A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

An Analysis of black-box optimization problems in reinsurance: evolutionary-based approaches

Black-box optimization problems (BBOP) are de ned as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the eld of insurance, and more speci cally in reinsurance problems. In this area, the complexity of the models and assumptions considered to de ne the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, nding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

A multi-objective model for a multi-period distribution management problem

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is relatedwith the design of the routes to distribute the products, in an efficient and inexpensive way.This article deals with a complex vehicle routing problem that can beseen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problemthat considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is costminimization, the second is balancing work levels and the third is amarketing objective. An application of the model on a small example, with5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

Optimal management of microgrids

Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.. Desenvolupament dels models matemàtics necessaris per a controlar de forma òptima la microxarxa existent als laboratoris del Institut de Recerca en Energia de Catalunya. Els algoritmes s'implementaran per tal de simular el comportament i posteriorment es programaran directament sobre els elements de la microxarxa per verificar el seu correcte funcionament.

Practical algorithms for a family of waterfilling solutions

Many engineering problems that can be formulatedas constrained optimization problems result in solutionsgiven by a waterfilling structure; the classical example is thecapacity-achieving solution for a frequency-selective channel.For simple waterfilling solutions with a single waterlevel and asingle constraint (typically, a power constraint), some algorithmshave been proposed in the literature to compute the solutionsnumerically. However, some other optimization problems result insignificantly more complicated waterfilling solutions that includemultiple waterlevels and multiple constraints. For such cases, itmay still be possible to obtain practical algorithms to evaluate thesolutions numerically but only after a painstaking inspection ofthe specific waterfilling structure. In addition, a unified view ofthe different types of waterfilling solutions and the correspondingpractical algorithms is missing.The purpose of this paper is twofold. On the one hand, itoverviews the waterfilling results existing in the literature from aunified viewpoint. On the other hand, it bridges the gap betweena wide family of waterfilling solutions and their efficient implementationin practice; to be more precise, it provides a practicalalgorithm to evaluate numerically a general waterfilling solution,which includes the currently existing waterfilling solutions andothers that may possibly appear in future problems.

Algorithm optimization for solving crew scheduling problems

In this paper, we are proposing a methodology to determine the most efficient and least costly way of crew pairing optimization. We are developing a methodology based on algorithm optimization on Eclipse opensource IDE using the Java programming language to solve the crew scheduling problems.

Some optimization and decision problems in proportional reinsurance

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function (Gerber & Shiu, 1998) is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs.

Solving Large Location-Allocation problems by Clustering and Simulated Annealing

Globalization involves several facility location problems that need to be handled at large scale. Location Allocation (LA) is a combinatorial problem in which the distance among points in the data space matter. Precisely, taking advantage of the distance property of the domain we exploit the capability of clustering techniques to partition the data space in order to convert an initial large LA problem into several simpler LA problems. Particularly, our motivation problem involves a huge geographical area that can be partitioned under overall conditions. We present different types of clustering techniques and then we perform a cluster analysis over our dataset in order to partition it. After that, we solve the LA problem applying simulated annealing algorithm to the clustered and non-clustered data in order to work out how profitable is the clustering and which of the presented methods is the most suitable

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.

Exploiting fitness distance correlation of set covering problems

The set covering problem is an NP-hard combinatorial optimization problemthat arises in applications ranging from crew scheduling in airlines todriver scheduling in public mass transport. In this paper we analyze searchspace characteristics of a widely used set of benchmark instances throughan analysis of the fitness-distance correlation. This analysis shows thatthere exist several classes of set covering instances that have a largelydifferent behavior. For instances with high fitness distance correlation,we propose new ways of generating core problems and analyze the performanceof algorithms exploiting these core problems.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.