Related papers: Stochastic Knapsack: Semi-Adaptivity Gaps and Impr…
We consider AC electrical systems where each electrical device has a power demand expressed as a complex number, and there is a limit on the magnitude of total power supply. Motivated by this scenario, we introduce the complex-demand…
We revisit the classic #Knapsack problem, which asks to count the Boolean points $(x_1,\dots,x_n)\in\{0,1\}^n$ in a given half-space $\sum_{i=1}^nW_ix_i\le T$. This #P-complete problem admits $(1\pm\epsilon)$-approximation. Before this…
Suppose we are given a submodular function $f$ over a set of elements, and we want to maximize its value subject to certain constraints. Good approximation algorithms are known for such problems under both monotone and non-monotone…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
We study the uniform $2$-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
The main contribution of this paper resides in providing novel algorithmic advances and analytical insights for the sequential hiring problem, a recently introduced dynamic optimization model where a firm adaptively fills a limited number…
In Part I \cite{Zhao13TSPasync1}, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We…
Datasets are often reused to perform multiple statistical analyses in an adaptive way, in which each analysis may depend on the outcomes of previous analyses on the same dataset. Standard statistical guarantees do not account for these…
Evolutionary algorithms are particularly effective for optimisation problems with dynamic and stochastic components. We propose multi-objective evolutionary approaches for the knapsack problem with stochastic profits under static and…
Many systems have to be maintained while the underlying constraints, costs and/or profits change over time. Although the state of a system may evolve during time, a non-negligible transition cost is incured for transitioning from one state…
We consider the problem of stochastic monotone submodular function maximization, subject to constraints. We give results on adaptivity gaps, and on the gap between the optimal offline and online solutions. We present a procedure that…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
The Knapsack problem is one of the most fundamental NP-complete problems at the intersection of computer science, optimization, and operations research. A recent line of research worked towards understanding the complexity of…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…