The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the ε constrained differential evolution εDE, which is the combination of the ε constrained...

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that F is ε-approximately submodular if there exists a submodular function f such that (1−ε)f(S) ≤ F (S) ≤ (1+ε)f(S) for ...

We present a Lagrangian decomposition algorithmwhich uses logarithmic potential reduction to compute an ε-approximate solution of the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. We show that this algorithm runs in O(M(ε+lnM)) iterations, a data independent bound which is optimal up to polylogarithmic factors for any fixed relative accuracy ...

We consider probabilistically constrained problems, in which the multivariate random variables are located in the right-hand sides. The objective function is linear, and its optimization is subject to a set of linear constraints as well as a joint probabilistic constraint enforcing that the joint fulfillment of a system of linear inequalities with random right-hand side variables be above a pre...

We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to only a small fraction of the data stored in primary memory. We propose the following streaming algorithms taking O(ε) passes: 1. a (1 − e − ε)-approximation al...

Effective constrained optimization algorithms have been proposed for engineering problems recently. It is common to consider constraint violation and algorithm as two separate parts. In this study, a pbest selection mechanism integrate the current mutation strategy in problems. Based on improved method, an adaptive differential evolution approach proposed, which helps population jump out of inf...

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In the optimization version, the goal is to maximize the number of satisfied constraints. An approximation algorithm for CSP is called robust if it outputs an as...

The use of semileptonic decays has become standard in constraining the unitarity triangle. Since precise calculations of these are very challenging, we propose an entirely new approach. The ε{K} constraint, which depends extremely sensitively on |V{cb}|, is replaced by the interplay between ε{K}, BR(B→τν), and ΔM{B{s}}. Improvements on the B→τν branching ratio and on the lattice determinations ...