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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
The Vehicle Routing Problem with Service Level Constraints
We consider a vehicle routing problem which seeks to minimize cost subject to
service level constraints on several groups of deliveries. This problem
captures some essential challenges faced by a logistics provider which operates
transportation services for a limited number of partners and should respect
contractual obligations on service levels. The problem also generalizes several
important classes of vehicle routing problems with profits. To solve it, we
propose a compact mathematical formulation, a branch-and-price algorithm, and a
hybrid genetic algorithm with population management, which relies on
problem-tailored solution representation, crossover and local search operators,
as well as an adaptive penalization mechanism establishing a good balance
between service levels and costs. Our computational experiments show that the
proposed heuristic returns very high-quality solutions for this difficult
problem, matches all optimal solutions found for small and medium-scale
benchmark instances, and improves upon existing algorithms for two important
special cases: the vehicle routing problem with private fleet and common
carrier, and the capacitated profitable tour problem. The branch-and-price
algorithm also produces new optimal solutions for all three problems
Accelerated Particle Swarm Optimization and Support Vector Machine for Business Optimization and Applications
Business optimization is becoming increasingly important because all business
activities aim to maximize the profit and performance of products and services,
under limited resources and appropriate constraints. Recent developments in
support vector machine and metaheuristics show many advantages of these
techniques. In particular, particle swarm optimization is now widely used in
solving tough optimization problems. In this paper, we use a combination of a
recently developed Accelerated PSO and a nonlinear support vector machine to
form a framework for solving business optimization problems. We first apply the
proposed APSO-SVM to production optimization, and then use it for income
prediction and project scheduling. We also carry out some parametric studies
and discuss the advantages of the proposed metaheuristic SVM.Comment: 12 page
Proposal and Comparative Study of Evolutionary Algorithms for Optimum Design of a Gear System
This paper proposes a novel metaheuristic framework using a Differential Evolution (DE) algorithm with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Both algorithms are combined employing a collaborative strategy with sequential execution, which is called DE-NSGA-II. The DE-NSGA-II takes advantage of the exploration abilities of the multi-objective evolutionary algorithms strengthened with the ability to search global mono-objective optimum of DE, that enhances the capability of finding those extreme solutions of Pareto Optimal Front (POF) difficult to achieve. Numerous experiments and performance comparisons between different evolutionary algorithms were performed on a referent problem for the mono-objective and multi-objective literature, which consists of the design of a double reduction gear train. A preliminary study of the problem, solved in an exhaustive way, discovers the low density of solutions in the vicinity of the optimal solution (mono-objective case) as well as in some areas of the POF of potential interest to a decision maker (multi-objective case). This characteristic of the problem would explain the considerable difficulties for its resolution when exact methods and/or metaheuristics are used, especially in the multi-objective case. However, the DE-NSGA-II framework exceeds these difficulties and obtains the whole POF which significantly improves the few previous multi-objective studies.Fil: MĂ©ndez Babey, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de IngenierĂa; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca. Instituto de Matemática BahĂa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahĂa Blanca; ArgentinaFil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de IngenierĂa; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca. Instituto de Investigaciones EconĂłmicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de EconomĂa. Instituto de Investigaciones EconĂłmicas y Sociales del Sur; Argentin
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