Handling practicalities in agricultural policy optimization for water quality improvements

A fast sampling based evolutionary algorithm for million-dimensional multiobjective 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.

We propose a procedure to construct evolutionary bilevel optimization algorithms based on recent theoretical advances that have established connections between bilevel optimization and multiobjective optimization. In the proposed procedure, a new algorithm is defined by integrating an evolutionary multiobjective optimization algorithm with a partial order that is compatible with bilevel optimization. The advantages of the procedure include the ability to harness the methodology of evolutionary multiobjective optimization for bilevel optimization and to systematically develop new algorithms for single-objective and multiobjective bilevel optimization. No regularity assumptions are used, which ensures maximal applicability of the optimization algorithms constructed by the procedure. The necessary theoretical foundation is developed and the steps of the procedure are illustrated with an example.

Bi-level multi-objective optimization of the structure and attitude for space solar power station

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.

Multi-objective evolutionary algorithms (MOEAs) of the state of the art are created with the only purpose of dealing with the number of objective functions in a multi-objective optimization problem (MOP) and treat the decision variables of a MOP as a whole. However, when dealing with MOPs with a large number of decision variables (more than 100) their efficacy decreases as the number of decision variables of the MOP increases. On the other hand, problem decomposition, in terms of decision variables, has been found to be extremely efficient and effective for solving large scale optimization problems. Nevertheless, most of the currently available approaches for large scale optimization rely on models based on cooperative coevolution or linkage learning methods that use multiple subpopulations or preliminary analysis, respectively, which is computationally expensive (in terms of function evaluations) when used within MOEAs. In this work, we study the effect of what we call operational decomposition, which is a novel framework based on coevolutionary concepts to apply MOEAs’s crossover operator without adding any extra cost. We investigate the improvements that NSGA-III can achieve when combined with our proposed coevolutionary operators. This new scheme is capable of improving efficiency of a MOEA when dealing with large scale MOPs having from 200 up to 1200 decision variables.

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

Optimizing the operation of a multireservoir system is challenging due to the high dimension of the decision variables that lead to a large and complex search space. A spectral optimization model (SOM), which transforms the decision variables from time domain to frequency domain, is proposed to reduce the dimensionality. The SOM couples a spectral dimensionality‐reduction method called Karhunen‐Loeve (KL) expansion within the routine of Nondominated Sorting Genetic Algorithm (NSGA‐II). The KL expansion is used to represent the decision variables as a series of terms that are deterministic orthogonal functions with undetermined coefficients. The KL expansion can be truncated into fewer significant terms, and consequently, fewer coefficients by a predetermined number. During optimization, operators of the NSGA‐II (e.g., crossover) are conducted only on the coefficients of the KL expansion rather than the large number of decision variables, significantly reducing the search space. The SOM is applied to the short‐term operation of a 10‐reservoir system in the Columbia River of the United States. Two scenarios are considered herein, the first with 140 decision variables and the second with 3360 decision variables. The hypervolume index is used to evaluate the optimization performance in terms of convergence and diversity. The evaluation of optimization performance is conducted for both conventional optimization model (i.e., NSGA‐II without KL) and the SOM with different number of KL terms. The results show that the number of decision variables can be greatly reduced in the SOM to achieve a similar or better performance compared to the conventional optimization model. For the scenario with 140 decision variables, the optimal performance of the SOM model is found with six KL terms. For the scenario with 3360 decision variables, the optimal performance of the SOM model is obtained with 11 KL terms.

Nested evolutionary algorithms (EAs) have been regarded as very promising tools for bi-level optimization. Due to the nested structure, the upper level population evaluation requires a set of complete lower level optimizations, thereby reducing the efficiency and practicability of EA methods. In this paper, a multi-objective transformation-based evolutionary algorithm (MOTEA) is proposed to perform multiple lower level optimizations in a parallel and collaborative manner. Specifically, the corresponding multiple lower level optimizations for each generation of the upper level population evaluation are transformed into locating a set of Pareto optimal solutions of a constructed multi-objective optimization problem. By utilizing the built-in implicit parallelism of evolutionary multi-objective optimization, multiple lower level problems can thus be optimized in parallel. Within one multi-objective search population, the collaboration among the parallel lower level optimization can be realized by exploiting and utilizing the implicit similarities among them for better efficiency. The effectiveness and efficiency of the proposed MOTEA are verified by comparing it with four state-of-the-art evolutionary bi-level optimization algorithms on two sets of popular bi-level optimization benchmark test problems and three application 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.

Large-scale high-dimensional many-objective optimization problems (LaMaOPs) are prevalent in fields such as autonomous driving, cloud resource scheduling, and smart grids. LaMaOPs involve a large number of decision variables and multiple conflicting objectives that need to be optimized simultaneously. The challenges posed by the curse of dimensionality due to the vast number of decision variables, and the conflict between convergence and diversity caused by the numerous objective variables, make traditional optimization methods inadequate. To address these issues, this paper proposes a two-population cooperative evolutionary algorithm based on large-scale decision variable analysis (DVA-TPCEA). This algorithm integrates quantitative analysis methods for decision variables to deeply examine their impact on each objective and introduces a contribution-based objective detection method. Additionally, a dual-population cooperative evolution mechanism is employed, with targeted optimization strategies designed for convergence and diversity populations, achieving synergistic and complementary optimization between the two populations. To validate the algorithm’s effectiveness in practical applications, a large-scale container resource scheduling strategy based on the DVA-TPCEA algorithm is also proposed. The experimental results indicate that the proposed algorithm demonstrates significant advantages in both general datasets DTLZ, WFG, and LSMOP, and practical models.

Many engineering optimization problems are typically multi-objective in their natures and multidisciplinary with a large number of decision variables. Furthermore, Pareto dominance loses its effectiveness in such situations. Thus, developing a robust optimization algorithm undoubtedly becomes a true challenge. This paper proposes a multi-objective orthogonal opposition-based crow search algorithm (M2O-CSA) for solving large-scale multi-objective optimization problems (LSMOPs). In the M2O-CSA, a multi-orthogonal opposition strategy is employed to mitigate the conflicts among the convergence and distribution of solutions. First, two individuals are randomly chosen to undergo the crossover stage and then orthogonal array is presented to obtain nine individuals. Then individuals are used in the opposition stage to improve the diversity of solutions. The effectiveness of the proposed M2O-CSA is investigated by implementing it on different dimensions of multi-objective optimization problems (MOPs). The Pareto front solutions of these MOPs have various characteristics such as convex, non-convex and discrete. It is also applied to solve multi-objective design applications with distinctive features such as four bar truss (FBT) design, welded beam (WB) deign, disk brake (DB) design, and speed reduced (SR) design, where they involve different characteristics. In this context, a new decision making tool based on multi-objective optimization on the basis of ratio analysis (MOORA) technique is employed to help the designer for extracting the operating point as the best compromise or satisfactory solution to execute the candidate engineering design. Simulation results affirm that the proposed M2O-CSA works efficiently and effectively.

The increasing energy crisis and environmental problems promote the development of distributed energy systems (DESs) that utilize combined heat and power technology, renewable energy technology, and waste heat recovery technology to meet various load requirements. Although there is existing work and research on a variety of DESs, most previous studies tend to focus on energy production with little consideration of a distributed energy network and its energy loss, which results in large errors in energy-efficiency calculations and performance analyses. In this paper, a new DES model is proposed with full consideration of an energy network and the full use of solar energy, terrestrial heat, and exhaust gases. At the same time, an effective bi-level optimization method is also proposed for the daily operation of the DES in order to improve the system performance and benefits in the energy, the economy, and the environment. Specifically, the co-generation energy station and water heating network in the DES are optimized separately with two different optimization models. The first-level optimization model is used to seek the optimal values of water mass flow rate and water temperature of the water heating network, and the second-level optimization model is built to determine the optimal energy purchasing strategy and the optimal energy outputs of the co-generation energy station. In order to verify the advantages and effectiveness of the proposed system and method, a contrastive simulation study is undertaken to provide a comparison of the global optimization method. Simulation results show that energy loss, energy cost, and energy consumption of the DES using the bi-level optimization operation strategy only account for 22.51%, 33.42%, and 51.31% of the quantities of the global optimization method, respectively. The hourly curves of the optimal operating variables also demonstrate that the proposed bi-level optimization method can improve the operating stability of the DES better than the global optimization method.

MotivationWithin Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.ResultsIn this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.ConclusionsThe method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

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.