Neural networks of nonlinear analog neurons are highly effective in solving optimization problems. These networks can rapidly compute solutions based on analog input information, often involving finding optimal solutions subject to constraints. The principles of constructing such networks are discussed, with results from simulations of a network solving the Traveling-Salesman Problem (TSP) illustrating their computational power. Solutions to TSP are computed within a few neural time constants, demonstrating the effectiveness of these networks. The power and speed of these collective networks are due to the nonlinear analog response of neurons and their large connectivity. Biological or microelectronic dedicated networks could solve a wide class of combinatorial problems. The computational power of nervous systems is immense, given the massive sensory data processed, the difficulty of recognition tasks, and the short time required for answers. General-purpose digital computers lack this power and speed. Neuroscience aims to understand how neurons and neural organization provide such computing power. Parallel processing is a key factor, with the mammalian visual system processing features in parallel. Neural networks and connectionist theories are studied to understand perception. A major feature of neural organization is collective analog computation, where neurons sum inputs to determine graded outputs. Analog systems are powerful due to their ability to adjust many variables simultaneously. Although analog summation is less accurate than digital, it is sufficient for perceptual tasks. This paper demonstrates the computational power and speed of collective analog networks in solving optimization problems. These networks can solve difficult problems rapidly, with each neuron receiving inputs from many others. Unlike connectionist approaches, these networks use analog computation. The TSP is used as an example of a well-defined optimization problem. The solution to TSP is discrete, but the networks operate in an analog mode.Neural networks of nonlinear analog neurons are highly effective in solving optimization problems. These networks can rapidly compute solutions based on analog input information, often involving finding optimal solutions subject to constraints. The principles of constructing such networks are discussed, with results from simulations of a network solving the Traveling-Salesman Problem (TSP) illustrating their computational power. Solutions to TSP are computed within a few neural time constants, demonstrating the effectiveness of these networks. The power and speed of these collective networks are due to the nonlinear analog response of neurons and their large connectivity. Biological or microelectronic dedicated networks could solve a wide class of combinatorial problems. The computational power of nervous systems is immense, given the massive sensory data processed, the difficulty of recognition tasks, and the short time required for answers. General-purpose digital computers lack this power and speed. Neuroscience aims to understand how neurons and neural organization provide such computing power. Parallel processing is a key factor, with the mammalian visual system processing features in parallel. Neural networks and connectionist theories are studied to understand perception. A major feature of neural organization is collective analog computation, where neurons sum inputs to determine graded outputs. Analog systems are powerful due to their ability to adjust many variables simultaneously. Although analog summation is less accurate than digital, it is sufficient for perceptual tasks. This paper demonstrates the computational power and speed of collective analog networks in solving optimization problems. These networks can solve difficult problems rapidly, with each neuron receiving inputs from many others. Unlike connectionist approaches, these networks use analog computation. The TSP is used as an example of a well-defined optimization problem. The solution to TSP is discrete, but the networks operate in an analog mode.