Decision-making Tools and Memetic Algorithms in Management and Linear Programming Problems

Operational Research uses a set of tools based on scientific research principles to achieve rational and meaningful management decisions. This article tries to give solution to a highly complex Linear Programming problem by using Simplex method, Solver and a hybrid prototype which combines the theories of Genetic Algorithms with a new local search heuristic technique. Hybridization of these two techniques is becoming known as Memetic Algorithm. Additionally, this article tries to present different techniques to support management decision-making, with the intention of being used increasingly in the business environment sustaining, thus, decisions by mathematics or artificial intelligence and not only by experience.quantitative management; quantitative methods; decision-making; linear programming; operational research; heuristics; hybrid methods; memetic algorithms.

Heuristic Methods for Optimization - Cornell University

Heuristic optimization algorithms are artificial intelligence search methods that can be used to find the optimal decisions for designing or managing a wide range of complex systems. This course describes a variety of (meta) heuristic search methods including simulated annealing, tabu search, genetic algorithms, genetic programming, dynamically dimensioned search, and multiobjective methods. Algorithms will be used to find values of discrete and/or continuous variables that optimize system performance or improve system reliability. Students can select application projects from a range of application areas. The advantages and disadvantages of heuristic search methods for both serial and parallel computation are discussed in comparison to other optimization algorithms. Course taught at Cornell University

The evolution of cell formation problem methodologies based on recent studies (1997-2008): review and directions for future research

This paper presents a literature review of the cell formation (CF) problem concentrating on formulations proposed in the last decade. It refers to a number of solution approaches that have been employed for CF such as mathematical programming, heuristic and metaheuristic methodologies and artificial intelligence strategies. A comparison and evaluation of all methodologies is attempted and some shortcomings are highlighted. Finally, suggestions for future research are proposed useful for CF researchers

MAA*: A Heuristic Search Algorithm for Solving Decentralized POMDPs

We present multi-agent A* (MAA*), the first complete and optimal heuristic search algorithm for solving decentralized partially-observable Markov decision problems (DEC-POMDPs) with finite horizon. The algorithm is suitable for computing optimal plans for a cooperative group of agents that operate in a stochastic environment such as multirobot coordination, network traffic control, `or distributed resource allocation. Solving such problems efiectively is a major challenge in the area of planning under uncertainty. Our solution is based on a synthesis of classical heuristic search and decentralized control theory. Experimental results show that MAA* has significant advantages. We introduce an anytime variant of MAA* and conclude with a discussion of promising extensions such as an approach to solving infinite horizon problems.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

New prioritized value iteration for Markov decision processes

The problem of solving large Markov decision processes accurately and quickly is challenging. Since the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose an improved value iteration algorithm based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach. © Springer Science+Business Media B.V. 2011.García Hernández, MDG.; Ruiz Pinales, J.; Onaindia De La Rivaherrera, E.; Aviña Cervantes, JG.; Ledesma Orozco, S.; Alvarado Mendez, E.; Reyes Ballesteros, A. (2012). New prioritized value iteration for Markov decision processes. Artificial Intelligence Review. 37(2):157-167. doi:10.1007/s10462-011-9224-zS157167372Agrawal S, Roth D (2002) Learning a sparse representation for object detection. In: Proceedings of the 7th European conference on computer vision. Copenhagen, Denmark, pp 1–15Bellman RE (1954) The theory of dynamic programming. Bull Amer Math Soc 60: 503–516Bellman RE (1957) Dynamic programming. Princeton University Press, New JerseyBertsekas DP (1995) Dynamic programming and optimal control. Athena Scientific, MassachusettsBhuma K, Goldsmith J (2003) Bidirectional LAO* algorithm. In: Proceedings of indian international conferences on artificial intelligence. p 980–992Blackwell D (1965) Discounted dynamic programming. Ann Math Stat 36: 226–235Bonet B, Geffner H (2003a) Faster heuristic search algorithms for planning with uncertainty and full feedback. In: Proceedings of the 18th international joint conference on artificial intelligence. Morgan Kaufmann, Acapulco, México, pp 1233–1238Bonet B, Geffner H (2003b) Labeled RTDP: improving the convergence of real-time dynamic programming. In: Proceedings of the international conference on automated planning and scheduling. Trento, Italy, pp 12–21Bonet B, Geffner H (2006) Learning depth-first search: a unified approach to heuristic search in deterministic and non-deterministic settings and its application to MDP. In: Proceedings of the 16th international conference on automated planning and scheduling. Cumbria, UKBoutilier C, Dean T, Hanks S (1999) Decision-theoretic planning: structural assumptions and computational leverage. J Artif Intell Res 11: 1–94Chang I, Soo H (2007) Simulation-based algorithms for Markov decision processes Communications and control engineering. Springer, LondonDai P, Goldsmith J (2007a) Faster dynamic programming for Markov decision processes. Technical report. Doctoral consortium, department of computer science and engineering. University of WashingtonDai P, Goldsmith J (2007b) Topological value iteration algorithm for Markov decision processes. In: Proceedings of the 20th international joint conference on artificial intelligence. Hyderabad, India, pp 1860–1865Dai P, Hansen EA (2007c) Prioritizing bellman backups without a priority queue. In: Proceedings of the 17th international conference on automated planning and scheduling, association for the advancement of artificial intelligence. Rhode Island, USA, pp 113–119Dibangoye JS, Chaib-draa B, Mouaddib A (2008) A Novel prioritization technique for solving Markov decision processes. In: Proceedings of the 21st international FLAIRS (The Florida Artificial Intelligence Research Society) conference, association for the advancement of artificial intelligence. Florida, USAFerguson D, Stentz A (2004) Focused propagation of MDPs for path planning. In: Proceedings of the 16th IEEE international conference on tools with artificial intelligence. pp 310–317Hansen EA, Zilberstein S (2001) LAO: a heuristic search algorithm that finds solutions with loops. Artif Intell 129: 35–62Hinderer K, Waldmann KH (2003) The critical discount factor for finite Markovian decision processes with an absorbing set. Math Methods Oper Res 57: 1–19Li L (2009) A unifying framework for computational reinforcement learning theory. PhD Thesis. The state university of New Jersey, New Brunswick. NJLittman ML, Dean TL, Kaelbling LP (1995) On the complexity of solving Markov decision problems.In: Proceedings of the 11th international conference on uncertainty in artificial intelligence. Montreal, Quebec pp 394–402McMahan HB, Gordon G (2005a) Fast exact planning in Markov decision processes. In: Proceedings of the 15th international conference on automated planning and scheduling. Monterey, CA, USAMcMahan HB, Gordon G (2005b) Generalizing Dijkstra’s algorithm and gaussian elimination for solving MDPs. Technical report, Carnegie Mellon University, PittsburghMeuleau N, Brafman R, Benazera E (2006) Stochastic over-subscription planning using hierarchies of MDPs. In: Proceedings of the 16th international conference on automated planning and scheduling. Cumbria, UK, pp 121–130Moore A, Atkeson C (1993) Prioritized sweeping: reinforcement learning with less data and less real time. Mach Learn 13: 103–130Puterman ML (1994) Markov decision processes. Wiley Editors, New YorkPuterman ML (2005) Markov decision processes. Wiley Inter Science Editors, New YorkRussell S (2005) Artificial intelligence: a modern approach. Making complex decisions (Ch-17), 2nd edn. Pearson Prentice Hill Ed., USAShani G, Brafman R, Shimony S (2008) Prioritizing point-based POMDP solvers. IEEE Trans Syst Man Cybern 38(6): 1592–1605Sniedovich M (2006) Dijkstra’s algorithm revisited: the dynamic programming connexion. Control Cybern 35: 599–620Sniedovich M (2010) Dynamic programming: foundations and principles, 2nd edn. Pure and Applied Mathematics Series, UKTijms HC (2003) A first course in stochastic models. Discrete-time Markov decision processes (Ch-6). Wiley Editors, UKVanderbei RJ (1996) Optimal sailing strategies. Statistics and operations research program, University of Princeton, USA ( http://www.orfe.princeton.edu/~rvdb/sail/sail.html )Vanderbei RJ (2008) Linear programming: foundations and extensions, 3rd edn. Springer, New YorkWingate D, Seppi KD (2005) Prioritization methods for accelerating MDP solvers. J Mach Learn Res 6: 851–88

CASP Solutions for Planning in Hybrid Domains

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP