This paper describes the design of a neural network architecture optimised for use with the Reactive Tabu Search (RTS) training algorithm. The neural network is built using the hybrid-Logarithmic Number System (hybrid-LNS) instead of the traditional fixed-point methods for the multiplyaccumulate (MAC) unit contained in each neuron. The circuits have been designed and implemented using between 4 and 8 bits of fractional precision for the logarithmic representation of the weights and the data. The architecture is based on the existing TOTEM VLSI chip and contains 32 neurons each having a 256 x 10-bit weight RAM. The device has been implemented on a Virtex XCV600 device where it consumed less 6025 slices with 4 bits of fractional precision of the logarithms and 6280 slices with 5 bits of fractional precision. At 4-bits This represents a (45%) reduction in logic resources required by the neuron array and an overall reduction of 10% of the FPGA resources when compared to the SoftTOTEM device built using the same technology.