A p-norm surrogate constraint method is proposed in this paper for integer programming. A single surrogate constraint can be always constructed using p-norm such that the feasible sets in a surrogate relaxation and the primal problem match exactly. The p-norm surro-gate constraint method is thus guaranteed to succeed in identifying the optimal solution of the primal problem with zero duality ga...

Surrogate reasoning is reasoning whose task is partially taken over by operations on external aids, such as sentences, diagrams, physical models, mathematical models, and computers. Drawing on the basic concepts in situation theory, we present a semi-formal model of surrogate reasoning. We claim that the relative advantages and disadvantages of different forms of surrogate reasoning can be expl...

Robust optimization problems, which have uncertain data, are considered. We prove surrogate duality theorems for robust quasiconvex optimization problems and surrogate min-max duality theorems for robust convex optimization problems. We give necessary and sufficient constraint qualifications for surrogate duality and surrogate min-max duality, and show some examples at which such duality result...

Many practical optimization problems are constrained black boxes. Covariance Matrix Adaptation Evolution Strategies (CMA-ES) belong to the most successful black box optimization methods. Up to now no sophisticated constraint handling method for Covariance Matrix Adaptation optimizers has been proposed. In our novel approach we learn a meta-model of the constraint function and use this surrogate...

When formulated as a system of linear inequalities, the image restoration problem yields huge, unstructured, sparse matrices even for images of small size. To solve the image restoration problem, we use the surrogate constraint methods that can work efficiently for large problems. Among variants of the surrogate constraint method, we consider a basic method performing a single block projection ...

In many applications of constrained continuous black box optimization, the evaluation of fitness and feasibility is expensive. Hence, the objective of reducing the constraint function calls remains a challenging research topic. In the past, various surrogate models have been proposed to solve this issue. In this paper, a local surrogate model of feasibility for a self-adaptive evolution strateg...

The exploitation of nested inequalities and surrogate constraints as originally proposed in Glover [Glover, F., 1965. A multiphase-dual algorithm for the zero–one integer programming problem. Operations Research 13, 879–919; Glover, F., 1971. Flows in arborescences. Management Science 17, 568–586] has been specialized to multidimensional knapsack problems in Osorio et al. [Osorio, M.A., Glover,...

The objective of this study is to develop an accurate surrogate modeling method for construction of the surrogate model to represent the performance measures of the compute-intensive simulation model in reliability-based design optimization (RBDO). In addition, an assessment method for the confidence level of the surrogate model and a conservative surrogate model to account the uncertainty of t...

The paper describes an evolutionary algorithm for the general nonlinear programming problem using a surrogate model. Surrogate models are used in optimization when model evaluation is expensive. Two surrogate models are implemented, one for the objective function and another for a penalty function based on the constraint violations. The proposed method uses a sequential technique for updating t...