Enumerative approaches, such as branch-and-bound, to solving optimization problems require a subroutine that produces a lower bound on the value of the optimal solution. In the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear-programming relaxation of the problem or the solution of a combinatorial relaxation. In this paper w...

We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, thereby concentrating amplitudes int...

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely speci ed constraints of di erent importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and i...

We introduce a metaheuristic framework for combinatorial optimization. Our framework is similar to others (e.g. [1]) in that it is modular enough that important components can be independently developed. Ours is different in several aspects. It supports several built-in components such as combinatorial representations and search heuristics to facilitate the creation of a new optimizer for a wid...

In this paper, we apply the parallel predator-prey model for multi-objective optimization to a combinatorial problem for the first time: Exemplarily, we optimize sequences of 50 jobs for an instance of the bi-criteria scheduling problem 1|dj |Cj , Lmax with this approach. The modular building block architecture of the predator-prey system and the distribution of acting entities enables the anal...

The set covering problem (SCP) is one of representative combinatorial optimization problems, which has many practical applications. The continuous development of mathematical programming has derived a number of impressive heuristic algorithms as well as exact branch-and-bound algorithms, which can solve huge SCP instances of bus, railway and airline crew scheduling problems. We survey heuristic...

The QAP is considered one of the most complex combinatorial optimization problems and it is the model for many real life problems such as facilities location, camp planning, computer keyboard design and electronic boards cabling, among other applications. This Paper solves some significant instances of this problem through an improved Parallel Genetic Algorithm based Grid by means of the local ...

This paper looks upon the standard genetic algorithm as an artificial self-organizing process. With the purpose to provide concepts that make the algorithm more open for scalability on the one hand, and that fight premature convergence on the other hand, this paper presents two extensions of the standard genetic algorithm without introducing any problem specific knowledge, as done in many probl...