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14th IEEE-RAS International Conference on Humanoid Robots (Humanoids)

作者： Deits, Robin Tedrake, Russ MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA MIT Fac Elect Engn & Comp Sci Cambridge MA 02139 USA

ISBN: (纸本)9781479971749

We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1].

关键词： collision avoidance convex programming integer programming legged locomotion piecewise linear techniques reachability analysis robot kinematics 2D environments 3D environments MIQCQP convex inner approximation footstep placement planning footstep placement rotation kinematic reachability mixed-integer convex optimization mixed-integer quadratically-constrained quadratic program nonconvex constraints obstacle avoidance obstacle-free configuration space piecewise linear approximation reachable space uneven terrain Collision avoidance Foot Linear approximation Piecewise linear approximation Planning Robots Piecewise linear approximation Collision avoidance Obstacle avoidance Piecewise linear techniques Foot Pedal Robot reachability analysis Biped locomotion Robot kinematics Linear approximation convex programming Foot Foot Foot British integer Programming

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Majority judgment over a convex candidate space

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OPERATIONS RESEARCH LETTERS 2019年第4期47卷 317-325页

作者： Yan, Chiwei Swaroop, Prem Ball, Michael O. Barnhart, Cynthia Vaze, Vikrant MIT Operat Res Ctr Cambridge MA 02139 USA Uber Technol Inc Louisville CO USA MIT Dept Civil & Environm Engn Cambridge MA 02139 USA Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA Univ Maryland Inst Syst Res College Pk MD 20742 USA Dartmouth Coll Thayer Sch Engn Hanover NH 03755 USA

Most voting methods can only deal with a finite number of candidates. In practice, there are important voting applications where the candidate space is continuous. We describe a new voting method by extending the Majority Judgment voting and ranking method to handle a continuous candidate space which is modeled as a convex set. We characterize the structure of the winner determination problem and present a practical iterative voting procedure for finding a (or the) winner when voter preferences are unknown. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Voting Majority judgment mixed-integer convex optimization Computational social choice

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Disjunctive cuts in mixed-integer Conic optimization

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MATHEMATICAL PROGRAMMING 2023年第1-2期199卷 671-719页

作者： Lodi, Andrea Tanneau, Mathieu Vielma, Juan-Pablo Polytech Montreal Canada Excellence Res Chair CERC CP 6079Succ Ctr Ville Montreal PQ H3C 3A7 Canada MIT Sloan Sch Management Cambridge MA USA

This paper studies disjunctive cutting planes in mixed-integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability and conic strong duality. Then, we highlight the shortcomings of separating conic-infeasible points in an outer-approximation context, and propose conic extensions to the classical lifting and monoidal strengthening procedures. Finally, we assess the computational behavior of various normalization conditions in terms of gap closed, computing time and cut sparsity. In the process, we show that our approach is competitive with the internal lift-and-project cuts of a state-of-the-art solver.

关键词： mixed-integer convex optimization Disjunctive Cutting Planes Conic optimization

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Proximity search for 0-1 mixed-integer convex programming

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JOURNAL OF HEURISTICS 2014年第6期20卷 709-731页

作者： Fischetti, Matteo Monaci, Michele Univ Padua DEI I-35100 Padua Italy

In this paper we investigate the effects of replacing the objective function of a 0-1 mixed-integer convex program (MIP) with a "proximity" one, with the aim of using a black-box solver as a refinement heuristic. Our starting observation is that enumerative MIP methods naturally tend to explore a neighborhood around the solution of a relaxation. A better heuristic performance can however be expected by searching a neighborhood of an integer solution-a result that we obtain by just modifying the objective function of the problem at hand. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, suggesting that proximity search can be quite effective in quickly refining a given feasible solution. This is particularly true when a sequence of similar MIPs has to be solved as, e.g., in a column-generation setting.

关键词： mixed-integer convex optimization Proximal methods Primal methods Heuristics

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Deployable, Data-Driven Unmanned Vehicle Navigation System in GPS-Denied, Feature-Deficient Environments

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JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS 2022年第2期105卷 1-21页

作者： Misra, Sohum Sundar, Kaarthik Sharma, Rajnikant Brink, Kevin Univ Cincinnati Dept Aerosp Engn Cincinnati OH USA Los Alamos Natl Lab Informat Syst & Modeling Los Alamos NM 87544 USA Air Force Res Lab Eglin AFB FL USA

This paper presents a novel data-driven navigation system to navigate an Unmanned Vehicle (UV) in GPS-denied, feature-deficient environments such as tunnels, or mines. The method utilizes landmarks that vehicle can deploy and measure range from to enable localization as the vehicle traverses its pre-defined path through the tunnel. A key question that arises in such scenario is determine apriori, i.e., before the start of the mission, the number of landmarks the vehicle has to carry, given some information about the environment. The main objective is to determine this number so as to keep the maximum position uncertainty less than or close to a desired value. In this article, we develop a novel vehicle navigation system in GPS-denied, feature-deficient environment by combining techniques from estimation, machine learning, and mixed-integer convex optimization. This article develops a novel, systematic method to perform localization and navigate the UV through the environment with minimum number of landmarks while maintaining desired localization accuracy. We also present extensive simulation experiments on different scenarios that corroborate the effectiveness of the proposed navigation system.

关键词： Localization mixed-integer convex optimization Machine learning Estimation Filtering GPS-denied environments

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Rate-sensitive CoMP beamforming plus sensible snooze for energy-QoE tradeoff in cognitive small cell networks

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COMPUTER NETWORKS 2017年 122卷 205-216页

作者： Yi, Leng-Gan Hubei Normal Univ Coll Comp Sci & Technol Huangshi 435002 Peoples R China

Small cells, specific femtocells aim to improve throughput and customer experience indoors, which prospectively develop into an indispensable part to complement macrocells. Since network operators progressively consider ecological and economical sustainable development, energy-saving and interference free have grown to be crucial challenges for "green" femtocells, especially under ultra-dense deployment. To this end, we introduce coordinated multi-point (CoMP) femto-base stations (FBSs) to exploit intra-femto interference and multiple-input single-output beamforming in cognitive underlay to mitigate cross-tier interference, integrated with another key effort to best conserve overall FBSs power. It is formulated as a quasi mixed-integer convex optimization problem, decomposed and carried out separately via innovative transformations. A novel FBSs CoMP-selecting scheme, sensitive to femto-user traffic rate, is proposed to rapidly obtain the effective solution to fundamental CoMP beamforming issue. Furthermore, a policy of diminishing the CoMP set by deactivating feasible no-load FBSs to snooze, is proposed to actually minimize entire power consumption, wherein FBSs static, dynamic and backhauling power is jointly evaluated by accordingly proposed two hierarchical iterative algorithms. Network-level simulations under practical configurations, in contrast to prior work, demonstrate the proposals can achieve a proper tradeoff between retaining significant energy-efficient FBSs operation and assuring preferable quality of consumers experience. (C) 2017 Elsevier B.V. All rights reserved.

关键词： CoMP Cognitive radio Energy efficiency Femtocell Interference mitigation Multiple-input single-output (MISO) beamforming mixed-integer convex optimization Quality of experience (QoE)

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Shapes and recession cones in mixed-integer convex representability

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MATHEMATICAL PROGRAMMING 2024年第1-2期204卷 739-752页

作者： Zadik, Ilias Lubin, Miles Vielma, Juan Pablo MIT Dept Math Boston MA 02139 USA

mixed-integer convex representable (MICP-R) sets are those sets that can be represented exactly through a mixed-integer convex programming formulation. Following up on recent work by Lubin et al. (in: Eisenbrand (ed) integer Programming and Combinatorial optimization - 19th International Conference, Springer, Waterloo), (Math. Oper. Res. 47:720-749, 2022) we investigate structural geometric properties of MICP-R sets, which strongly differentiate them from the class of mixed-integer linear representable (MILP-R) sets. First, we provide an example of an MICP-R set which is the countably infinite union of convex sets with countably infinitely many different recession cones. This is in sharp contrast with MILP-R sets which are (countable) unions of polyhedra that share the same recession cone. Second, we provide an example of an MICP-R set which is the countably infinite union of polytopes all of which have different shapes (no pair is combinatorially equivalent, which implies they are not affine transformations of each other). Again, this is in sharp contrast with MILP-R sets which are (countable) unions of polyhedra that are all translations of a finite subset of themselves.

关键词： mixed-integer convex optimization mixed-integer programming formulations mixed-integer programming representability

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Optimal Pole-Swapping in Bipolar DC Networks With Multiple CPLs Using an MIQP Model

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2023年第9期70卷 3564-3568页

作者： Montoya, Oscar Danilo Grisales-Norena, Luis Fernando Gil-Gonzalez, Walter Univ Distrital Francisco Jose Caldas Fac Engn Bogota 110231 Colombia Univ Talca Fac Engn Dept Elect Engn Curico 3340000 Chile Univ Tecnol Pereira Dept Elect Engn Pereira 660003 Colombia

This express brief presents a mixed-integer quadratic programming (MIQP) model to address the problem of optimal pole-swapping in asymmetric bipolar DC networks. The exact mixed-integer nonlinear programming model is convexified by using two stages. Using Taylor's series expansion, the first stage corresponds to linearizing the hyperbolic relationship between voltage and powers in the constant power loads. The second stage applies the concept of the big-M number in order to obtain a linear equivalent for the product between binary and continuous variables. The proposed MIQP model is solved using the MATLAB programming environment, with the convex disciplined tool known as CVX and the Gurobi solver. Numerical results in the 21- and 85-bus grids demonstrate the effectiveness of the proposed MIQP formulation when compared to combinatorial optimization methods. The MIQP model ensures reductions of about 3.7609 and 49.7928kW in the total grid power losses for the 21- and 85-bus grids, respectively, when the neutral wire is assumed to be floating in all the nodes of the network except for the substation bus.

关键词： Optimal pole-swapping problem unbalanced bipolar DC networks power loss reduction mixed-integer convex optimization

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Optimal Reactive Power Compensation in Distribution Networks with Radial and Meshed Structures Using D-STATCOMs: A mixed-integer convex Approach

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SENSORS 2022年第22期22卷 8676页

作者： Garrido, Victor Manuel Montoya, Oscar Danilo Medina-Quesada, Angeles Hernandez, Jesus C. Univ Pamplona Fac Ingn & Arquitectura Programa Ingn Elect Pamplona 543050 Colombia Univ Dist Francisco Jose de Caldas Fac Ingn Grp Compatibilidad & Interferencia Electromagnet Bogota 110231 Colombia Univ Tecnol Bolivar Fac Ingn Lab Inteligente Energia Cartagena 131001 Colombia Univ Jaen Dept Elect Engn Campus Lagunillas S-NEdificio A3 Jaen 23071 Spain

This paper deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) in electrical distribution networks to minimize the expected total annual operating costs. These costs are associated with the investments made in D-STATCOMs and expected energy losses costs. To represent the electrical behavior of the distribution networks, a power flow formulation is used which includes voltages, currents, and power as variables via incidence matrix representation. This formulation generates a mixed-integer nonlinear programming (MINLP) model that accurately represents the studied problem. However, in light of the complexities involved in solving this MINLP model efficiently, this research proposes a mixed-integer convex reformulation. Numerical results regarding the final annual operating costs of the network demonstrate that the proposed mixed-integer convex model is efficient for selecting and locating D-STATCOMs in distribution networks, with the main advantage that it is applicable to radial and meshed distribution grid configurations. A comparative analysis with respect to metaheuristic optimizers and convex approximations confirms the robustness of the proposed formulation. All numerical validations were conducted in the MATLAB programming environment with our own scripts (in the case of metaheuristics) and the CVX convex disciplined tool via the Gurobi solver. In addition, the exact MINLP model is solved using the GAMS software.

关键词： radial and meshed distribution networks distribution static compensators mixed-integer convex optimization optimal power flow approximation

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A New Combinatorial Algorithm for Separable convex Resource Allocation with Nested Bound Constraints

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INFORMS JOURNAL ON COMPUTING 2021年第3期33卷 1197-1212页

作者： Wu, Zeyang Nip, Kameng He, Qie Univ Minnesota Dept Ind & Syst Engn Minneapolis MN 55455 USA Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China

The separable convex resource allocation problem with nested bound constraints aims to allocate B units of resources to n activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve this model exactly. Our algorithm is capable of solving instances with millions of activities in several minutes. The running time of our algorithm is at most 73% of the running time of the current best algorithm for benchmark instances with three classes of convex objectives. The efficiency of our algorithm derives from a combination of constraint relaxation and divide and conquer based on infeasibility information. In particular, nested bound constraints are relaxed first;if the solution obtained violates some bound constraints, we show that the problem can be divided into two subproblems of the same structure and smaller sizes according to the bound constraint with the largest violation. Summary of Contribution. The resource allocation problem is a collection of optimization models with a wide range of applications in production planning, logistics, portfolio management, telecommunications, statistical surveys, and machine learning. This paper studies the resource allocation model with prescribed lower and upper bounds on the total amount of resources consumed by nested subsets of activities. These nested bound constraints are motivated by storage limits, time-window requirements, and budget constraints in various applications. The model also appears as a subproblem in models for green logistics and machine learning, and it has to be solved repeatedly. The model belongs to the class of computationally challenging convex mixed-integer nonlinear programs. We develop a combinatorial algorithm to solve this model exactly. Our algorithm is faster than the algorithm that currently has the best theoretical complexity in the literatu

关键词： resource allocation constraint relaxation divide and conquer polynomial-time algorithms mixed-integer convex optimization

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