Showing papers on "Linear programming published in 2016"

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

Abstract: In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming

Abstract: This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities,fi(x)_ bi, i=1, 2, , m, the feasible region is defined via set containment. Here n convex activity sets {Kj, j=1, 2, * * *, n} and a convex resource set K are specified and the feasible region is given by

A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables

Abstract: State-of-the-art multiobjective evolutionary algorithms (MOEAs) treat all the decision variables as a whole to optimize performance. Inspired by the cooperative coevolution and linkage learning methods in the field of single objective optimization, it is interesting to decompose a difficult high-dimensional problem into a set of simpler and low-dimensional subproblems that are easier to solve. However, with no prior knowledge about the objective function, it is not clear how to decompose the objective function. Moreover, it is difficult to use such a decomposition method to solve multiobjective optimization problems (MOPs) because their objective functions are commonly conflicting with one another. That is to say, changing decision variables will generate incomparable solutions. This paper introduces interdependence variable analysis and control variable analysis to deal with the above two difficulties. Thereby, an MOEA based on decision variable analyses (DVAs) is proposed in this paper. Control variable analysis is used to recognize the conflicts among objective functions. More specifically, which variables affect the diversity of generated solutions and which variables play an important role in the convergence of population. Based on learned variable linkages, interdependence variable analysis decomposes decision variables into a set of low-dimensional subcomponents. The empirical studies show that DVA can improve the solution quality on most difficult MOPs. The code and supplementary material of the proposed algorithm are available at http://web.xidian.edu.cn/fliu/paper.html .

Efficient algorithm for k-barrier coverage based on integer linear programming

Abstract: Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest. However, in certain applications, barrier coverage cannot be satisfied after random deployment. In this paper, we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage. In particular, two problems are studied: relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost. These two problems were formulated as 0–1 integer linear programming (ILP). The formulation is computationally intractable because of integrality and complicated constraints. Therefore, we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming. Theoretical analysis and simulation were performed to verify the effectiveness of our approach.

Robust Restoration Method for Active Distribution Networks

Abstract: Distributed generations (DGs) introduce significant uncertainties to restoration of active distribution networks, in addition to roughly estimated load demands. An adjustable robust restoration optimization model with a two-stage objective is proposed in this paper, involving the uncertain DG outputs and load demands. The first stage generates optimal strategies for recovery of outage power and the second stage seeks the worst-case fluctuation scenarios. The model is formulated as a mixed-integer linear programming problem and solved using the column-and-constraint generation method. The feasibility and reliability of the strategies obtained via this robust optimization model can be guaranteed for all cases in the predefined uncertainty sets with good performance. A technique known as the uncertainty budget is used to adjust the conservativeness of this model, providing a tradeoff between conservativeness and robustness. Numerical tests are carried out on the modified PG&E 69-bus system and a modified 246-bus system to compare the robust optimization model against a deterministic restoration model, which verifies the superiority of this proposed model.

The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion

Abstract: The green vehicle routing and scheduling problem (GVRSP) aims to minimize green-house gas emissions in logistics systems through better planning of deliveries/pickups made by a fleet of vehicles. We define a new mixed integer liner programming (MIP) model which considers heterogeneous vehicles, time-varying traffic congestion, customer/vehicle time window constraints, the impact of vehicle loads on emissions, and vehicle capacity/range constraints in the GVRSP. The proposed model allows vehicles to stop on arcs, which is shown to reduce emissions up to additional 8% on simulated data. A hybrid algorithm of MIP and iterated neighborhood search is proposed to solve the problem.

Wireless-Powered Communications With Non-Orthogonal Multiple Access

Abstract: We study a wireless-powered uplink communication system with non-orthogonal multiple access (NOMA), consisting of one base station and multiple energy harvesting users. More specifically, we focus on the individual data rate optimization and fairness improvement and we show that the formulated problems can be optimally and efficiently solved by either linear programming or convex optimization. In the provided analysis, two types of decoding order strategies are considered, namely fixed decoding order and time sharing . Furthermore, we propose an efficient greedy algorithm, which is suitable for the practical implementation of the time-sharing strategy. The simulation results illustrate that the proposed scheme outperforms the baseline orthogonal multiple access scheme. More specifically, it is shown that the NOMA offers a considerable improvement in throughput, fairness, and energy efficiency. Also, the dependence among system throughput, minimum individual data rate, and harvested energy is revealed, as well as an interesting tradeoff between rates and energy efficiency. Finally, the convergence speed of the proposed greedy algorithm is evaluated, and it is shown that the required number of iterations is linear with respect to the number of users.

New analysis and results for the Frank---Wolfe method

Abstract: We present new results for the Frank---Wolfe method (also known as the conditional gradient method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial (and subsequent) iterates. Our results include computational guarantees for both duality/bound gaps and the so-called FW gaps. Lastly, we present complexity bounds in the presence of approximate computation of gradients and/or linear optimization subproblem solutions.

Regularized Primal–Dual Subgradient Method for Distributed Constrained Optimization

Abstract: In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal–dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an $ {\mathcal {O}} {(} {K}^{ {-1/4}} {)}$ convergence rate for general distributed constrained optimization, where ${K}$ is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.

Constrained Subproblems in a Decomposition-Based Multiobjective Evolutionary Algorithm

Abstract: A decomposition approach decomposes a multiobjective optimization problem into a number of scalar objective optimization subproblems. It plays a key role in decomposition-based multiobjective evolutionary algorithms. However, many widely used decomposition approaches, originally proposed for mathematical programming algorithms, may not be very suitable for evolutionary algorithms. To help decomposition-based multiobjective evolutionary algorithms balance the population diversity and convergence in an appropriate manner, this letter proposes to impose some constraints on the subproblems. Experiments have been conducted to demonstrate that our proposed constrained decomposition approach works well on most test instances. We further propose a strategy for adaptively adjusting constraints by using information collected from the search. Experimental results show that it can significantly improve the algorithm performance.

Ant colony optimization for the real-time train routing selection problem

Abstract: This paper deals with the real-time problem of scheduling and routing trains in a railway network. In the related literature, this problem is usually solved starting from a subset of routing alternatives and computing the near-optimal solution of the simplified routing problem. We study how to select the best subset of routing alternatives for each train among all possible alternatives. The real-time train routing selection problem is formulated as an integer linear programming formulation and solved via an algorithm inspired by the ant colonies’ behavior. The real-time railway traffic management problem takes as input the best subset of routing alternatives and is solved as a mixed-integer linear program. The proposed methodology is tested on two practical case studies of the French railway infrastructure: the Lille terminal station area and the Rouen line. The computational experiments are based on several practical disturbed scenarios. Our methodology allows the improvement of the state of the art in terms of the minimization of train consecutive delays. The improvement is around 22% for the Rouen instances and around 56% for the Lille instances.

Evasion and hardening of tree ensemble classifiers

Abstract: Classifier evasion consists in finding for a given instance x the "nearest" instance x′ such that the classifier predictions of x and x′ are different. We present two novel algorithms for systematically computing evasions for tree ensembles such as boosted trees and random forests. Our first algorithm uses a Mixed Integer Linear Program solver and finds the optimal evading instance under an expressive set of constraints. Our second algorithm trades off optimality for speed by using symbolic prediction, a novel algorithm for fast finite differences on tree ensembles. On a digit recognition task, we demonstrate that both gradient boosted trees and random forests are extremely susceptible to evasions. Finally, we harden a boosted tree model without loss of predictive accuracy by augmenting the training set of each boosting round with evading instances, a technique we call adversarial boosting.

Network-Constrained AC Unit Commitment Under Uncertainty: A Benders’ Decomposition Approach

Abstract: This paper proposes an efficient solution approach based on Benders’ decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders’ approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach.

Model predictive control of autonomous mobility-on-demand systems

Abstract: In this paper we present a model predictive control (MPC) approach to optimize vehicle scheduling and routing in an autonomous mobility-on-demand (AMoD) system. In AMoD systems, robotic, self-driving vehicles transport customers within an urban environment and are coordinated to optimize service throughout the entire network. Specifically, we first propose a novel discrete-time model of an AMoD system and we show that this formulation allows the easy integration of a number of real-world constraints, e.g., electric vehicle charging constraints. Second, leveraging our model, we design a model predictive control algorithm for the optimal coordination of an AMoD system and prove its stability in the sense of Lyapunov. At each optimization step, the vehicle scheduling and routing problem is solved as a mixed integer linear program (MILP) where the decision variables are binary variables representing whether a vehicle will 1) wait at a station, 2) service a customer, or 3) rebalance to another station. Finally, by using real-world data, we show that the MPC algorithm can be run in real-time for moderately-sized systems and outperforms previous control strategies for AMoD systems.

Super-resolution of positive sources: the discrete setup

Abstract: In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by ${f_c}$, which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about $1/{f_c}$. The theoretical performance guarantee is complemented with a converse result showing that our simple convex program is nearly optimal. Finally, numerical experiments illustrate our methods.

A Benders decomposition approach for the charging station location problem with plug-in hybrid electric vehicles

Abstract: The flow refueling location problem (FRLP) locates p stations in order to maximize the flow volume that can be accommodated in a road network respecting the range limitations of the vehicles. This paper introduces the charging station location problem with plug-in hybrid electric vehicles (CSLP-PHEV) as a generalization of the FRLP. We consider not only the electric vehicles but also the plug-in hybrid electric vehicles when locating the stations. Furthermore, we accommodate multiple types of these vehicles with different ranges. Our objective is to maximize the vehicle-miles-traveled using electricity and thereby minimize the total cost of transportation under the existing cost structure between electricity and gasoline. This is also indirectly equivalent to maximizing the environmental benefits. We present an arc-cover formulation and a Benders decomposition algorithm as exact solution methodologies to solve the CSLP-PHEV. The decomposition algorithm is accelerated using Pareto-optimal cut generation schemes. The structure of the formulation allows us to construct the subproblem solutions, dual solutions and nondominated Pareto-optimal cuts as closed form expressions without having to solve any linear programs. This increases the efficiency of the decomposition algorithm by orders of magnitude and the results of the computational studies show that the proposed algorithm both accelerates the solution process and effectively handles instances of realistic size for both CSLP-PHEV and FRLP.

A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems

Abstract: This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimizations. We propose a convexification procedure relying on an efficient iterative re-weighted $\ell_{1}$ -minimization algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to the proposed iterative re-weighted $\ell_{1}$ -minimization algorithm. In the supplementary material available online (arXiv:1408.3549), we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators.

Optimal Content Placement for a Large-Scale VoD System

Abstract: IPTV service providers offering Video-on-Demand currently use servers at each metropolitan office to store all the videos in their library. With the rapid increase in library sizes, it will soon become infeasible to replicate the entire library at each office. We present an approach for intelligent content placement that scales to large library sizes (e.g., 100 Ks of videos). We formulate the problem as a mixed integer program (MIP) that takes into account constraints such as disk space, link bandwidth, and content popularity. To overcome the challenges of scale, we employ a Lagrangian relaxation-based decomposition technique combined with integer rounding. Our technique finds a near-optimal solution (e.g., within 1%–2%) with orders of magnitude speedup relative to solving even the linear programming (LP) relaxation via standard software. We also present simple strategies to address practical issues such as popularity estimation, content updates, short-term popularity fluctuation, and frequency of placement updates. Using traces from an operational system, we show that our approach significantly outperforms simpler placement strategies. For instance, our MIP-based solution can serve all requests using only half the link bandwidth used by least recently used (LRU) or least frequently used (LFU) cache replacement policies. We also investigate the tradeoff between disk space and network bandwidth.

Multistage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty Set

Abstract: In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problem finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets, one can differentiate the later-period decisions based on the revealed uncertain parameters. At the same time, the problem’s computational complexity stays at the same level, as for the static robust problem. This also holds in the nonfixed recourse situation. In the fixed recourse situation our approach can be combined with linear decision rules for the continuous decision variables. We provide theoretical results on splitting the uncertainty set by identifying sets of uncertain parameter scenarios to be divided for an improvement in the worst-case objective value. Based on this theory, we propose several splitting heuristics. Numerical examples entailing...

Multi-Objective Reconfiguration of Radial Distribution Systems Using Reliability Indices

Abstract: This paper deals with the distribution network reconfiguration problem in a multi-objective scope, aiming to determine the optimal radial configuration by means of minimizing the active power losses and a set of commonly used reliability indices formulated with reference to the number of customers. The indices are developed in a way consistent with a mixed-integer linear programming (MILP) approach. A key contribution of the paper is the efficient implementation of the ${\mmb\varepsilon}$ -constraint method using lexicographic optimization in order to solve the multi-objective optimization problem. After the Pareto efficient solution set is generated, the resulting configurations are evaluated using a backward/forward sweep load-flow algorithm to verify that the solutions obtained are both non-dominated and feasible. Since the ${\mmb\varepsilon}$ -constraint method generates the Pareto front but does not incorporate decision maker (DM) preferences, a multi-attribute decision making procedure, namely, the technique for order preference by similarity to ideal solution (TOPSIS) method, is used in order to rank the obtained solutions according to the DM preferences, facilitating the final selection. The applicability of the proposed method is assessed on a classical test system and on a practical distribution system.

Mechanism Design A Linear Programming Approach

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Energy Efficiency and Delay Tradeoff in Device-to-Device Communications Underlaying Cellular Networks

Abstract: This paper investigates the problem of revealing the tradeoff between energy efficiency (EE) and delay in device-to-device (D2D) communications underlaying cellular networks. Considering both stochastic traffic arrivals and time-varying channel conditions, we formulate it as a stochastic optimization problem, which optimizes EE subject to the average power, interference-control, and network stability constraints. With the help of fractional programming and the Lyapunov optimization technique, we develop an algorithm, referred to as the TRADEOFF, to solve the problem. To deal with the nonconvex and NP-hard power allocation subproblem in the TRADEOFF, we adopt the prismatic branch and bound algorithm to find its globally optimal solution, where only a linear programming needs to be solved in each iteration. Thus, the TRADEOFF serves as an important benchmark to evaluate performance of other heuristic algorithms and is usually cost-efficient. The theoretical analysis and simulation results show that the TRADEOFF achieves an EE-delay tradeoff of $[O(1/V),O(V)]$ with $V$ being a control parameter and can strike a flexible balance between them by simply tuning $V$ .

A New Mathematical Model for the Restoration Problem in Balanced Radial Distribution Systems

Abstract: This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions.

Multistage Long-Term Expansion Planning of Electrical Distribution Systems Considering Multiple Alternatives

Abstract: This paper presents a new mixed-integer linear programming (MILP) model to solve the multistage long-term expansion planning problem of electrical distribution systems (EDSs) considering the following alternatives: increasing the capacity of existing substations, constructing new substations, allocating capacitor banks and/or voltage regulators, constructing and/or reinforcing circuits, and modifying, if necessary, the system's topology. The aim is to minimize the investment and operation costs of the EDS over an established planning horizon. The proposed model uses a linearization technique and an approximation for transforming the original problem into an MILP model. The MILP model guarantees convergence to optimality by using existing classical optimization tools. In order to verify the efficiency of the proposed methodology, a 24-node test system was employed.