Combinatorial optimization problems (COPs) arise in many practical applications in the fields of management science, biology, chemistry, physics, engineering, and computer science. Although the search space is comprised of a finite number of candidate solutions, many of these problems are very complex and thus hard to solve. Often, the search space grows exponentially with the problem size rend...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadra...

Ant colony optimization (ACO) is a novel and promising meta-heuristic for solving hard combinatorial optimization problems, such as travelling salesman[3] [4] [5] [6] [7] [8], quadratic assignment[9] [10] [11] [12] and set covering problem [13]. Unfortunately, according to systems performance evaluation literature, the methods adopted to experimentally validate the current ACO are not enough ac...

There are two major criticisms about simulated annealing as a general method for solving combinatorial optimization problems: its effectiveness when compared with other welldesigned heuristics and its excessive computation time. In this paper, we show that simulated annealing, with properly des~gned annealing schedule and move generation strategy, achieves significant speerlups for high quality...

This paper considers structural optimization problems featuring discrete variables, as well as nonlinear implicit constraints which can only be evaluated through time-expensive computations. A prominent application consists in the preliminary structural design of large ships, where many of the variables take their values in discrete sets which model standard element dimensions to be selected fr...

Many real-world optimization problems in, e. g., engineering or biology have the property that not much is known about the function to be optimized. This excludes the application of problem-specific algorithms. Simple randomized search heuristics are then used with surprisingly good results. In order to understand the working principles behind such heuristics, they are analyzed on combinatorial...

In this article we present an Ant Colony Optimization approach to the Flow Shop Problem. ACO is a new algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. Artificial ants are used to construct solutions for Flow Shop Problems that subsequently are improved by a local search procedure. Comparisons with o...

In this paper we present the use of Constraint Programming for solving balanced academic curriculum problems. We discuss the important role that heuristics play when solving a problem using a constraint-based approach. We also show how constraint solving techniques allow to very efficiently solve combinatorial optimization problems that are too hard for integer programming techniques.

Task: Pack all the items into a minimum number of unit-capacity bins An algorithm A is said to be a δ-approximation algorithm if it runs in polynomial time and for every problem instance π with optimal solution value OP T (π) minimization: A(π) OP T (π) ≤ δ δ ≥ 1 maximization: A(π) OP T (π) ≥ δ δ ≤ 1 A family of approximation algorithms for a problem Π, {A } , is called a polynomial approximati...