Virtual power plants (VPPs), as a novel integrated energy aggregation model, can effectively realize peak shaving and valley filling in the power system. This paper mainly investigates the model of a VPP consisting of distributed energy resources (DERs) as energy producers and converters, and an electric vehicle parking lot (EVPL) serving as both a battery storage system and an energy consumer. To mitigate the risks associated with uncertainties, a downside risk constraint method is concerned, which has not yet been applied to this model with multiple uncertainties. We concentrate on the risk-embedded scheduling of the VPP with EVPL, taking into account key uncertain factors, such as, the arrival and departure times of the EVs. Numerical results reveal that the primary factor affecting VPP profits is the instability of renewable energy. In our model, compared to risk-neutral strategies, risk-averse strategies lead to a reduction in average profits by 5.66% , highlighting the trade-off between minimizing risk and maximizing profits.

In this paper, we consider the two-agent scheduling with time-dependent and position-dependent processing time in a two-machine flow-shop system. The objective is to minimize the makespan of agent A under the constraint that the objective of agent B cannot exceed a given upper bound. In the time-dependent processing time model, the constraint is the makespan of agent B. We first show that the problem is NP-hard in the ordinary sense. Then we prove that there exists an optimal schedule which is a permutation schedule, and there exists an optimal schedule in which the adapted version of Johnson's rule do not hold for neither agent A nor agent B. Furthermore, we show that three special cases are polynomially solvable. In the position-dependent processing time model, if the constraint is the makespan of agent B, we show that the problem is NP-hard in the ordinary sense. If the constraint is the total completion times of agent B and jobs have different release dates, the problem is strongly NP-hard.

In modern warfare, decoy targets are often set up to interfere with enemy reconnaissance and operations. To avoid being disrupted by decoys during combat, it is necessary to consider the implementation of robust combat strategies. In this paper, we consider the problem of collaborative target assignment for unmanned aerial vehicle (UAV) swarms with decoy targets. We model it as a deletion-robust submodular maximization problem, and develop a two-stage algorithm that attains a 1/(4+1/β ) -approximation guarantee, where β≤ 1 is the approximation ratio for the unconstrained submodular function maximization algorithm.

In modern warfare, decoy targets are often set up by the enemy to interfere with the combat of unmanned aerial vehicle (UAV) swarms. To enhance the combat effectiveness of UAV swarm collaborative target assignment and improve its anti-interference ability, we model this problem as a deletion-robust submodular maximization problem with a knapsack constraint. We provide a two-stage framework consisting of a preprocessing algorithm and postprocessing algorithms. Simulation experiments are carried out through the weapon allocation problem and the UAV swarm collaborative target assignment problem. The results show that the proposed algorithms perform better than non-deletion-robust algorithms in terms of objective function values and running time, verifying the effectiveness of the algorithms.

The exploration of submodular optimization problems on the integer lattice offers a more precise approach to handling the dynamic interactions among repetitive elements in practical applications. In today’s data-driven world, the importance of efficient and reliable privacy-preserving algorithms has become paramount for safeguarding sensitive information. In this paper, we delve into the DR-submodular and lattice submodular maximization problems subject to cardinality constraints on the integer lattice, respectively. For DR-submodular functions, we devise a differential privacy algorithm that attains a (1-1/e-ρ ) -approximation guarantee with additive error O(rσln |N|/ϵ ) for any ρ >0 , where N is the number of groundset, ϵ is the privacy budget, r is the cardinality constraint, and σ is the sensitivity of a function. Our algorithm preserves O(ϵ r^2) -differential privacy. Meanwhile, for lattice submodular functions, we present a differential privacy algorithm that achieves a (1-1/e-O(ρ )) -approximation guarantee with additive error O(rσln |N|/ϵ ) . We evaluate their effectiveness using instances of the combinatorial public projects problem and the budget allocation problem within the bipartite influence model.

We consider the problem of local privacy where actions are subsets of a ground multiset and expectation rewards are modeled by a [Formula: see text]decomposable monotone submodular function. For the DR-submodular maximization problem under a polymatroid constraint, Soma and Yoshida [26] provide a continuous greedy algorithm for no-privacy setting. In this paper, we obtain the first differentially private algorithm for DR-submodular maximization subject to a polymatroid constraint. Our algorithm achieves a [Formula: see text]approximation with a little loss and runs in [Formula: see text][Formula: see text] times where [Formula: see text] is the rank of the base polymatroid and [Formula: see text] is the size of ground set. Along the way, we analyze the utility and privacy of our algorithm. A concrete experiment to simulate the privacy Uber pickups location problem is provided, and our algorithm performs well within the agreed range.

研究了具有累积效应的两台同类机排序问题,目标是极小化机器总载重.半积函数在组合优化通常用于算法设计与分析.对该文中涉及的问题,用该函数设计了一个γ-完全多项式近似方案,并进行了算法分析.

Many machine learning problems, such as medical data summarization and social welfare maximization, can be modeled as the problems of maximizing monotone submodular functions. Differentially private submodular functions under cardinality constraints are first proposed and studied to solve the Combinatorial Public Projects (CPP) problem, in order to protect personal data privacy while processing sensitive data. However, the research of these functions for privacy protection has received little attention so far. In this paper, we propose to study the differentially private submodular maximization problem over the integer lattice. Our main contributions are to present differentially private approximation algorithms for both DR-submodular and integer submodular function maximization problems under cardinality constraints and analyze the sensitivity of our algorithms.

研究具有入树约束的两台同类机排序问题,工件具有不同的到达时间且具有单位的加工时间,目标为极小化最大完工时间.对于该NP-难问题,首先设计了一个分支定界算法并证明了算法的最优性.然后通过一个具体算例,详细验证了算法的执行过程.