Biochemical parameter estimation vs. benchmark functions: A comparative study of optimization performance and representation design

© 2019 Elsevier B.V. Computational Intelligence methods, which include Evolutionary Computation and Swarm Intelligence, can efficiently and effectively identify optimal solutions to complex optimization problems by exploiting the cooperative and competitive interplay among their individuals. The exploration and exploitation capabilities of these meta-heuristics are typically assessed by considering well-known suites of benchmark functions, specifically designed for numerical global optimization purposes. However, their performances could drastically change in the case of real-world optimization problems. In this paper, we investigate this issue by considering the Parameter Estimation (PE) of biochemical systems, a common computational problem in the field of Systems Biology. In order to evaluate the effectiveness of various meta-heuristics in solving the PE problem, we compare their performance by considering a set of benchmark functions and a set of synthetic biochemical models characterized by a search space with an increasing number of dimensions. Our results show that some state-of-the-art optimization methods – able to largely outperform the other meta-heuristics on benchmark functions – are characterized by considerably poor performances when applied to the PE problem. We also show that a limiting factor of these optimization methods concerns the representation of the solutions: indeed, by means of a simple semantic transformation, it is possible to turn these algorithms into competitive alternatives. We corroborate this finding by performing the PE of a model of metabolic pathways in red blood cells. Overall, in this work we state that classic benchmark functions cannot be fully representative of all the features that make real-world optimization problems hard to solve. This is the case, in particular, of the PE of biochemical systems. We also show that optimization problems must be carefully analyzed to select an appropriate representation, in order to actually obtain the performance promised by benchmark results

Nature-inspired optimization algorithms: challenges and open problems

Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional algorithms may struggle to deal with such problems. A current trend is to use nature-inspired algorithms due to their flexibility and effectiveness. However, there are some key issues concerning nature-inspired computation and swarm intelligence. This paper provides an in-depth review of some recent nature-inspired algorithms with the emphasis on their search mechanisms and mathematical foundations. Some challenging issues are identified and five open problems are highlighted, concerning the analysis of algorithmic convergence and stability, parameter tuning, mathematical framework, role of benchmarking and scalability. These problems are discussed with the directions for future research

No-Free-Lunch Theorems in the continuum

No-Free-Lunch Theorems state, roughly speaking, that the performance of all search algorithms is the same when averaged over all possible objective functions. This fact was precisely formulated for the first time in a now famous paper by Wolpert and Macready, and then subsequently refined and extended by several authors, always in the context of a set of functions with discrete domain and codomain. Recently, Auger and Teytaud have shown that for continuum domains there is typically no No-Free-Lunch theorems. In this paper we provide another approach, which is simpler, requires less assumptions, relates the discrete and continuum cases, and that we believe that clarifies the role of the cardinality and structure of the domain

TUNING OPTIMIZATION SOFTWARE PARAMETERS FOR MIXED INTEGER PROGRAMMING PROBLEMS

The tuning of optimization software is of key interest to researchers solving mixed integer programming (MIP) problems. The efficiency of the optimization software can be greatly impacted by the solver’s parameter settings and the structure of the MIP. A designed experiment approach is used to fit a statistical model that would suggest settings of the parameters that provided the largest reduction in the primal integral metric. Tuning exemplars of six and 59 factors (parameters) of optimization software, experimentation takes place on three classes of MIPs: survivable fixed telecommunication network design, a formulation of the support vector machine with the ramp loss and L1-norm regularization, and node packing for coding theory graphs. This research presents and demonstrates a framework for tuning a portfolio of MIP instances to not only obtain good parameter settings used for future instances of the same class of MIPs, but to also gain insights into which parameters and interactions of parameters are significant for that class of MIPs. The framework is used for benchmarking of solvers with tuned parameters on a portfolio of instances. A group screening method provides a way to reduce the number of factors in a design and reduces the time it takes to perform the tuning process. Portfolio benchmarking provides performance information of optimization solvers on a class with instances of a similar structure