اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA simulation-based approach for solving optimisation problems with ODE-type steady state constraints
67
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article proposes a simple simulation-based approach for solving optimisation problems with steady state constraints relying on an ODE. This simulation-based optimisation method is tailored to the problem structure and exploits the local geometry of the steady state manifold and its stability properties. A parameterisation of the steady state manifold is not required. We prove local convergence of the method for locally strictly convex objective functions. Effciency and reliability of the proposed method are demonstrated in two examples. The proposed method demonstrated better convergence properties than existing general purpose methods and a significantly higher number of converged starts per time.
قيم البحث
اقرأ أيضاً
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In particular,
the worst case complexity of our dual method improves over the best-known result for this problem in Padakandla and Sundaresan [SIAM J. Optimization, 20 (2009), pp. 1185-1204]. We then propose a gradient projection method to solve a more general class of problems in which the objective function is not necessarily separable. Numerical experiments show that both our algorithms work well in test problems.
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by itera
tively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.
We consider the classic School Bus Routing Problem (SBRP) with a multi modal generalization, where students are either picked up by a fleet of school buses or transported by an alternate transportation mode, subject to a set of constraints. The const
raints that are typically imposed for school buses are a maximum fleet size, a maximum walking distance to a pickup point and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Moreover, we simplify the problem by introducing the connection between the SBRP and the weighted set covering problem (WSCP). To scale this method to large-scale problem instances, we propose i) a node compression method for the shareability network based decomposition approach, and ii) heuristic-based edge compression techniques that perform well in practice. We show that the compressed problem leads to an Integer Linear Programming (ILP) of reduced dimensionality that can be solved efficiently using off-the-shelf ILP solvers. Numerical experiments on small-scale, large-scale and benchmark networks are used to evaluate the performance of our approach and compare it to existing large-scale SBRP solving techniques.
We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is guarantee
d by gradient-based algorithms developed to date. We first show that the objective function is monotone submodular, a class of functions for which a simple greedy algorithm is known to be within 0.63 of the optimal solution. We then derive two tighter lower bounds by exploiting the curvature information (total curvature and elemental curvature) of the objective function. We further show that the tightness of these lower bounds is complementary with respect to the sensing capabilities of the agents. The greedy algorithm solution can be subsequently used as an initial point for a gradient-based algorithm to obtain solutions even closer to the global optimum. Simulation results show that this approach leads to significantly better performance relative to previously used algorithms.
As a widely used method in metabolic network studies, Monte-Carlo sampling in the steady state flux space is known for its flexibility and convenience of carrying out different purposes, simply by alternating constraints or objective functions, or ap
pending post processes. Recently the concept of a non-linear constraint based on the second thermodynamic law, known as Loop Law, is challenging current sampling algorithms which will inevitably give rise to the internal loops. A generalized method is proposed here to eradicate the probability of the appearance of internal loops during sampling process. Based on Artificial Centered Hit and Run (ACHR) method, each step of the new sampling process will avoid entering loop-forming subspaces. This method has been applied on the metabolic network of Helicobacter pylori with three different objective functions: uniform sampling, optimizing biomass synthesis, optimizing biomass synthesis efficiency over resources ingested. Comparison between results from the new method and conventional ACHR method shows effective elimination of loop fluxes without affecting non-loop fluxes.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
