A contraction approach to dynamic optimization problems
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ABSTRACT:
SUBMITTER: Sandal L
PROVIDER: S-EPMC8608347 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Metaheuristic optimization algorithms play an essential role in optimizing problems. In this article, a new metaheuristic approach called the drawer algorithm (DA) is developed to provide quasi-optimal solutions to optimization problems. The main inspiration for the DA is to simulate the selection of objects from different drawers to create an optimal combination. The optimization process involves a dresser with a given number of drawers, where similar items are placed in each drawer. The optimization is based on selecting suitable items, discarding unsuitable ones from different drawers, and assembling them into an appropriate combination. The DA is described, and its mathematical modeling is presented. The performance of the DA in optimization is tested by solving fifty-two objective functions of various unimodal and multimodal types and the CEC 2017 test suite. The results of the DA are compared to the performance of twelve well-known algorithms. The simulation results demonstrate that the DA, with a proper balance between exploration and exploitation, produces suitable solutions. Furthermore, comparing the performance of optimization algorithms shows that the DA is an effective approach for solving optimization problems and is much more competitive than the twelve algorithms against which it was compared to. Additionally, the implementation of the DA on twenty-two constrained problems from the CEC 2011 test suite demonstrates its high efficiency in handling optimization problems in real-world applications.
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Project description:BACKGROUND: During the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been successfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework. RESULTS: In this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results. CONCLUSIONS: The proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.
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Project description: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.
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