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

Comparing policy gradient and value function based reinforcement learning methods in simulated electrical power trade

In electrical power engineering, reinforcement learning algorithms can be used to model the strategies of electricity market participants. However, traditional value function based reinforcement learning algorithms suffer from convergence issues when used with value function approximators. Function approximation is required in this domain to capture the characteristics of the complex and continuous multivariate problem space. The contribution of this paper is the comparison of policy gradient reinforcement learning methods, using artificial neural networks for policy function approximation, with traditional value function based methods in simulations of electricity trade. The methods are compared using an AC optimal power flow based power exchange auction market model and a reference electric power system model

Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.Comment: 51 pages, 8 tables, 3 figure

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

From metaheuristics to learnheuristics: Applications to logistics, finance, and computing

Un gran nombre de processos de presa de decisions en sectors estratègics com el transport i la producció representen problemes NP-difícils. Sovint, aquests processos es caracteritzen per alts nivells d'incertesa i dinamisme. Les metaheurístiques són mètodes populars per a resoldre problemes d'optimització difícils en temps de càlcul raonables. No obstant això, sovint assumeixen que els inputs, les funcions objectiu, i les restriccions són deterministes i conegudes. Aquests constitueixen supòsits forts que obliguen a treballar amb problemes simplificats. Com a conseqüència, les solucions poden conduir a resultats pobres. Les simheurístiques integren la simulació a les metaheurístiques per resoldre problemes estocàstics d'una manera natural. Anàlogament, les learnheurístiques combinen l'estadística amb les metaheurístiques per fer front a problemes en entorns dinàmics, en què els inputs poden dependre de l'estructura de la solució. En aquest context, les principals contribucions d'aquesta tesi són: el disseny de les learnheurístiques, una classificació dels treballs que combinen l'estadística / l'aprenentatge automàtic i les metaheurístiques, i diverses aplicacions en transport, producció, finances i computació.Un gran número de procesos de toma de decisiones en sectores estratégicos como el transporte y la producción representan problemas NP-difíciles. Frecuentemente, estos problemas se caracterizan por altos niveles de incertidumbre y dinamismo. Las metaheurísticas son métodos populares para resolver problemas difíciles de optimización de manera rápida. Sin embargo, suelen asumir que los inputs, las funciones objetivo y las restricciones son deterministas y se conocen de antemano. Estas fuertes suposiciones conducen a trabajar con problemas simplificados. Como consecuencia, las soluciones obtenidas pueden tener un pobre rendimiento. Las simheurísticas integran simulación en metaheurísticas para resolver problemas estocásticos de una manera natural. De manera similar, las learnheurísticas combinan aprendizaje estadístico y metaheurísticas para abordar problemas en entornos dinámicos, donde los inputs pueden depender de la estructura de la solución. En este contexto, las principales aportaciones de esta tesis son: el diseño de las learnheurísticas, una clasificación de trabajos que combinan estadística / aprendizaje automático y metaheurísticas, y varias aplicaciones en transporte, producción, finanzas y computación.A large number of decision-making processes in strategic sectors such as transport and production involve NP-hard problems, which are frequently characterized by high levels of uncertainty and dynamism. Metaheuristics have become the predominant method for solving challenging optimization problems in reasonable computing times. However, they frequently assume that inputs, objective functions and constraints are deterministic and known in advance. These strong assumptions lead to work on oversimplified problems, and the solutions may demonstrate poor performance when implemented. Simheuristics, in turn, integrate simulation into metaheuristics as a way to naturally solve stochastic problems, and, in a similar fashion, learnheuristics combine statistical learning and metaheuristics to tackle problems in dynamic environments, where inputs may depend on the structure of the solution. The main contributions of this thesis include (i) a design for learnheuristics; (ii) a classification of works that hybridize statistical and machine learning and metaheuristics; and (iii) several applications for the fields of transport, production, finance and computing

Why simheuristics? : Benefits, limitations, and best practices when combining metaheuristics with simulation

Many decision-making processes in our society involve NP-hard optimization problems. The largescale, dynamism, and uncertainty of these problems constrain the potential use of stand-alone optimization methods. The same applies for isolated simulation models, which do not have the potential to find optimal solutions in a combinatorial environment. This paper discusses the utilization of modelling and solving approaches based on the integration of simulation with metaheuristics. These 'simheuristic' algorithms, which constitute a natural extension of both metaheuristics and simulation techniques, should be used as a 'first-resort' method when addressing large-scale and NP-hard optimization problems under uncertainty -which is a frequent case in real-life applications. We outline the benefits and limitations of simheuristic algorithms, provide numerical experiments that validate our arguments, review some recent publications, and outline the best practices to consider during their design and implementation stages

Solution methods for the dynamic stochastic dial-a-ride problem with time-dependent travel speeds

Die wissenschaftliche Forschung in Bezug auf humanitäre Hilfe sowie Gesundheitsfürsorge ist sehr weitläufig. Im Laufe der letzten Jahrzehnte stiegen die Anstrengungen welche in einschlägige Forschungsprojekte investiert wurden stetig an. In diesem Buch betrachten wir einen konkreten Problemfall aus diesem großen Forschungsbereich: den Transport von alten, kranken oder in ihrer Mobilität eingeschränkten Personen. Probleme dieser Art werden in der Fachliteratur regelmäßig als dial-a-ride Probleme bezeichnet. Wir studieren drei dynamische und stochastische Varianten dieser Problemklasse mit dem Ziel, Effekte, welche durch das Ausnutzen von stochastischen Informationen über zukünftige Umstände während der Planung verursacht werden, zu untersuchen. Zunächst betrachten wir stochastische Informationen über zukünftige Rücktransporte und adaptieren zwei Paare von metaheuristischen Lösungsverfahren für diese Problemstellung. Anschließend untersuchen wir die Ausnutzung stochastischer Informationen über zukünftige Verkehrsbedingungen während der Planung der Fahrzeugrouten. Schlussendlich kombinieren wir diese beiden stochastischen Einflüsse mit zusätzlichen Aspekten bezüglich heterogener Fahrzeugflotten, heterogener Patienten sowie mehrerer Heimatstandorte. Basierend auf unseren Ergebnissen identifizieren wir Faktoren, welche starken Einfluss auf das mögliche Verbesserungspotential haben, das durch Ausnutzung der stochastischen Informationen erreichbar ist. Grundsätzlich sind die Vorteile, die durch eine stochastische Planung erreicht werden können bemerkenswert, sofern die entsprechenden Rahmenbedingungen vorliegen. Insbesondere das in einer Problemstellung vorhandene Ausmaß an Dynamik erweist sich als mit der erreichten Lösungsqualität stark negativ korrelierend.The field of research regarding the optimization of humanitarian aid as well as health care efforts is very wide. During the last decades, the efforts expended in research projects related to this area are steadily increasing. In this book, we address a specific problem out of this large field: the transportation of elderly, ill and disabled persons. Such problems are commonly referred to as dial-a-ride problem (DARP) in the literature. We study three dynamic and stochastic variants of this problem type with the aim of examining the effects of exploiting stochastic information about different future circumstances while planning. First, we consider stochastic information about future return transports and tailor two pairs of metaheuristic solution methods to the requirements of this problem. Second, we study the usage of stochastic information about future travel speeds while constructing the vehicle routes. Finally, we combine these two stochastic aspects with additional heterogeneous extensions regarding the vehicle fleet, the transported patients and multiple depots. Based on our findings we identify factors which have a strong influence on the potential benefits of exploiting stochastic information about future circumstances. Generally speaking, the benefits obtainable by planning in a stochastic way can be remarkable if the underlying conditions are suitable. Especially the total degree of dynamism present in a problem setting turns out to be negatively correlated with the achieved solution quality

Applied Methuerstic computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC