This paper considers a multi-period, multi-product inventory-routing problem in a two-level supply chain consisting of a distributor and a set of customers. This problem is modeled with the aim of minimizing bi-objectives, namely the total system cost (including startup, distribution and maintenance costs) and risk-based transportation. Products are delivered to customers by some heterogeneous ...

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 ...

The reservoir flood control operation problem has the characteristics of multiconstraint, high-dimension, nonlinearity, and being difficult to solve. In order better solve this problem, paper proposes an improved bald eagle search algorithm (CABES) coupled with ε-constraint method (ε-CABES). test performance CABES algorithm, a typical function is used simulate verify CABES. results are compared...

We give a proximal bundle method for minimizing a convex function f over R+. It requires evaluating f and its subgradients with a possibly unknown accuracy ε ≥ 0, and maintains a set of free variables I to simplify its prox subproblems. The method asymptotically finds points that are ε-optimal. In Lagrangian relaxation of convex programs, it allows for ε-accurate solutions of Lagrangian subprob...

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...

We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of subset selection problems with linear constraints. Given a problem in this class and some small ε ∈ (0, 1), we show that if there exists a ρ-approximation algorithm for the Lagrangia...

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 ...

We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of subset selection problems with linear constraints. Given a problem in this class and some small ε ∈ (0, 1), we show that if there exists an r-approximation algorithm for the Lagrangi...

We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

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...