{"title": "Neural Network Methods for Optimization Problems", "book": "Advances in Neural Information Processing Systems", "page_first": 1184, "page_last": 1185, "abstract": "", "full_text": "Neural Network Methods for \n\nOptimization Problems \n\nArun Jagota \n\nDepartment of Mathematical Sciences \n\nMemphis State University \n\nMemphis, TN 38152 \n\nE-mail: jagota~nextl.msci.memst.edu \n\nIn a talk entitled \"Trajectory Control of Convergent Networks with applications \nto TSP\", Natan Peterfreund (Computer Science, Technion) dealt with the problem \nof controlling the trajectories of continuous convergent neural networks models for \nsolving optimization problems, without affecting their equilibria set and their con(cid:173)\nvergence properties. Natan presented a class of feedback control functions which \nachieve this objective, while also improving the convergence rates. A modified Hop(cid:173)\nfield and Tank neural network model, developed through the proposed feedback \napproach, was found to substantially improve the results of the original model in \nsolving the Traveling Salesman Problem. The proposed feedback overcame the 2n \nsymmetric property of the TSP problem. \n\nIn a talk entitled \"Training Feedforward Neural Networks quickly and accurately \nusing Very Fast Simulated Reannealing Methods\", Bruce Rosen (Asst. Professor, \nComputer Science, UT San Antonio) presented the Very Fast Simulated Reanneal(cid:173)\ning (VFSR) algorithm for training feedforward neural networks [2]. VFSR Trained \nnetworks avoid getting stuck in local minima and statistically guarantee the find(cid:173)\ning of an optimal weights set. The method can be used when network activation \nfunctions are nondifferentiable, and although often slower than gradient descent, it \nis faster than other Simulated Annealing methods. The performances of conjugate \ngradient descent and VFSR trained networks were demonstrated on a set of difficult \nlogic problems. \nIn a talk entitled \"A General Method for Finding Solutions of Covering problems \nby Neural Computation\", Tal Grossman (Complex Systems, Los Alamos) presented \na neural network algorithm for finding small minimal covers of hypergraphs. The \nnetwork has two sets of units, the first representing the hyperedges to be covered \nand the second representing the vertices. The connections between the units are \ndetermined by the edges of the incidence graph. The dynamics of these two types \nof units are different. When the parameters of the units are correctly tuned, the \nstable states of the system correspond to the possible covers. As an example, he \nfound new large square free subgraphs of the hypercube. \n\nIn a talk entitled \"Algebraic and Grammatical Design of Relaxation Nets\", Eric \n\n1184 \n\n\fNeural Network Methods for Optimization Problems \n\n1185 \n\nMjolsness (Professor, Computer Science, Yale University) presented useful algebraic \nnotation and computer-algebraic syntax for general \"programming\" with optimiza(cid:173)\ntion ideas; and also some optimization methods that can be succinctly stated in \nthe proposed notation. He addressed global versus local optimization, time and \nspace cost, learning, expressiveness and scope, and validation on applications. He \ndiscussed the methods of algebraic expression (optimization syntax and transforma(cid:173)\ntions, grammar models), quantitative methods (statistics and statistical mechanics, \nmultiscale algorithms, optimization methods), and the systematic design approach. \n\nIn a talk entitled \"Algorithms for Touring Knights\", Ian Parberry (Associate Pro(cid:173)\nfessor, Computer Sciences, University of North Texas) compared Takefuji and Lee's \nneural network for knight's tours with a random walk and a divide-and-conquer \nalgorithm. The experimental and theoretical evidence indicated that the neural \nnetwork is the slowest approach, both on a sequential computer and in parallel, \nand for the problems of generating a single tour, and generating as many tours as \npossible. \n\nIn a talk entitled \"Report on the DIMACS Combinatorial Optimization Challenge\" , \nArun Jagota (Asst. Professor, Math Sciences, Memphis State University) presented \nhis work, towards the said challenge, on neural network methods for the fast ap(cid:173)\nproximate solution of the Maximum Clique problem. The Mean Field Anneal(cid:173)\ning algorithm was implemented on the Connection Machine CM-5. A fast (two(cid:173)\ntemperature) annealing schedule was experimentally evaluated on random graphs \nand on the challenge benchmark graphs, and was shown to work well. Several other \nalgorithms, of the randomized local search kind, including one employing reinforce(cid:173)\nment learning ideas, were also evaluated on the same graphs. It was concluded that \nthe neural network algorithms were in the middle in the solution quality versus \nrunning time trade-off, in comparison with a variety of conventional methods. \n\nIn a talk entitled \"Optimality in Biological and Artificial Networks\" , Daniel Levine \n(Professor, Mathematics, UT Arlington) previewed a book to appear in 1995 [1]. \nThen he expanded his own view, that human cognitive functioning is sometimes, \nbut not always or even most of the time, optimal. There is a continuum from the \nmost \"disintegrated\" behavior, associated with frontal lobe damage, to stereotyped \nor obsessive-compulsive behavior, to entrenched neurotic and bureaucratic habits, \nto rational maximization of some measurable criteria, and finally to the most \"in(cid:173)\ntegrated\" , self-actualization (Abraham Maslow's term) which includes both reason \nand intuition. He outlined an alternative to simulated annealing, whereby a net(cid:173)\nwork that has reached an energy minimum in some but not all of its variables can \nmove out of it through a \"negative affect\" signal that responds to a comparison of \nenergy functions between the current state and imagined alternative states. \n\nReferences \n\n[1] D.S. Levine & W. Elsberry, editors. Optimality in Biological and Artificial \n\nNetworks? Lawrence Erlbaum Associates, 1995. \n\n[2] B. E. Rosen & J. M. Goodwin. Training hard to learn networks using advanced \n\nsimulated annealing methods. In Proc. of A CM Symp. on Applied Comp .. \n\n\f", "award": [], "sourceid": 753, "authors": [{"given_name": "Arun", "family_name": "Jagota", "institution": null}]}