Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Generalized resolution and cutting planes
Annals of Operations Research
Computational experience with an interior point algorithm on the satisfiability problem
Annals of Operations Research
The hardest constraint problems: a double phase transition
Artificial Intelligence
Exploiting the deep structure of constraint problems
Artificial Intelligence
Locomotion with unit-modular reconfigurable robot
Locomotion with unit-modular reconfigurable robot
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
SIAM Journal on Optimization
A Discrete Lagrangian-Based Global-SearchMethod for Solving Satisfiability Problems
Journal of Global Optimization
Evolutionary algorithms for constrained parameter optimization problems
Evolutionary Computation
Test-case generator for nonlinear continuous parameter optimizationtechniques
IEEE Transactions on Evolutionary Computation
Solving non-linear arithmetic constraints in soft realtime environments
Proceedings of the 27th Annual ACM Symposium on Applied Computing
ICHEA: a constraint guided search for improving evolutionary algorithms
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
Solving dynamic constraint optimization problems using ICHEA
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
ICHEA for discrete constraint satisfaction problems
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
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Continuous constraint satisfaction problems are at the core of many real-world applications, including planning, scheduling, control, and diagnosis of physical systems such as car, planes, and factories. Yet in order to be effective in such resource-constrained environments, constraint-based techniques must take into account the complexity of continuous constrained problems. In this paper, we study complexity phase transition phenomena of continuous constraint satisfaction problems (CSPs). First, we analyze three continuous constraint satisfaction formulations based on (discrete) 3-SAT problems, which have a strong relation between structure and search cost. Then, we propose a generic benchmarking model for comparing continuous CSPs and algorithms, and present two example problems based on sine functions. In our experiments, these problems are solved using both local and global search methods. Besides comparing the complexities of different continuous CSPs and search algorithms, we also connect these back to results from similar studies on SAT problems. In solving continuous 3-SAT and sine-based CSPs, we find that the median search cost is characterized by simple parameters such as the constraint-to-variable ratio and constraint tightness, and that discrete search algorithms such as GSAT have continuous counter-parts with similar behavior. Regarding local versus global search techniques for constraint solving, our results show that local search methods are more efficient for weakly constrained problems, whereas global search methods work better on highly constrained problems.