Binary constraint

Abstract: We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (+ and X) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.

Abstract: A simple optimization procedure for constraint-based problems is described which works with a simplified cost function or even without one. The simplification of the problem formulation makes this method particularly attractive. The new method lends itself to parallel computation and is well suited for constraint satisfaction, constrained optimization, and design centering problems. A further asset is its self-steering property which makes the new method easy to use.

Abstract: During the last three decades, several constraint handling techniques have been developed to be used with evolutionary algorithms (EAs). According to the no free lunch theorem, it is impossible for a single constraint handling technique to outperform all other techniques on every problem. In other words, depending on several factors such as the ratio between feasible search space and the whole search space, multimodality of the problem, the chosen EA, and global exploration/local exploitation stages of the search process, different constraint handling methods can be effective during different stages of the search process. Motivated by these observations, we propose an ensemble of constraint handling techniques (ECHT) to solve constrained real-parameter optimization problems, where each constraint handling method has its own population. A distinguishing feature of the ECHT is the usage of every function call by each population associated with each constraint handling technique. Being a general concept, the ECHT can be realized with any existing EA. In this paper, we present two instantiations of the ECHT using four constraint handling methods with the evolutionary programming and differential evolution as the EAs. Experimental results show that the performance of ECHT is better than each single constraint handling method used to form the ensemble with the respective EA, and competitive to the state-of-the-art algorithms.