67,573 research outputs found
GENETIC ALGORITHM FOR BINARY AND FUNCTIONAL DECISION DIAGRAMS OPTIMIZATION
Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applicationsis the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented
Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams
Decision diagrams are an increasingly important tool in cutting-edge solvers
for discrete optimization. However, the field of decision diagrams is
relatively new, and is still incorporating the library of techniques that
conventional solvers have had decades to build. We drew inspiration from the
warm-start technique used in conventional solvers to address one of the major
challenges faced by decision diagram based methods. Decision diagrams become
more useful the wider they are allowed to be, but also become more costly to
generate, especially with large numbers of variables. In the original version
of this paper, we presented a method of peeling off a sub-graph of previously
constructed diagrams and using it as the initial diagram for subsequent
iterations that we call peel-and-bound. We tested the method on the sequence
ordering problem, and our results indicate that our peel-and-bound scheme
generates stronger bounds than a branch-and-bound scheme using the same
propagators, and at significantly less computational cost. In this extended
version of the paper, we also propose new methods for using relaxed decision
diagrams to improve the solutions found using restricted decision diagrams,
discuss the heuristic decisions involved with the parallelization of
peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for
sequencing problems. Furthermore, we test the new methods on the sequence
ordering problem and the traveling salesman problem with time-windows (TSPTW),
and include an updated and generalized implementation of the algorithm capable
of handling any discrete optimization problem. The new results show that
peel-and-bound outperforms ddo (a decision diagram based branch-and-bound
solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.Comment: 50 pages, 31 figures, published by JAIR, supplementary materials at
https://github.com/IsaacRudich/ImprovedPnB. arXiv admin note: substantial
text overlap with arXiv:2205.0521
Integrated optimization of nonlinear R/C frames with reliability constraints
A structural optimization algorithm was researched including global displacements as decision variables. The algorithm was applied to planar reinforced concrete frames with nonlinear material behavior submitted to static loading. The flexural performance of the elements was evaluated as a function of the actual stress-strain diagrams of the materials. Formation of rotational hinges with strain hardening were allowed and the equilibrium constraints were updated accordingly. The adequacy of the frames was guaranteed by imposing as constraints required reliability indices for the members, maximum global displacements for the structure and a maximum system probability of failure
Optimal pilot decisions and flight trajectories in air combat
The thesis concerns the analysis and synthesis of pilot decision-making and the design of optimal flight trajectories. In the synthesis framework, the methodology of influence diagrams is applied for modeling and simulating the maneuvering decision process of the pilot in one-on-one air combat. The influence diagram representations describing the maneuvering decision in a one sided optimization setting and in a game setting are constructed. The synthesis of team decision-making in a multiplayer air combat is tackled by formulating a decision theoretical information prioritization approach based on a value function and interval analysis. It gives the team optimal sequence of tactical data that is transmitted between cooperating air units for improving the situation awareness of the friendly pilots in the best possible way. In the optimal trajectory planning framework, an approach towards the interactive automated solution of deterministic aircraft trajectory optimization problems is presented. It offers design principles for a trajectory optimization software that can be operated automatically by a nonexpert user. In addition, the representation of preferences and uncertainties in trajectory optimization is considered by developing a multistage influence diagram that describes a series of the maneuvering decisions in a one-on-one air combat setting. This influence diagram representation as well as the synthesis elaborations provide seminal ways to treat uncertainties in air combat modeling. The work on influence diagrams can also be seen as the extension of the methodology to dynamically evolving decision situations involving possibly multiple actors with conflicting objectives. From the practical point of view, all the synthesis models can be utilized in decision-making systems of air combat simulators. The information prioritization approach can also be implemented in an onboard data link system.reviewe
A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization
[EN] New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem. (c) 2008 Elsevier Inc. All rights reserved.Partially supported by MEC (Spanish Government) and FEDER funds: Projects DPI2005-07835, DPI2004-8383-C03-02 and GVA-026.Blasco, X.; Herrero Durá, JM.; Sanchís Saez, J.; Martínez Iranzo, MA. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences. 178(20):3908-3928. https://doi.org/10.1016/j.ins.2008.06.010S390839281782
A New Approach to Robot’s Imitation of Behaviors by Decomposition of Multiple-Valued Relations
Relation decomposition has been used for FPGA mapping, layout optimization, and data mining. Decision trees are very popular in data mining and robotics. We present relation decomposition as a new general-purpose machine learning method which generalizes the methods of inducing decision trees, decision diagrams and other structures. Relation decomposition can be used in robotics also in place of classical learning methods such as Reinforcement Learning or Artificial Neural Networks. This paper presents an approach to imitation learning based on decomposition. A Head/Hand robot learns simple behaviors using features extracted from computer vision, speech recognition and sensors
Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning
Finding tight bounds on the optimal solution is a critical element of
practical solution methods for discrete optimization problems. In the last
decade, decision diagrams (DDs) have brought a new perspective on obtaining
upper and lower bounds that can be significantly better than classical bounding
mechanisms, such as linear relaxations. It is well known that the quality of
the bounds achieved through this flexible bounding method is highly reliant on
the ordering of variables chosen for building the diagram, and finding an
ordering that optimizes standard metrics is an NP-hard problem. In this paper,
we propose an innovative and generic approach based on deep reinforcement
learning for obtaining an ordering for tightening the bounds obtained with
relaxed and restricted DDs. We apply the approach to both the Maximum
Independent Set Problem and the Maximum Cut Problem. Experimental results on
synthetic instances show that the deep reinforcement learning approach, by
achieving tighter objective function bounds, generally outperforms ordering
methods commonly used in the literature when the distribution of instances is
known. To the best knowledge of the authors, this is the first paper to apply
machine learning to directly improve relaxation bounds obtained by
general-purpose bounding mechanisms for combinatorial optimization problems.Comment: Accepted and presented at AAAI'1
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