On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Physiology-Aware Rural Ambulance Routing

In emergency patient transport from rural medical facility to center tertiary hospital, real-time monitoring of the patient in the ambulance by a physician expert at the tertiary center is crucial. While telemetry healthcare services using mobile networks may enable remote real-time monitoring of transported patients, physiologic measures and tracking are at least as important and requires the existence of high-fidelity communication coverage. However, the wireless networks along the roads especially in rural areas can range from 4G to low-speed 2G, some parts with communication breakage. From a patient care perspective, transport during critical illness can make route selection patient state dependent. Prompt decisions with the relative advantage of a longer more secure bandwidth route versus a shorter, more rapid transport route but with less secure bandwidth must be made. The trade-off between route selection and the quality of wireless communication is an important optimization problem which unfortunately has remained unaddressed by prior work. In this paper, we propose a novel physiology-aware route scheduling approach for emergency ambulance transport of rural patients with acute, high risk diseases in need of continuous remote monitoring. We mathematically model the problem into an NP-hard graph theory problem, and approximate a solution based on a trade-off between communication coverage and shortest path. We profile communication along two major routes in a large rural hospital settings in Illinois, and use the traces to manifest the concept. Further, we design our algorithms and run preliminary experiments for scalability analysis. We believe that our scheduling techniques can become a compelling aid that enables an always-connected remote monitoring system in emergency patient transfer scenarios aimed to prevent morbidity and mortality with early diagnosis treatment.Comment: 6 pages, The Fifth IEEE International Conference on Healthcare Informatics (ICHI 2017), Park City, Utah, 201

Optimal logistics scheduling with dynamic information in emergency response: case studies for humanitarian objectives

The mathematical model of infectious disease is a typical problem in mathematical modeling, and the common infectious disease models include the susceptible-infected (SI) model, the susceptible-infected-recovered model (SIR), the susceptible-infected-recovered-susceptible model (SIRS) and the susceptible-exposed-infected-recovered (SEIR) model. These models can be used to predict the impact of regional return to work after the epidemic. In this paper, we use the SEIR model to solve the dynamic medicine demand information in humanitarian relief phase. A multistage mixed integer programming model for the humanitarian logistics and transport resource is proposed. The objective functions of the model include delay cost and minimum running time in the time-space network. The model describes that how to distribute and deliver medicine resources from supply locations to demand locations with an efficient and lower-cost way through a transportation network. The linear programming problem is solved by the proposed Benders decomposition algorithm. Finally, we use two cases to calculate model and algorithm. The results of the case prove the validity of the model and algorithm

Emergency medical supplies scheduling during public health emergencies: algorithm design based on AI techniques

Based on AI technology, this study proposes a novel large-scale emergency medical supplies scheduling (EMSS) algorithm to address the issues of low turnover efficiency of medical supplies and unbalanced supply and demand point scheduling in public health emergencies. We construct a fairness index using an improved Gini coefficient by considering the demand for emergency medical supplies (EMS), actual distribution, and the degree of emergency at disaster sites. We developed a bi-objective optimisation model with a minimum Gini index and scheduling time. We employ a heterogeneous ant colony algorithm to solve the Pareto boundary based on reinforcement learning. A reinforcement learning mechanism is introduced to update and exchange pheromones among populations, with reward factors set to adjust pheromones and improve algorithm convergence speed. The effectiveness of the algorithm for a large EMSS problem is verified by comparing its comprehensive performance against a super-large capacity evaluation index. Results demonstrate the algorithm's effectiveness in reducing convergence time and facilitating escape from local optima in EMSS problems. The algorithm addresses the issue of demand differences at each disaster point affecting fair distribution. This study optimises early-stage EMSS schemes for public health events to minimise losses and casualties while mitigating emotional distress among disaster victims

A multi-objective evolutionary optimisation model for heterogeneous vehicles routing and relief items scheduling in humanitarian crises

In a disaster scenario, relief items distribution is required as early as possible for the disaster victims to reduce the associated risks. For the distribution tasks, an effective and efficient relief items distribution model is essential to generate relief items distribution schedules to minimise the impact of disaster to the disaster victims. However, developing efficient distribution schedules is challenging as the relief items distribution problem has multiple objectives to look after where the objectives are mostly contradictorily creating a barrier to simultaneous optimisation of each objective. Also, the relief items distribution model has added complexity with the consideration of multiple supply points having heterogeneous and limited vehicles with varying capacity, cost and time. In this paper, multi-objective evolutionary optimisation with the greedy heuristic search has been applied for the generation of relief items distribution schedules under heterogeneous vehicles condition at supply points. The evolutionary algorithm generates the disaster region distribution sequence by applying a global greedy heuristic search along with a local search that finds the efficient assignment of heterogeneous vehicles for the distribution. This multi-objective evolutionary approach provides Pareto optimal solutions that decision-makers can apply to generate effective distribution schedules to optimise the distribution time and vehicles’ operational cost. In addition, this optimisation process also incorporated the minimisation of unmet relief items demand at the disaster regions. The optimised distribution schedules with the proposed approach are compared with the single-objective optimisation, weighted single-objective optimisation and greedy multi-objective optimisation approaches. The comparative results showed that the proposed multi-objective evolutionary approach is an efficient alternative for finding the distribution schedules with optimisation of distribution time and operational cost for the relief items distribution with heterogeneous vehicles in humanitarian crisis

A multi-objective evolutionary optimisation model for heterogeneous vehicles routing and relief items scheduling in humanitarian crises

In a disaster scenario, relief items distribution is required as early as possible for the disaster victims to reduce the associated risks. For the distribution tasks, an effective and efficient relief items distribution model to generated relief items distribution schedules is essential to minimise the impact of disaster to the disaster victims. However, developing efficient distribution schedules is challenging as the relief items distribution problem has multiple objectives to look after where the objectives are mostly contradictorily creating a barrier to simultaneous optimisation of each objective. Also, the relief items distribution model has added complexity with the consideration of multiple supply points having heterogeneous and limited vehicles with varying capacity, cost and time. In this paper, multi-objective evolutionary optimisation with the greedy heuristic search has been applied for the generation of relief items distribution schedules under heterogeneous vehicles condition at supply points. The evolutionary algorithm generates the disaster region distribution sequence by applying a global greedy heuristic search along with a local search that finds the efficient assignment of heterogeneous vehicles for the distribution. This multi-objective evolutionary approach provides Pareto optimal solutions that decision-makers can apply to generate effective distribution schedules that optimise the distribution time and vehicles’ operational cost. In addition, this optimisation also incorporated the minimisation of unmet relief items demand at the disaster regions. The optimised distribution schedules with the proposed approach are compared with the single-objective optimisation, weighted single-objective optimisation and greedy multi-objective optimisation approaches. The comparative results showed that the proposed multi-objective evolutionary approach is an efficient alternative for finding the distribution schedules with optimisation of distribution time and operational cost for the relief items distribution with heterogeneous vehicles

A MATHEMATICAL FRAMEWORK FOR OPTIMIZING DISASTER RELIEF LOGISTICS

In today's society that disasters seem to be striking all corners of the globe, the importance of emergency management is undeniable. Much human loss and unnecessary destruction of infrastructure can be avoided with better planning and foresight. When a disaster strikes, various aid organizations often face significant problems of transporting large amounts of many different commodities including food, clothing, medicine, medical supplies, machinery, and personnel from several points of origin to a number of destinations in the disaster areas. The transportation of supplies and relief personnel must be done quickly and efficiently to maximize the survival rate of the affected population. The goal of this research is to develop a comprehensive model that describes the integrated logistics operations in response to natural disasters at the operational level. The proposed mathematical model integrates three main components. First, it controls the flow of several relief commodities from sources through the supply chain until they are delivered to the hands of recipients. Second, it considers a large-scale unconventional vehicle routing problem with mixed pickup and delivery schedules for multiple transportation modes. And third, following FEMA's complex logistics structure, a special facility location problem is considered that involves four layers of temporary facilities at the federal and state levels. Such integrated model provides the opportunity for a centralized operation plan that can effectively eliminate delays and assign the limited resources in a way that is optimal for the entire system. The proposed model is a large-scale mixed integer program. To solve the model, two sets of heuristic algorithms are proposed. For solving the multi-echelon facility location problem, four heuristic approaches are proposed. Also four heuristic algorithms are proposed to solve the general integer vehicle routing problem. Overall, the proposed heuristics could efficiently find optimal or near optimal solution in minutes of CPU time where solving the same problems with a commercial solver needed hours of computation time. Numerical case studies and extensive sensitivity analysis are conducted to evaluate the properties of the model and solution algorithms. The numerical analysis indicated the capabilities of the model to handle large-scale relief operations with adequate details. Solution algorithms were tested for several random generated cases and showed robustness in solution quality as well as computation time

Drone location and scheduling problems in humanitarian logistics.

Unmanned Aerial Vehicles (UAVs), commonly referred to as drones, are a promising technology for the last-mile delivery of medical and aid items in humanitarian logistics. In emergency scenarios, like disasters, where transportation networks are destroyed and people are stranded, drones can accelerate the delivery of urgently needed items, e.g., food and water, insulin shots and blood pressure pills, to those trapped in the disaster-affected areas. Drones can also provide logistics services in many non-emergency situations by delivering medical items, e.g., vaccine shots and lab specimens, to remote communities and hard-to-access locations. The contribution of using UAVs goes beyond merely having access to remote and disaster-affected areas. With inexpensive launching infrastructures and no need for on-board pilots, drones can offer an inexpensive, agile, and ready-to-use alternative to traditional last-mile delivery modes. Motivated by the challenges associated with the last-mile delivery of aid items to hard-to-access areas, this dissertation studies the problem of drone-based delivery of aid items, e.g., medical and relief packages, to hard-to-access areas in humanitarian logistics. The main goal of this dissertation is to design the logistics and orchestrate a fleet of drones to provide the timely delivery of items to hard-to-access areas in emergency and non-emergency scenarios. In this dissertation, we develop multiple extensions of a drone location and scheduling problem while taking into account the critical aspects of drone- based delivery systems in humanitarian logistics. These critical aspects include: i) limited coverage range, ii) limited payload capacity, iii) energy consumption, iv) timeliness, and v) uncertainty. Chapter II presents a general case of the drone location and scheduling (DLS) problem for the delivery of aid items in disaster-affected areas. In this chapter, we first develop a time-slot formulation to address the problem of optimally locating drone take- off platforms and concurrently scheduling and sequencing a set of trips for each drone to minimize total disutility for product delivery. We extend a two-period problem of DLS where the platforms can be relocated using useable road networks after the first period in order to provide a higher level of coverage. Chapter III proposes a multi-stop drone location and scheduling (MDLS) problem for the delivery of medical items in rural and suburban areas. In this chapter, we assume drones are allowed to stop at one or multiple charging stations, installed on existing platforms having access to electricity, e.g., streetlights, during each trip in order to improve the drones’ coverage range while considering the drones’ energy consumption. The problem is to find optimum locations for medical item providers and charging stations as well as optimally scheduling and sequencing drone trips over a long-term horizon. Chapter IV presents a stochastic extension for the drone location and scheduling (SDLS) problem. Due to the lack of information and instability of the situation, we assume the set of demand locations is not known. The main problem is to locate a set of drone take-off platforms so that with a given probability, the maximum total disutility (or cost) under all realizations of the demand locations is minimized. Finally, Chapter V presents a simulation-based performance evaluation model for the drone-based delivery of aid items to disaster-affected areas in humanitarian logistics. Our goal is to develop a simulation-based system to perform analytical/numerical studies, evaluate the performance of a drone delivery system in humanitarian logistics, and support the decision-making process in such a context while considering multiple sources of variabilities