A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

Abstract

BackgroundWe consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs).MethodsWe present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems.ResultsWe illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores).ConclusionsThese results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

A metaheuristic penalty approach for the starting point in nonlinear programming

“…In the last two decades, metaheuristic algorithms have gained significant attention as efficient solvers for hard global optimization problems appearing in real engineering and science modeling applications. A metaheuristic is a higher-level procedure designed to find or generate a heuristic that may provide a sufficiently good solution to an optimization problem, especially when the set of solutions is too large to be fully sampled; see, e.g., [22,27,28,36]. The central common feature of all heuristic optimization methods is that they start off with a more or less arbitrary initial guess, iteratively produce new solutions by combining randomness and a generation rule, evaluate these new solutions using a suitable merit function, and eventually report the best solution found during the search process; see, e.g., [2,31].…”

Hybrid parallel multimethod hyperheuristic for mixed-integer dynamic optimization problems in computational systems biology

“…As it can be seen, the performance of the proposed saCMM method to solve this challenging problem improves with the number of islands. Moreover, the performance of saCeSS, one of the cooperative single-method metaheuristics used in Section 5.1.2 to compare the performance of the proposed multimethod, was also evaluated in [36] using the HPN-DREAM benchmark. The results of saCMM are much better than those obtained in [36] for saCeSS.…”

“…Moreover, the performance of saCeSS, one of the cooperative single-method metaheuristics used in Section 5.1.2 to compare the performance of the proposed multimethod, was also evaluated in [36] using the HPN-DREAM benchmark. The results of saCMM are much better than those obtained in [36] for saCeSS. For instance, when using 40 islands, saCMM obtains in 2 days a solution of the same quality for which saCeSS needs more that 5 days.…”

libRCGA: a C library for real-coded genetic algorithms for rapid parameter estimation of kinetic models

“…There are other numerous applications for parameter estimation [41], [42], [43], [44], [45], [46], including our previously proposed CADLIVE [47], [48], [49], [50], [51]. However, most of them are designed for unconstrained optimizations and/or run on MATLAB or in specially provided environments.…”