Amoeba-inspired combinatorial optimization machines

Abstract

Domain-specific computing architectures are expected to enable the development of new technologies after the saturation of the performance growth concerning conventional general-purpose computers. One such approach is to develop a combinatorial optimization machine (COM), which enables searching for an approximately optimal solution across a vast number of candidates more rapidly than conventional computers. To achieve the rapidity and optimality of the search, a COM exploits physical processes in specific hardware, exhibiting parallelism and stochasticity. This paper summarizes a unique biologically inspired approach to perform combinatorial optimization, which we have been investigated for over a decade. We first performed a series of biological experiments to evaluate the problem-solving ability of a single-celled amoeba that changes its shape into an optimal one by maximizing its body area for foraging and by minimizing the risk of being exposed to aversive light stimuli. Mathematically modeling the shape-changing dynamics of the amoeba, we formulated two algorithms for solving the traveling salesman problem (TSP) and Boolean satisfiability problem (SAT), named "AmoebaTSP" and "AmoebaSAT," respectively. AmoebaTSP and AmoebaSAT were implemented using analog and/or digital electronic circuits, to maximize their rapid search performance, by exploiting the parallel and stochastic nature of the circuits. We demonstrated that these COMs, called "electronic amoebae" are advantageous in diverse applications, as they can easily handle arbitrary problem instances of TSP and SAT without any costly preprocessing for problem mapping and their dynamics stabilize only at legal solutions that satisfy all given constraints. As electronic amoebae can be composed of conventional complementary metal-oxide semiconductor devices, they are highly scalable, energy-efficient, and suitable for both cloud-and edge computing applications.

Amoeba-inspired analog electronic computing system integrating resistance crossbar for solving the travelling salesman problem

“…The rate was found to be 100%; the system certainly converged to one of the legal solutions for every try. This is because the amoeba core always stabilizes at a steady state in which no variable violates the TSP constraints 39 ; in such a state, no further change in all units in the amoeba core is induced by the bounceback signals. Figure 4 a shows the length of the route obtained by the circuit simulator.…”

“…We focus on a living amoeboid organism that performs trialand-error behaviour to survive efficiently and resiliently in a harsh environment, deforming its gel-like body 30,31 . Here, we demonstrate, as a proof of concept, an analogue electronic computing system called an "electronic amoeba" 32,33 , inspired by the food search and risk avoidance behaviour of a single-celled amoeboid organism, Physarum polycephalum 30,31,[34][35][36][37][38][39] . In the electronic amoeba, an arbitrary TSP instance can be mapped on the resistor network of a crossbar structure shown in Fig.…”

“…The electronic amoeba is highly scalable and energy-efficient as it comprises existing complementary metal-oxide semiconductor (CMOS) devices and is expected to be useful for wide range of applications. Figure 2a shows a schematic of the electronic amoeba composed of the amoeba core and IMC, which electronically mimics the solution-searching dynamics of a so-called "amoeba-based computer" that employs a living amoeba to search for a solution to the TSP 38,39 (see Supplementary Information). The state of each unit in the amoeba core represents the decision on where and when to visit.…”

“…The state of each unit in the amoeba core represents the decision on where and when to visit. The IMC implements a type of feedback control, called the "bounceback control", which refers to the TSP constraints and intercity distances from the given map and sends a "bounceback signal" to each unit in the amoeba core [36][37][38][39] ; the signal is determined in accordance with the recurrent neural network dynamics defined by Eq. (1) in "Methods".…”

“…2 a, it is connected with the “amoeba core”, which contributes to avoiding the convergence at an illegal state. In the author’s previous works 35 , 38 , 39 , we formulated an algorithm representing a primitive idea of the electronic amoeba and predicted its potential performance without any physical implementation. In this paper, with results obtained from numerical simulations using a conventional computer and laboratory experiments using a physically fabricated circuit (Fig.…”