It has been over a decade since neural networks were first applied to solve combinatorial optimization problems. During this period, enthusiasm has been erratic as new approaches are developed and (sometimes years later) their limitations are realized. This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial optimization problems. Areas which have not yet been studied are identified for future research.

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Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research

Composite stock cutting through simulated annealing

An algorithm, called self-organization assisted placement (SOAP), for circuit placement in arbitrarily shaped regions, including two-dimensional (2-D) rectilinear regions, nonplanar surfaces of three-dimensional objects, and three-dimensional volumes, is presented. SOAP is based on the self-organizing which adjusts the weight of synapses connected to neurons such that topologically close neurons become sensitive to inputs that are physically similar. A standard cell placement method and a global placement method of macro cells using SOAP algorithm are described. Several examples showing the circuit placement on rectilinear regions, nonplanar surfaces, and 3-D volumes are shown. Experimental results on benchmark circuits show that the SOAP algorithm is competitive with the state-of-the-art algorithms even for the case of placement in a rectangular region, which is a special case of a 2-D rectilinear region. >

Circuit placement on arbitrarily shaped regions using the self-organization principle

This paper explores the problem of joint computational offloading and content caching (OCP) in the wireless heterogeneous mobile edge computing (MEC) system, where each small-cell base station (BS) is equipped with the MEC server having the content caching/processing capabilities. The communication and computing resources of the system are allocated to users requesting or offloading their contents via the BSs to minimize the system-wide computational overhead. Due to the non-deterministic polynomial time hardness of the OCP, it is difficult to solve it with an exact integer-programming (IP) method. Instead, the problem is solved by adopting the Hopfield neural network (HNN) based approach. In particular, the HNN model representing the OCP is constructed. The global energy minimum of the model corresponds to a solution of the OCP. However, because of the negativity of diagonal weights, the convergence of this model to a stable state cannot be guaranteed. Subsequently, a range of “synthetic” HNN models with the global convergence property is developed to replace the original HNN. Based on these models, three different search algorithms are formulated and implemented in a long-term evolution advanced network. The algorithms demonstrate an improved performance when compared to other relevant IP methods in simulations.

Optimal Computational Offloading and Content Caching in Wireless Heterogeneous Mobile Edge Computing Systems With Hopfield Neural Networks

We have developed mapping and hierarchical self-organizing neural networks for placement of very large scale integrated (VLST) circuits. In this paper, we introduce MHSO and MHSO2 as two versions of mapping and hierarchical self-organizing network (MHSO) algorithms. By using the MHSO, each module in the placement wins the competition with a probability density function that is defined according to different design styles, e.g., the gate arrays and standard cell circuits. The relation between a placement carrier and movable modules is met by the algorithm's ability to map an input space (somatosensory source) into an output space where the circuit modules are located, MHSO2 is designed for macro cell circuits. In this algorithm, the shape and dimension of each module is simultaneously considered together with the wire length by a hierarchical order. In comparison with other conventional placement approaches, the MHSO algorithms have shown their distinct advantages. The results for benchmark circuits so far obtained are quite comparable to simulated annealing (SA), but the computation time is about eight-ten times faster than with SA.

Mapping and hierarchical self-organizing neural networks for VLSI placement

The authors present a modified Tank and Hopfield neural network for solving the problem of cell placement in integrated circuits, a constrained optimization problem that is NP-complete. The neural network is composed of two mutually interconnected subcircuits. One determines the configuration of cells on the plane for which the bounding box area and connections reach a minimum, whereas the other satisfies the nonoverlapping constraints among cells. The global-local minima issue is addressed and solved in two steps. First, the initial X-Y condition from which the system is permitted to evolve toward minima is determined by solving a relaxed problem that has global minima located in regions of the state space close to those of the original problem. Second, the initial orientation of blocks is determined by a more detailed analysis of connectivity requirements. The proposed neural network paradigm has been simulated and tested for small and medium-sized integrated circuits. >

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Papers

Neural algorithms for cell placement in VLSI design