Partial inhibition and bilevel optimization in flux balance analysis.

Combinatorial bi-level optimization remains a challenging topic, especially when the lower-level is an NP-hard problem. In this paper, we tackle large-scale and combinatorial bi-level problems using GP hyper-heuristics, i.e., an approach that permits to train heuristics like a machine learning model. Our contribution aims at targeting the intensive and complex lower-level optimizations that occur when solving a large-scale and combinatorial bi-level problem. For this purpose, we consider hyper-heuristics through heuristic generation. Using a GP hyper-heuristic approach, we train greedy heuristics in order to make them more reliable when encountering unseen lower-level instances that could be generated during bi-level optimization. To validate our approach referred to as GA+AGH, we tackle instances from the bi-level cloud pricing optimization problem (BCPOP) that model the trading interactions between a cloud service provider and cloud service customers. Numerical results demonstrate the abilities of the trained heuristics to cope with the inherent nested structure that makes bi-level optimization problems so hard. Furthermore, it has been shown that training heuristics for lower-level optimization permits to outperform human-based heuristics and metaheuristics which constitute an excellent outcome for bi-level optimization.

Bilevel optimization problems require every feasible upper-level solution to satisfy optimality of a lower-level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy development, transportation problems, and others. In the context of a bilevel single objective problem, there exists a number of theoretical, numerical, and evolutionary optimization results. However, there does not exist too many studies in the context of having multiple objectives in each level of a bilevel optimization problem. In this paper, we address bilevel multi-objective optimization issues and propose a viable algorithm based on evolutionary multi-objective optimization (EMO) principles. Proof-of-principle simulation results bring out the challenges in solving such problems and demonstrate the viability of the proposed EMO technique for solving such problems. This paper scratches the surface of EMO-based solution methodologies for bilevel multi-objective optimization problems and should motivate other EMO researchers to engage more into this important optimization task of practical importance.

BackgroundOptimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation.MethodsIn this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock.ResultsOur new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

Bilevel and multi-objective optimization methods are often useful to spatially target agri-environmental policy throughout a watershed. This type of problem is complex and is comprised of a number of practicalities: (i) a large number of decision variables, (ii) at least two inter-dependent levels of optimization between policy makers and policy followers, and (iii) uncertainty in decision variables and problem parameters. Given agricultural and economic data from the Raccoon watershed in central Iowa, we formulate a bilevel multi-objective optimization problem that accommodates objectives of both policy makers and farmers. The solution procedure then explicitly accounts for the nested nature of farm-level management decisions in response to agri-environmental policy incentives constructed by policy makers. We specifically examine the spatial targeting of a fertilizer-reduction incentive policy while seeking to maximize farm-level productivity while generating mandated water quality improvements using this framework. We test three different evolutionary optimization algorithms - m-BLEAQ, NSGA-II, and SPEA2 - and show that m-BLEAQ is well suited for handling the bilevel optimization problems and the considered practicalities.

Uncertainties in variables and parameters cause optimization problems to move away from globally-optimal and uncertain solutions. Practitioners resort to finding robust and reliable solutions in such situations. Bilevel optimization problems involving a hierarchy of two nested optimization problems have received a growing attention in the recent past due to their relevance in practice. While a number of studies on bilevel solution methodologies and applications are available for a deterministic setup, but studies on uncertainties in bilevel optimization are rare. In this paper, we suggest methodologies for handling uncertainty in both lower and upper level variables that may occur from different practicalities. For the first time, we perform a systematic study demonstrating the effect of uncertainties in each level along with the definition of robustness and reliability in the context of bilevel optimization. The issues and complexities introduced due to such uncertainties are then studied through a number of test cases, for brevity, we only show results on three test cases. Finally, two real-world bilevel problems involving uncertainties in their variables are solved. The study provides foundations and demon- strates viable directions for further research in uncertainty-based bilevel optimization problems.

Bi-level optimisation problems (BOPs) are a class of challenging problems with two levels of optimisation tasks. These problems allow to model a large number of real-life situations in which a first decision maker, hereafter the leader, optimises his objective by taking the follower's response to his decisions explicitly into account. In this context, a new proposed algorithm called CODBA-II was suggested to solve combinatorial BOPs. The latter was able to improve the quality of generated bi-level solutions regarding to recently proposed methods. In fact, a wide range of applications fit the bi-level programming framework and real-life implementations still scarce. For this reason, we propose in this paper a co-evolutionary decomposition-based bi-level algorithm for the bi-level knapsack optimisation problem. The computational algorithm turned out to be quite efficient on both computation time and solution quality regarding to other competitive EAs.

We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg–Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem by means of the value function reformulation, we conduct a careful experimental study to this effect, in the context of the Levenberg–Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems. This study enables the construction of some safeguarding mechanisms for practical robust convergence of the method and can also serve as base for the selection of the penalty parameter for other bilevel optimization algorithms. We also compare the Levenberg–Marquardt method introduced in this paper to other existing algorithms of similar nature.

The bilevel optimisation problem (BLP) is a subclass of optimisation problems in which one of the constraints of an optimisation problem is another optimisation problem. BLP is widely used to model hierarchical decision making where the leader and the follower correspond to the upper level and lower level optimisation problem, respectively. In BLP, the optimal solutions to the lower level optimisation problem are the feasible solutions to the upper level problem, which makes it particularly difficult to solve. This paper proposes a novel hardware architecture known as Recursive Pipelined Genetic Propagation (RPGP), to solve BLP efficiently on FPGA. RPGP features a graph of genetic operation nodes which can be scaled to exploit hardware resources. In addition, the topology of the RPGP graph can be changed at run-time to escape from local optima. We evaluate the proposed architecture on an Altera Stratix-V FPGA, using a benchmark bilevel optimisation problem set. Our experimental results show that RPGP can achieve a significant speed-up against previous work.

In this paper, we consider the problem of scheduling N robots interacting with a moving target. Both, the sequence of the robots and their trajectories are unknown and subject to optimization. Such type of problems appear in highly automated production plants and in the simulation of virtual factories. The purpose of the paper is to provide a mathematical model and to suggest a numerical solution approach. Our approach is based on the formulation of the problem as a bilevel optimization problem, where the lower level problem is an optimal control problem, while the upper level problem is a finite dimensional mixed-integer optimization problem. We approach the problem by exploitation of necessary optimality conditions for the lower level problem and by application of a Branch & Bound method for the resulting single level optimization problem. Two settings are taken into account. Firstly, no state constraints are assumed on the lower level problem, thus the local minimum principle applies directly. Secondly, the problem setting is augmented by pure state constraints, which are being handled by virtual controls in order to regularize the problem.

Digital Twin (DT) and mobile edge computing are two promising solutions for achieving latency-sensitive and computing-intensive applications in Industrial Internet of Things (IIoT). However, existing task offloading schemes with DT empowerment are faced with challenges, such as the spatio-temporal heterogeneity of edge server (ES) resources, resource-constrained ESs, and the explosive growth of data in emerging applications. This paper investigates the issues of task offloading and resource allocation under the assistance of DT and multiple ESs parallel collaboration. One novel scheme, abbreviated as Mes-PCORA, is proposed. With comprehensive information within the digital space, the Mes-PCORA scheme dynamically adjusts task allocation ratios across multiple ESs to achieve collaborative task offloading. The offloading request is formulated as a non-convex problem. To make the non-convex problem solvable in polynomial time, the original problem transformed into a bilevel optimization problem. Then, a bilevel iterative optimization approach is proposed. Specifically, the upper-level optimization problem is formulated as a multi-agent Markov Decision Process, and a deep reinforcement learning-based resource allocation algorithm is designed to solve it. Subsequently, for the lower-level optimization problem, it is solved by the interior point method. Numerical results demonstrate that the proposed scheme reduces the average task completion latency by 27.16%–63.44% and decreases the task offloading failure rate by 35.83%–73.95%, compared to state-of-the-art baselines.

Genome-scale metabolic models have lead to the development of computational methods to understand the underlying mechanism about the metabolism of an organism. With the foundation of Flux balance analysis (FBA), optimization methods are developed to suggest optimal knockout strategies to achieve the maximum production of the target metabolite of interest including industrial and pharmaceutical chemicals. Many of these existing methods employ bi-level optimization formulations to maximize the production of the desired biochemical at the outer-level while the organism still maintains living modeled as the inner-level optimization model, for example, by maximizing biomass production yield under the constraints imposed by gene knockouts as in the well-known OptKnock. OptKnock always selects the most optimistic flux for the production of the desired biochemical under the maximum biomass condition although the actual flux can be less than this maximum. This is because optimal knockout strategies derived in such a bi-level optimization framework may heavily depend on the closeness and robustness of the inner-level optimization model in capturing actual cell survival states. By examining the non-uniqueness of the surviving mutants from the inner-level optimization model and the fact that there may be a non-cooperative environment between the inner-level and outer-level decision makers, the suggested mutants produced by OptKnock may be different from the actual knockout strategies in practice. In order to prevent these limitations of the optimistic OptKnock, we propose a modification of it through a novel pessimistic bi-level optimization perspective. We compute pessimistic knockout solutions and compare with those from OptKnock on a core E. coli metabolic network, and observe that the solutions through pessimistic view are more reliable and perform better. For future research, we believe that the proposed pessimistic bi-level optimization model will lead to more practical and robust knockout strategies.

Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leader’s level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular level’s optimization problem is solved the solution will be adapted the level’s variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.KeywordsMultilevel optimization(1+1)-Evolutionary strategymetaheuristic algorithmsNatural adaptation

Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated text-analysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.

Electronic countermeasure (ECM) has become one of the most significant factors in modern warfare, in the course of combat, the electronic jamming allocation tasks need to be flexibly adjusted with the change of combat stage, which puts forward higher requirements for the modeling and solution method of this kind of problems. To solve the ECM dynamic weapon target assignment (ECM-DWTA) problem, a hybrid multi-target bi-level programming model is established. The upper level takes the sum of the electronic jamming effects in the whole combat stage as an optimization objective, and locally optimizes the ECM weapon (ECM-WP) assignment scheme in each stage. The lower level takes the importance expectation value of the target subjected to interference and combat consumption as double optimization objectives to globally optimize the ECM-WP assignment scheme. Focus on solving this complex model, a hybrid multi-objective bi-level interactive fuzzy programming algorithm (HMOBIF) is proposed, in this method, exponential membership function is used to describe the satisfaction degree of each level. When solving the multi-objective optimization problem composed of membership functions in the upper and lower levels, we use the MOEA/D algorithm to obtain the Pareto Front (PF) solution set, and then each solution in PF is evaluated and selected by the TOPSIS multi-criteria evaluation method. This local and global interactive optimization process of bi-level model is actually the process of executing observation-orientation-decision-action loop in practical combat. According to the current example, we conduct numerical simulation on the parameters in the model and obtain the parameter values suitable for the model solution. The computational experiments on different scale ECM-DWTA problems show that HMOBIF method is superior to four bi-level programming algorithms in terms of performance index, and can better solve ECM-DWTA problems.

A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements