scholarly journals Communication-Based Decomposition Mechanisms for Decentralized MDPs

2008 ◽  
Vol 32 ◽  
pp. 169-202 ◽  
Author(s):  
C. V. Goldman ◽  
S. Zilberstein
Keyword(s):  
Search Algorithm ◽  
Single Agent ◽  
Real Life ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Markov Decision Problem ◽  
Heuristic Search Algorithm ◽  
Markov Decision

Multi-agent planning in stochastic environments can be framed formally as a decentralized Markov decision problem. Many real-life distributed problems that arise in manufacturing, multi-robot coordination and information gathering scenarios can be formalized using this framework. However, finding the optimal solution in the general case is hard, limiting the applicability of recently developed algorithms. This paper provides a practical approach for solving decentralized control problems when communication among the decision makers is possible, but costly. We develop the notion of communication-based mechanism that allows us to decompose a decentralized MDP into multiple single-agent problems. In this framework, referred to as decentralized semi-Markov decision process with direct communication (Dec-SMDP-Com), agents operate separately between communications. We show that finding an optimal mechanism is equivalent to solving optimally a Dec-SMDP-Com. We also provide a heuristic search algorithm that converges on the optimal decomposition. Restricting the decomposition to some specific types of local behaviors reduces significantly the complexity of planning. In particular, we present a polynomial-time algorithm for the case in which individual agents perform goal-oriented behaviors between communications. The paper concludes with an additional tractable algorithm that enables the introduction of human knowledge, thereby reducing the overall problem to finding the best time to communicate. Empirical results show that these approaches provide good approximate solutions.

scholarly journals Heuristic Search Algorithm for Dimensionality Reduction Optimally Combining Feature Selection and Feature Extraction

2019 ◽  
Vol 33 ◽  
pp. 2280-2287 ◽  
Author(s):  
Baokun He ◽  
Swair Shah ◽  
Crystal Maung ◽  
Gordon Arnold ◽  
Guihong Wan ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Feature Selection ◽  
Dimensionality Reduction ◽  
Heuristic Search ◽  
Search Algorithm ◽  
A Priori ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Combinatorial Search ◽  
Heuristic Search Algorithm

The following are two classical approaches to dimensionality reduction: 1. Approximating the data with a small number of features that exist in the data (feature selection). 2. Approximating the data with a small number of arbitrary features (feature extraction). We study a generalization that approximates the data with both selected and extracted features. We show that an optimal solution to this hybrid problem involves a combinatorial search, and cannot be trivially obtained even if one can solve optimally the separate problems of selection and extraction. Our approach that gives optimal and approximate solutions uses a “best first” heuristic search. The algorithm comes with both an a priori and an a posteriori optimality guarantee similar to those that can be obtained for the classical weighted A* algorithm. Experimental results show the effectiveness of the proposed approach.

scholarly journals Anytime Heuristic Search

2007 ◽  
Vol 28 ◽  
pp. 267-297 ◽  
Author(s):  
E. A. Hansen ◽  
R. Zhou
Keyword(s):  
Heuristic Search ◽  
Search Algorithm ◽  
Search Time ◽  
Optimal Solution ◽  
Search Problem ◽  
A Algorithm ◽  
Solution Quality ◽  
Multiple Sequence ◽  
Anytime Algorithm ◽  
Heuristic Search Algorithm

We describe how to convert the heuristic search algorithm A* into an anytime algorithm that finds a sequence of improved solutions and eventually converges to an optimal solution. The approach we adopt uses weighted heuristic search to find an approximate solution quickly, and then continues the weighted search to find improved solutions as well as to improve a bound on the suboptimality of the current solution. When the time available to solve a search problem is limited or uncertain, this creates an anytime heuristic search algorithm that allows a flexible tradeoff between search time and solution quality. We analyze the properties of the resulting Anytime A* algorithm, and consider its performance in three domains; sliding-tile puzzles, STRIPS planning, and multiple sequence alignment. To illustrate the generality of this approach, we also describe how to transform the memory-efficient search algorithm Recursive Best-First Search (RBFS) into an anytime algorithm.

scholarly journals Scheduling Jobs and a Variable Maintenance on a Single Machine with Common Due-Date Assignment

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Long Wan
Keyword(s):  
Single Machine ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Common Due Date ◽  
Optimal Polynomial ◽  
Special Case ◽  
Identical Jobs

We investigate a common due-date assignment scheduling problem with a variable maintenance on a single machine. The goal is to minimize the total earliness, tardiness, and due-date cost. We derive some properties on an optimal solution for our problem. For a special case with identical jobs we propose an optimal polynomial time algorithm followed by a numerical example.

scholarly journals Efficient Algorithms for Learning Revenue-Maximizing Two-Part Tariffs

2020 ◽  
Author(s):  
Maria-Florina Balcan ◽  
Siddharth Prasad ◽  
Tuomas Sandholm
Keyword(s):  
Cell Phone ◽  
High Probability ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Problem Instance ◽  
Lump Sum ◽  
Multiple Markets ◽  
Pricing Scheme ◽  
Generalization Theory

A two-part tariff is a pricing scheme that consists of an up-front lump sum fee and a per unit fee. Various products in the real world are sold via a menu, or list, of two-part tariffs---for example gym memberships, cell phone data plans, etc. We study learning high-revenue menus of two-part tariffs from buyer valuation data, in the setting where the mechanism designer has access to samples from the distribution over buyers' values rather than an explicit description thereof. Our algorithms have clear direct uses, and provide the missing piece for the recent generalization theory of two-part tariffs. We present a polynomial time algorithm for optimizing one two-part tariff. We also present an algorithm for optimizing a length-L menu of two-part tariffs with run time exponential in L but polynomial in all other problem parameters. We then generalize the problem to multiple markets. We prove how many samples suffice to guarantee that a two-part tariff scheme that is feasible on the samples is also feasible on a new problem instance with high probability. We then show that computing revenue-maximizing feasible prices is hard even for buyers with additive valuations. Then, for buyers with identical valuation distributions, we present a condition that is sufficient for the two-part tariff scheme from the unsegmented setting to be optimal for the market-segmented setting. Finally, we prove a generalization result that states how many samples suffice so that we can compute the unsegmented solution on the samples and still be guaranteed that we get a near-optimal solution for the market-segmented setting with high probability.

Harmony Search Algorithm

2018 ◽  
pp. 1-30 ◽  
Author(s):  
Alireza Askarzadeh ◽  
Esmat Rashedi
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Optimal Solution ◽  
Harmony Search Algorithm ◽  
Computational Time ◽  
Engineering Applications ◽  
Heuristic Search Algorithm ◽  
And Performance ◽  
Significant Attention

Harmony search (HS) is a meta-heuristic search algorithm which tries to mimic the improvisation process of musicians in finding a pleasing harmony. In recent years, due to some advantages, HS has received a significant attention. HS is easy to implement, converges quickly to the optimal solution and finds a good enough solution in a reasonable amount of computational time. The merits of HS algorithm have led to its application to optimization problems of different engineering areas. In this chapter, the concepts and performance of HS algorithm are shown and some engineering applications are reviewed. It is observed that HS has shown promising performance in solving difficult optimization problems and different versions of this algorithm have been developed. In the next years, it is expected that HS is applied to more real optimization problems.

scholarly journals Two New Beetle Antennae Search (BAS) Algorithms and Their Comparative Investigation

2018 ◽  
Vol 2 (1) ◽  
pp. 9 ◽  
Author(s):  
Zongyuan Lin ◽  
Sile Ma ◽  
Xiaojing Ma ◽  
Xiangyuan Jiang ◽  
Shuai Li
Keyword(s):  
Heuristic Search ◽  
Search Strategy ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Comparative Investigation ◽  
Test Results ◽  
Heuristic Search Algorithm ◽  
Fitness Value ◽  
Stability And Accuracy ◽  
Environment Parameters

The Beetle Antennae Search (BAS) algorithm is a meta-heuristic search algorithm, which has efficient search capabilities. This paper presents two different variant algorithms based on the BAS algorithm, which are the BAS with fitness value (BASF) algorithm and BAS with local fast search (BASL) algorithm. The test results of 23 benchmark functions will be used to verify the reliability and accuracy of these algorithm. These benchmark functions include unimodal and multimodal high-dimensional functions, as well as fixed-dimensional multimodal functions. The test results show that the improved algorithm can search for the optimal solution globally and accurately with its own search strategy without environment parameters. Stability and accuracy are significantly improved while the calculation time does not change much.

Harmony Search Algorithm

2017 ◽  
pp. 1-36 ◽  
Author(s):  
Alireza Askarzadeh ◽  
Esmat Rashedi
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Optimal Solution ◽  
Harmony Search Algorithm ◽  
Computational Time ◽  
Engineering Applications ◽  
Heuristic Search Algorithm ◽  
And Performance ◽  
Significant Attention

Harmony search (HS) is a meta-heuristic search algorithm which tries to mimic the improvisation process of musicians in finding a pleasing harmony. In recent years, due to some advantages, HS has received a significant attention. HS is easy to implement, converges quickly to the optimal solution and finds a good enough solution in a reasonable amount of computational time. The merits of HS algorithm have led to its application to optimization problems of different engineering areas. In this chapter, the concepts and performance of HS algorithm are shown and some engineering applications are reviewed. It is observed that HS has shown promising performance in solving difficult optimization problems and different versions of this algorithm have been developed. In the next years, it is expected that HS is applied to more real optimization problems.

scholarly journals Research on Reactive Power Optimization for Distribution Network Based on Dual Population Improved Ant Colony Algorithm

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Yiran Jiang
Keyword(s):  
Ant Colony Algorithm ◽  
Reactive Power ◽  
Power Optimization ◽  
Search Algorithm ◽  
Distribution Network ◽  
Optimal Solution ◽  
Ant Colony ◽  
Reactive Power Optimization ◽  
Heuristic Search Algorithm ◽  
Improved Ant Colony Algorithm

Ant Colony Algorithm is a heuristic search algorithm based on probability selection. It fits for solving the reactive power optimization problem of distribution network, but at the same time, easily falling into the problems of local optimal solution. So Dual Population Improved Ant Colony Algorithm is used to study Reactive Power Optimization Solution. Finally, with an actual example calculation and analysis, and node voltage comparison with and without compensation, the results are proved to be satisfactory. It verified the effectiveness and feasibility of the algorithm and the results show that the algorithm has better effect on optimization.

scholarly journals An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Bo Zhang ◽  
YueLin Gao ◽  
Xia Liu ◽  
XiaoLi Huang
Keyword(s):  
Polynomial Time ◽  
Outer Space ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Acceleration Technique ◽  
Region Division ◽  
Positive Exponent ◽  
Linear Programming Problems ◽  
Multiplicative Programs

This paper explains a region-division-linearization algorithm for solving a class of generalized linear multiplicative programs (GLMPs) with positive exponent. In this algorithm, the original nonconvex problem GLMP is transformed into a series of linear programming problems by dividing the outer space of the problem GLMP into finite polynomial rectangles. A new two-stage acceleration technique is put in place to improve the computational efficiency of the algorithm, which removes part of the region of the optimal solution without problems GLMP in outer space. In addition, the global convergence of the algorithm is discussed, and the computational complexity of the algorithm is investigated. It demonstrates that the algorithm is a complete polynomial time approximation scheme. Finally, the numerical results show that the algorithm is effective and feasible.

scholarly journals A Maximal Tractable Class of Soft Constraints

2004 ◽  
Vol 22 ◽  
pp. 1-22 ◽  
Author(s):  
D. Cohen ◽  
M. Cooper ◽  
P. Jeavons ◽  
A. Krokhin
Keyword(s):  
Artificial Intelligence ◽  
Computational Complexity ◽  
Polynomial Time ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Soft Constraints ◽  
Soft Constraint ◽  
Binary Constraints ◽  
Binary Constraint

Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which associates some measure of desirability with each possible combination of values for those variables. However, the crucial question of the computational complexity of finding the optimal solution to a collection of soft constraints has so far received very little attention. In this paper we identify a class of soft binary constraints for which the problem of finding the optimal solution is tractable. In other words, we show that for any given set of such constraints, there exists a polynomial time algorithm to determine the assignment having the best overall combined measure of desirability. This tractable class includes many commonly-occurring soft constraints, such as 'as near as possible' or 'as soon as possible after', as well as crisp constraints such as 'greater than'. Finally, we show that this tractable class is maximal, in the sense that adding any other form of soft binary constraint which is not in the class gives rise to a class of problems which is NP-hard.

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