods do not offer solutions to such a complex problem in a reasonable time. This work proposes a data-driven framework for heuristic scheduling in a fully self-managed hyper-heuristic to solve the simultaneous stochastic optimization of mining complexes. The proposed learn-to-perturb hyper-heuristic is a multi-neighborhood simulated annealing algorithm that selects the heuristic (perturbation) to be applied in a self-adaptive manner using reinforcement learning to efficiently explore the local search that is best suited to a particular search point. By learning from data that describes the performance of the heuristics, a problem-specific ordering of heuristics that collectively find better solutions faster is obtained. To the best of our knowledge, this research proposes the first data-driven heuristic search tree for mine planning. Results from several instances of two types of large-scale industrial mining complexes show a reduction of up to 80% in execution time and an order of magnitude reduction in primal suboptimality compared to state-of-the-art methods.

Problem-driven scenario clustering in stochastic optimization

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by finding a smaller subset of scenarios, reduce the numerical complexity while keeping the error at an acceptable level. In this paper we propose a novel and computationally efficient methodology to tackle the scenario reduction problem for two-stage problems when the error to be minimised is the implementation error, i.e. the error incurred by implementing the solution of the reduced problem in the original problem. Specifically, we develop a problem-driven scenario clustering method that produces a partition of the scenario set. Each cluster contains a representative scenario that best reflects the optimal value of the objective function in each cluster of the partition to be identified. We demonstrate the efficiency of our method by applying it to two challenging two-stage stochastic combinatorial optimization problems: the two-stage stochastic network design problem and the two-stage facility location problem. When compared to alternative clustering methods and Monte Carlo sampling, our method is shown to clearly outperform all other methods.

Investigation of ant colony optimization with Levy flight technique for a class of stochastic combinatorial optimization problem

The demand for efficient solutions to optimization problems with uncertain and stochastic data is increasing. Probabilistic traveling salesman problem (PTSP) is a class of Stochastic Combinatorial Optimization Problems (SCOPs) involving partially unknown information about problem data with a known probability distribution. It consists to minimize the expected length of the tour where each customer requires a visit only with a given probability, at which customers who do not need a tour are just ignored without further optimization. Since the PTSP is NP-hard, the usage of metaheuristic methods is necessary to solve the problem. In this paper, we present the Ant Colony Optimization (ACO) algorithm combined with the Levy Flight mechanism (LFACO), which is based on Levy distribution to balance searching space and speed global optimization. Experimental results on a large number of instances show that the proposed Levy ACO algorithm on the probabilistic traveling salesman problem allows to obtain better results compared with the classical ACO algorithm.

Risk-averse rehabilitation decision framework for roadside slopes vulnerable to rainfall-induced geohazards

Rainfall-induced slope failures disrupt the traffic and warrant urgent slope repair works. The impact of roadside slope failures can be minimized if slopes are proactively rehabilitated. Nonetheless, transportation agencies are constrained in their budget to rehabilitate a limited number of slope segments due to competing maintenance needs among different transportation assets. Therefore, the transportation agencies should identify the critical slope combination that should be proactively rehabilitated under constraint budgets to lessen the impact on the transportation network during extreme rainfall events. The decision-making approach for slope rehabilitation should also ensure low risk associated with the selected rehabilitation strategy. Current slope-rehabilitation decision models do not consider the risk associated with the rehabilitation strategies in the decision-making process. The objective of this study is to develop a risk-averse stochastic combinatorial optimization to facilitate the selection of slope rehabilitation strategies, which leads to the least expected cost and conditional value at risk (CVaR) for extreme rainfall events. The simulated annealing approach is used to solve the risk-averse combinatorial optimization rehabilitation problem with the objective function that measures the total cost of traffic disruption and slope restoration post-failures. The approach is demonstrated using a transportation network in Lamar County, Texas. Unlike a genetic algorithm-based approach in the literature that yields a single slope rehabilitation strategy, the proposed risk-averse simulated annealing approach identifies rehabilitation strategies along the Pareto efficient frontier facilitating the rehabilitation decisions based on the tradeoff between expected cost and CVaR. For the network in Lamar County, the proposed risk-averse simulated annealing provided a solution in the Pareto front that reduced CVaR by 2.0% compared to the solution obtained from the genetic algorithm-based approach while only increasing the expected cost by 0.8%. The risk-averse optimization approach will aid transportation agencies in determining slope rehabilitation strategies for minimizing the impact of rainfall-induced failures at appropriate risk aversion levels.

Cost-Efficient Beam Management and Resource Allocation in Millimeter Wave Backhaul HetNets With Hybrid Energy Supply

Energy consumption accounts for a significant portion of OPEX in 5G networks, which will be further increased when millimeter-wave (mmWave) base stations are deployed. To reduce the cost, renewable energy has been introduced to provide complementary power supply. Nevertheless, how to cost-efficiently utilize radio resources and renewable energy remains a challenge. In this paper, we jointly investigate the beamwidth management and resource allocation in mmWave backhaul HetNets with hybrid energy supply aiming to maximize long-term cost efficiency. This requires solving a mixed stochastic combinatorial optimization problem, characterizing the causal property of renewable energy harvesting process, stochastic channel conditions, and imperfect antenna alignment. Considering the complexity and dynamic environment, a learning system is established instead of using traditional optimization methods which typically experience exponential worst-case complexity and require complete information. Specifically, we propose a Learning-based Cost-efficient Resource Allocation (LCRA) algorithm that employs deep neural network to learn policies from experiences to ensure system performance while achieving cost-efficiency. To enhance the sampling efficiency and stability of the conventional deep reinforcement learning methods for our problem, an improved proximal policy optimization method is proposed to reuse the history samples. Specifically, a modified clip function is designed to deal with the hard restrictions between current and old policies. Furthermore, random network distillation is introduced to enhance the exploration capability. Numerical results reveal the convergence performance of the LCRA and the superiority in improving the cost efficiency in a hybrid energy powered mmWave backhaul HetNet compared with state-of-the-arts

Stochastic Planning and Scheduling with Logic-Based Benders Decomposition

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple no-good cuts as well as analytic logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method. In particular, a branch-and-check variant of LBBD can be faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classic Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem and the first comparison of LBBD with the integer L-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse. Summary of Contribution: We study an important class of optimization problems, namely, two-stage stochastic programs with integer recourse, which are known to be extremely difficult to solve in general. We focus on an application in which the second-stage problem is a scheduling problem, a first in the literature to the best of our knowledge. Our study exemplifies how one can exploit the combinatorial structure of the scheduling problem to derive novel analytic Benders cuts and use them within a branch-and-check algorithm. The proposed algorithm solves instances that are intractable for commercial solvers and state-of-the-art decomposition-based methods, such as the integer L-shaped method. We believe that our study will inspire further research in the use of hybrid logic-based optimization methods for solving stochastic combinatorial optimization problems.

A Data-Driven Approach for the Simultaneous Stochastic Optimization of Mining Complexes

The simultaneous stochastic optimization of mining complexes (SSOMC) is a large-scale stochastic combinatorial optimization problem that simultaneously manages the extraction of materials from multiple mines and their processing using interconnected facilities to generate a set of finished products while taking into account geological uncertainty to manage the associated risk. To address the need for self-managed solution approaches that are able to tackle large-scale instances without resorting to aggregation, this work proposes a data-driven framework for heuristic scheduling in a fully self-managed hyper-heuristic to solve the SSOMC. The proposed hyper-heuristic selects the heuristic (perturbation) to be applied in a self-adaptive manner using state-of-the-art reinforcement learning methods to efficiently explore which local search is best suited for a particular search point. Experiments on real-world mining complexes show a significant reduction in the computational time by 30–45%.

Stochastic makespan minimization in structured set systems

We study stochastic combinatorial optimization problems where the objective is to minimize the expected maximum load (a.k.a. the makespan). In this framework, we have a set of n tasks and m resources, where each task j uses some subset of the resources. Tasks have random sizes \(X_j\), and our goal is to non-adaptively select t tasks to minimize the expected maximum load over all resources, where the load on any resource i is the total size of all selected tasks that use i. For example, when resources are points and tasks are intervals in a line, we obtain an \(O(\log \log m)\)-approximation algorithm. Our technique is also applicable to other problems with some geometric structure in the relation between tasks and resources; e.g., packing paths, rectangles, and “fat” objects. Our approach uses a strong LP relaxation using the cumulant generating functions of the random variables. We also show that this LP has an \(\varOmega (\log ^* m)\) integrality gap, even for the problem of selecting intervals on a line; here \(\log ^* m\) is the iterated logarithm function.

Dynamic dispatch algorithm proposal for last-mile delivery vehicle

The complex urban scenario demands decisions which needs to be taken not only fast, but considering a high level of uncertainty. In such context, this study proposes an algorithm to address the vehicle allocation scheduling with a request list unknown a priori, and is revealed along the operation horizon. Based on the OSCO (online stochastic combinatorial optimization) problem, it is presented a framework to operate such problem in a last-mile delivery system where customers requests from e-commerce (or food delivery) along an operations day. The deterministic calculation was realized using a permutational flowshop scheduling problem with the objective of minimizing makespan. Experiments indicated convergence in the algorithm along the planning trials, and a satisfactory makespan prediction, before the orders are revealed, with accuracy. The probability distribution adheres with a bell-shaped (normal) distribution with its population parameters estimated using classical statistics inference theory. Incorporating uncertain in such type of mathematical modeling could open doors for a new era of systems in current days with cloud computing, big data, smart cities, and artificial intelligence.

Hybrid Niche Immune Genetic Algorithm for Fault Detection Coverage in Industry Wireless Sensor Network

The industry wireless sensor network (IWSN) technology, which is used to monitor industrial equipment, has attracted more and more attention in recent years. Sensor nodes in IWSN can spontaneously complete distributed networking and carry out monitoring tasks under random deployment conditions. Therefore, a self‐organized IWSN is particularly suitable for the fault detection and diagnosis of industrial equipment in complex environments. However, due to the detection, ability of a single sensor node is limited, and the monitoring distribution problem is a typical multidimensional discrete NP‐hard combinatorial stochastic optimization problem, which is challenging to solve for the traditional mathematical methods. With the purpose of improving the target monitoring capability and prolonging lifetime of IWSN, a novel hybrid niche immune genetic algorithm (HNIGA) for optimizing the target coverage model of fault detection is proposed. It uses the genetic operation to evolve antibody groups and applies niche technology to maintain the diversity of antibody groups. As a result, HNIGA can effectively reduce the failure rate of detection targets. To verify the performance of HNIGA, a series of simulations under different simulation conditions are carried out. Specifically, HNIGA is compared with genetic algorithm (GA) and simulated annealing (SA). Simulation results show that HNIGA has a faster convergence speed and more robust global search capability than the other two algorithms.

A simheuristic approach for the flexible job shop scheduling problem with stochastic processing times

In this work, we address the flexible job shop scheduling problem (FJSSP), which is a classification of the well-known job shop scheduling problem. This problem can be encountered in real-life applications such as automobile assembly, aeronautical, textile, and semiconductor manufacturing industries. To represent inherent uncertainties in the production process, we consider stochastic flexible job shop scheduling problem (SFJSSP) with operation processing times represented by random variables following a known probability distribution. To solve this stochastic combinatorial optimization problem we propose a simulation-optimization approach to minimize the expected makespan. Our approach employs Monte Carlo simulation integrated into a Jaya algorithm framework. Due to the unavailability of standard benchmark instances in SFJSSP, our algorithm is evaluated on an extensive set of well-known FJSSP benchmark instances that are extended to SFJSSP instances. Computational results demonstrate the performance of the algorithm at different variability levels through the use of reliability-based methods.

A structured view on weighted counting with relations to counting, quantum computation and applications

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines. The goal is to compute the sum of weights of all paths (instead of number of accepting paths). Useful properties and plenty of applications make them interesting. The definition captures even undecidable problems, but obtaining an exponentially small additive approximation is just as hard as solving conventional counting. We present a structured view by defining classes that depend on the functions that assign weights to paths and by showing their relationships and how they generalize counting problems. Weighted counting is flexible and allows us to cast a number of famous results of computational complexity, including quantum computation, probabilistic graphical models and stochastic combinatorial optimization. Using the weighted counting terminology, we are able to simplify and to answer some open questions.

An Immune Chaotic Niche Genetic Algorithm for Monitoring Distribution Problem in Self-Organizing Wireless Sensor Network

Due to the sensors are restricted in sensing capabilities, monitoring distribution has become a challenging problem in self-organizing wireless sensor network (SOWSN). Micro nodes are self-organized tiny devices with limited sensing capabilities. Careful monitoring distribution scheme can be a suitable optimizing means for achieving the required high target detection rate goals, comprising sensing capacity restrictions. However, the monitoring distribution problem is a typical NP-hard combinatorial stochastic optimization problem. In this study, an immune chaotic niche genetic algorithm (ICNGA) to enhance the target detection rate is explored. Advanced operators such as immune operator and chaotic operator are also incorporated into the ICNGA to increase the explore capacity. The represented immune selection and chaotic generation depending on ICNGA with global search capability can simultaneously optimize multiple variables. Simulation results identify that the proposed algorithm can get a higher target detection rate over SFLA and SA. Besides that, the convergence speed of the presented ICNGA is much higher than that of SFLA and SA. So the proposed method significantly enhanced the efficiency.

Analysing the Police Patrol Routing Problem: A Review

Police patrol is a complex process. While on patrol, police officers must balance many intersecting responsibilities. Most notably, police must proactively patrol and prevent offenders from committing crimes but must also reactively respond to real-time incidents. Efficient patrol strategies are crucial to manage scarce police resources and minimize emergency response times. The objective of this review paper is to discuss solution methods that can be used to solve the so-called police patrol routing problem (PPRP). The starting point of the review is the existing literature on the dynamic vehicle routing problem (DVRP). A keyword search resulted in 30 articles that focus on the DVRP with a link to police. Although the articles refer to policing, there is no specific focus on the PPRP; hence, there is a knowledge gap. A diversity of approaches is put forward ranging from more convenient solution methods such as a (hybrid) Genetic Algorithm (GA), linear programming and routing policies, to more complex Markov Decision Processes and Online Stochastic Combinatorial Optimization. Given the objectives, characteristics, advantages and limitations, the (hybrid) GA, routing policies and local search seem the most valuable solution methods for solving the PPRP.

Robust university course timetabling problem subject to single and multiple disruptions

University course timetables are often finalized in stages, in between which, changes in the data make the earlier version infeasible. As each version is announced to the community, it is desirable to have a robust initial timetable, i.e. one that can be repaired with limited number of changes and yielding a new solution whose quality is degraded as little as possible. We define two versions of the robust timetabling problem, first one assuming that only one lecture is disrupted (its scheduled period ceasing to be feasible) and the second one assuming multiple lectures are disrupted. The objective of the algorithms is to identify a good Pareto front defined by the solution quality (penalty associated with soft-constraint violations) and the robustness measure. Two versions of a multi-objective simulated annealing (MOSA) algorithm is developed (MOSA-SD and MOSA-SAA, for single and multiple disruptions, respectively), with the difference being in the way robustness of a solution is estimated within the MOSA algorithm. Extensive computational experiments done using the International Timetabling Competition ITC-2007 data set confirm that MOSA-SD outperforms a genetic algorithm from the literature, and MOSA-SAA outperforms MOSA-SD when there are multiple disruptions. For MOSA-SAA an innovative solution network to structure feasible solutions for a set of disruption scenarios has been developed to efficiently perform sample average approximation (SAA) calculations, which can be adopted for other stochastic combinatorial optimization problems.

A Stochastic Dual Dynamic Integer Programming for the Uncapacitated Lot-Sizing Problem with Uncertain Demand and Costs

We study the uncapacitated lot-sizing problem with uncertain demand and costs. We consider a multi-stage decision process and rely on a scenario tree to represent the uncertainty. We propose to solve this stochastic combinatorial optimization problem thanks to a new extension of the stochastic dual dynamic integer programming algorithm. Our results show that this approach can provide good quality solutions in a reasonable time for large-size instances.

K-adaptability in stochastic combinatorial optimization under objective uncertainty

Abstract We address combinatorial optimization problems with uncertain objective functions, given by discrete probability distributions. Within this setting, we investigate the so-called K-adaptability approach: the aim is to calculate a set of K feasible solutions such that the objective value of the best of these solutions, calculated in each scenario independently, is optimal in expectation. Interpreted as a stochastic optimization problem, we only consider second-stage variables, however, the corresponding candidate solutions are selected in the first stage, i.e., before the scenario is known. We show that this problem is NP-hard even if the underlying certain problem is trivial, and present further complexity results concerning approximability and fixed-parameter tractability with respect to K. Moreover, we present exact solution methods as well as a heuristic for this problem and compare them in an extensive experimental evaluation, where the underlying problem is the Unconstrained Binary Optimization Problem, the Shortest Path Problem or the Spanning Tree Problem. It turns out that the performance and the ranking of these approaches strongly depends on the parameter K and on the number of scenarios.

Stochastic packing integer programs with few queries

We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms. We also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching, matroid, and stable set problems.