A survey on metaheuristics for stochastic combinatorial optimization

Metaheuristics are general algorithmic frameworks, often nature-inspired, designed to solve complex optimization problems, and they are a growing research area since a few decades. In recent years, metaheuristics are emerging as successful alternatives to more classical approaches also for solving optimization problems that include in their mathematical formulation uncertain, stochastic, and dynamic information. In this paper metaheuristics such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others are introduced, and their applications to the class of Stochastic Combinatorial Optimization Problems (SCOPs) is thoroughly reviewed. Issues common to all metaheuristics, open problems, and possible directions of research are proposed and discussed. In this survey, the reader familiar to metaheuristics finds also pointers to classical algorithmic approaches to optimization under uncertainty, and useful informations to start working on this problem domain, while the reader new to metaheuristics should find a good tutorial in those metaheuristics that are currently being applied to optimization under uncertainty, and motivations for interest in this fiel

New Solution Methods for Joint Chance-Constrained Stochastic Programs with Random Left-Hand Sides

We consider joint chance-constrained programs with random lefthand sides. The motivation of this project is that this class of problem has many important applications, but there are few existing solution methods. For the most part, we deal with the subclass of problems for which the underlying parameter distributions are discrete. This assumption allows the original problem to be formulated as a deterministic equivalent mixed-integer program. We rst approach the problem as a mixed-integer program and derive a class of optimality cuts based on irreducibly infeasible subsets of the constraints of the scenarios of the problem. The IIS cuts can be computed effciently by means of a linear program. We give a method for improving the upper bound of the problem when no IIS cut can be identifi ed. We also give an implementation of an algorithm incorporating these ideas and finish with some computational results. We present a tabu search metaheuristic for fi nding good feasible solutions to the mixed-integer formulation of the problem. Our heuristic works by de ning a sufficient set of scenarios with the characteristic that all other scenarios do not have to be considered when generating upper bounds. We then use tabu search on the one-opt neighborhood of the problem. We give computational results that show our metaheuristic outperforming the state-of-the-art industrial solvers. We then show how to reformulate the problem so that the chance-constraints are monotonic functions. We then derive a convergent global branch-and-bound algorithm using the principles of monotonic optimization. We give a finitely convergent modi cation of the algorithm. Finally, we give a discussion on why this algorithm is computationally ine ffective. The last section of this dissertation details an application of joint chance-constrained stochastic programs to a vaccination allocation problem. We show why it is necessary to formulate the problem with random parameters and also why chance-constraints are a good framework for de fining an optimal policy. We give an example of the problem formulated as a chance constraint and a short numerical example to illustrate the concepts

The SNS logistics network design : location and vehicle routing.

Large-scale emergencies caused by earthquake, tornado, pandemic flu, terrorism attacks and so on can wreak havoc to communities. In order to mitigate the impact of the events, emergency stockpiles of food, water, medicine and other materials have been set up around the US to be delivered to the affected areas during relief operations. One type of stockpile is called the Strategic National Stockpile (SNS). The SNS logistics network is designed to have multiple stages of facilities, each of which is managed by different levels of governmental authorities - federal, state and local authorities. The design of a logistics network for delivery of the SNS materials within a state are explored in this dissertation. There are three major areas of focus in this dissertation: (1) the SNS facility location model, which is used to determine sites for locating Receiving, Staging and Storage (RSS) and Regional Distribution Nodes (RDNs) to form a logistics network to deliver relief material to Points of Demand (PODs), where the materials are directly delivered to the affected population; (2) the SNS Vehicle Routing Problem (VRP), which is used to assist the SNS staff in determining the numbers of various types of trucks, and the routing schedules of each truck to develop an operational plan for delivering the required relief materials to the assigned PODs within the required duration; (3) the location-routing analysis of emergency scenarios, in which the facility location model and the VRP solution are integrated through the use of a computer program to run on several assumed emergency scenarios. Using real data from the department of public health in the Commonwealth of Kentucky, a transshipment and location model is formulated to determine the facility locations and the transshipment quantities of materials; a multiple-vehicle routing model allowing split deliveries and multiple routes per vehicle that must be completed within a required duration is formulated to determine the routing and scheduling of trucks. The facility location model is implemented using Microsoft Solver Foundation and C#. An algorithm combining the Clark and Wright saving algorithm and Simulated Annealing is designed and implemented in C# to solve the VRP. The algorithm can determine whether there is shortage of transportation capacity, and if so, how many of various types of trucks should be added for optimal performance. All the solution algorithms are integrated into a web-based SNS planning tool. In the location-routing analysis of emergency scenarios, a binary location model and an algorithm for solving VRP solution are integrated as a computer program to forecast the feasibility of distribution plans and the numbers of required trucks of various types. The model also compares the costs and benefits of direct and indirect shipment. A large-scale emergency scenario in which a specific type of vaccine is required to be delivered to the entire state of Kentucky is considered. The experiments are designed based on the real data provided by the Kentucky state government. Thus the experimental results provide valuable suggestions for future SNS preparedness planning

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Service scheduling and vehicle routing problem to minimise the risk of missing appointments

This research studies a workforce scheduling and vehicle routing problem where technicians drive a vehicle to customer locations to perform service tasks. The service times and travel times are subject to stochastic events. There is an agreed time window for starting each service task. The risk of missing the time window for a task is defined as the probability that the technician assigned to the task arrives at the customer site later than the time window. The problem is to generate a schedule that minimises the maximum of risks and the sum of risks of all the tasks considering the effect of skill levels and task priorities. A new approach is taken to build schedules that minimise the risks of missing appointments as well as the risks of technicians not being able to complete their daily tours on time.We first analyse the probability distribution of the arrival time to any customer location considering the distributions of activities prior to this arrival. Based on the analysis, an efficient estimation method for calculating the risks is proposed, which is highly accurate and this is verified by comparing the results of the estimation method with a numerical integral method.We then develop three new workforce scheduling and vehicle routing models that minimise the risks with different considerations such as an identical standard deviation of the duration for all uncertain tasks in the linear risk minimisation model, and task priorities in the priority task risk minimisation model. A simulated annealing algorithm is implemented for solving the models at the start of the day and for re-optimisation during the day. Computational experiments are carried out to compare the results of the risk minimisation models with those of the traditional travel cost model. The performance is measured using risks and robustness. Simulation is used to compare the numbers of missed appointments and test the effect of re-optimisation.The results of the experiments demonstrate that the new models significantly reduce the risks and generate schedules with more contingency time allowances. Simulation results also show that re-optimisation reduces the number of missed appointments significantly. The risk calculation methods and risk minimisation algorithm are applied to a real-world problem in the telecommunication sector.</div

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions