This paper describes a methodology for transmission expansion planning (TEP) within a deregulated electricity market. Two objective functions including investment cost (IC) and congestion cost (CC) are considered. The proposed model forms a bi-level optimization problem in which upper level problem represents an independent system operator (ISO) making its decisions on investment while in the l...

This paper presents a multi-periodic, multi-echelon blood supply chain network consisting of blood donors, mobile collection units, local blood centers, main blood centers and demand points in which the local and main blood centers are subject to random failure in dispatching blood products to demand points. The problem has two objectives including minimization of the total chain costs and maxi...

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 ...

where w = ((ei)i≥0, (fi)i≥0 ) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y i = Cx w i , i ≥ 0. Let ε be a tolerance index on the output. The disturbance w is said to be ε-admissible if ‖y i −yi‖ ≤ ε, ∀ i ≥ 0, where (yi)i≥0 is the output signal associated with the case of an uninfected system. The set ...

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 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...

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...

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.

We study the problem of maximizing a monotone submodular function subject to Multiple Knapsack constraint. The input is set I items, each has non-negative weight, and bins arbitrary capacities. Also, we are given submodular, f over subsets items. objective find packing subset items A⊆I in such that f(A) maximized. Our main result an almost optimal polynomial time (1−e−1−ε)-approximation algorit...