Combinatorial Optimization

Operations research is usually employed to solve the facility location problem, mainly using mixed integer linear programming (MILP). Meanwhile, some MILP models were not originally designed to solve a large class of location problems, corresponding to those where customers are served in a routing operation. In this case location and routing decisions are strongly interrelated. Moreover, this modeling approach has

In a recent paper [I. Wegener, Simulated Annealing beats Metropolis in combinatorial optimization, in: L. Caires, G.F. Italiano, L. Monteiro, C. Palamidessi, M. Yung (Eds.), Proc. ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 589–601] Wegener gave a first natural example of a combinatorial optimization problem where for certain instances a Simulated Annealing algorithm provably performs better than the Metropolis

A fundamental research area in relation with analyzing the complexity of optimization problems are approximation algorithms. For combinatorial optimization a vast theory of approximation algorithms has been developed, see (1). Many natural optimization problems involve real numbers and thus an uncountable search space of feasible solutions. A uniform complexity theory for real number decision problems was in- troduced by Blum, Shub, and Smale (4). However, approximation algo- rithms were not yet formally studied in their model. In this paper we develop a structural theory of optimization problems and approximation algorithms for the BSS model similar to the above men- tioned one for combinatorial optimization. We introduce a class NP OR of real optimization problems closely related to NPR: The class NP OR has four natural subclasses. For each of those we introduce and study real approximation classes AP XR and P T ASR together with reducibil- ity and completeness notions. As main results we establish the existence of natural complete problems for all these classes.

The combinatorial design, known as covering array, has been used mainly to exercise tests for software and hardware components. It has also been used in machine learning applications and the design of experiments for various applications. In this paper, a new approach to construct covering arrays is defined; it is called CAEX (stands for Covering Array EXtender). CAEX approach was tested in the construction of covering arrays of order three and strength two. The CAEX approach's performance was evident by the definition of new upper-bounds in the size of some covering arrays; 34 new upper bounds for covering arrays were defined, remarkably a covering array with 112,770 parameters only requires 50 rows. One important goodness of the CAEX approach is that it can provide the genealogy of each covering array (how each covering array was constructed).

... A detailed calculation procedure of ICP T can be found in Carlyle et al. ... Ten problem instances are generated randomly in each set, resulting in 360 test problem instances. ... r Crossover probability: 0.6 r Mutation probability: 0.01 r Population size: 20 r Elitism: three elite solutions ...

Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multiple objective optimization problem, assigns a numerical value to that point set. This value provides a quantitative measure for comparing different sets of points generated by solution procedures for difficult multiple objective optimization problems. We introduced the IPF for bi-criteria optimization problems in