Joint Stocking and Product Offer Decisions Under the Multinomial Logit Model

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.

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.

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.

Many real-world multi-objective optimization problems have hundreds or even thousands of decision variables, which contrast with the current practice of multi-objective metaheuristics whose performance is typically assessed using benchmark problems with a relatively low number of decision variables (normally, no more than 30). In this paper, we propose a cooperative coevolution framework that is capable of optimizing large scale (in decision variable space) multi-objective optimization problems. We adopt a benchmark that is scalable in the number of decision variables (the ZDT test suite) and compare our proposed algorithm with respect to two state-of-the-art multi-objective evolutionary algorithms (GDE3 and NSGA-II) when using a large number of decision variables (from 200 up to 5000). The results clearly indicate that our proposed approach is effective as well as efficient for solving large scale multi-objective optimization problems.

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

Microgrid dynamic combined power–heat economic-emission dispatch with deferrable loads and price-based energy storage elements and power exchange

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.

The present paper deals with the development of a new multi-objective evolution strategy in combination with an integrated pollution-load and water-quality model to optimise the performance of an urban wastewater system. The optimisation algorithm combines the advantages of the non-dominated sorting genetic algorithm and self-adaptive evolution strategies and contains further development improving convergence and diversity. The identification of a good spread of solutions on the Pareto-optimum front and the optimisation of a large number of decision variables equally demands numerous simulation runs. In addition, evaluation of criteria with regard to the frequency of critical concentrations in the river and peak discharges to the receiving water requires continuous long-term simulations. Therefore, a fast operating integrated simulation model is needed providing the required precision of results. For this purpose, a hydrological deterministic pollution-load model has been coupled with a river water-quality and a rainfall-runoff model. Wastewater treatment plants (WWTP) are simulated in a simplified way. The integrated simulation model and the multi-objective optimisation algorithm were implemented in a modular common software shell. The functionality of the optimisation and simulation tool has been validated by analysing a real catchment area including sewer system, WWTP, water body and natural river basin. For the optimisation/rehabilitation of the urban drainage system, both innovative and approved measures have been examined and used as decision variables. As objective functions, investment costs and river water quality criteria have been used.

Optimal classification trees with leaf-branch and binary constraints

Gradient-free methods applied to optimisation of advanced ultra-supercritical power plant

The low recovery factor associated with carbonate reservoir and the availability of affordable gas has drawn new attention to a Water Alternative Gas (WAG) strategy to enhance hydrocarbon recovery for reservoir at early stage of production. The use of WAG allows to improve sweep efficiency limiting fingering and hydrocarbon trapping at macroscopic (Water injection - WI) and microscopic (pore) (Gas Injection - GI) level.The purpose of this work is twofold: present a new field development plan optimization formulation generalized for continuous and/or WAG injection and its suggested application to a real reservoir test case. Optimum field development plans for different strategies are presented and the advantages of a WAG strategy as opposite to a continuous water injection are further discussed. The proposed optimization problem covers well placement, control, schedule and gas lift under uncertainty. This problem is formulated as Mixed Integer Nonlinear Programing (MINLP) with non-linear constrains in order to take into account operational restrictions.A carbonate deep water reservoir at the early stages of its exploitation has been used to evaluate this new workflow. An in-house Particle Swarm Optimization (PSO) algorithm has been used to solve this nonlinear optimization problem. The use of a real field as test bench poses additional strength on the robustness of the formulation in presence of a large number of decision variables and constrains. Special care has been taken in the field development plan selection, taking into account the optimal solution as well as additional objectives and sentiments added by the decision makers which increase the realism of the final solution.The optima selected were compared to a WAG base case adjusted using standard commercial tools according to best practice. The results obtained for the current reservoir highlight key performances of the optimization algorithm applied to the WAG strategy. WAG increases the recovery factor and enhance an early production (paramount to improve the NPV according to the economic model) with respect to a continuous WI. The optimization of WAG cycles allows to find the best hydrocarbon production under the constrain imposed by the facilities and the gas availability. The optimum inter-well-distance and schedule results from the compromise between a strong sweep yet avoiding an early water breakthrough and reducing interference among producers. The well layout is therefore an output of the NPV optimization, the carbonate geological characterization and the operation risk. The optimal field development plan has shown a 35% of increment in NPV compared to the base case.This workflow presented and discussed presents an innovative and general formulation for the optimization of a WAG and/or continuous injection for real reservoir under uncertainty. The optimization algorithm allows fast convergence and accurate results. The extension to multiple objective functions and the inclusion of the human decision in the optimization process is also considered.

Airline seat inventory optimization is a very profitable tool for airline. Current researches are focused on network seat inventory optimization, which has high complication of combination of the ODF (Origin, Destination, Fare) and seat number. Due to the large number of decision variables, traditional optimization models are hard to compute. Although some LP approximation methods of traditional models improve their practical applicability, they still take long time to compute and have high complexity when network is large. We used ant colony algorithm to solve network seat inventory optimization in this paper. It is shown that ant colony algorithm can solve problem quickly and gain good results, and it is easy to implement.

The widely used support vector machine (SVM) method has shown to yield very good results in supervised classification problems. Other methods such as classification trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in data mining.In this work, we propose an SVM-based method that automatically detects the most important predictor variables and the role they play in the classifier. In particular, the proposed method is able to detect those values and intervals that are critical for the classification. The method involves the optimization of a linear programming problem in the spirit of the Lasso method with a large number of decision variables. The numerical experience reported shows that a rather direct use of the standard column generation strategy leads to a classification method that, in terms of classification ability, is competitive against the standard linear SVM and classification trees. Moreover, the proposed method is robust; i.e., it is stable in the presence of outliers and invariant to change of scale or measurement units of the predictor variables.When the complexity of the classifier is an important issue, a wrapper feature selection method is applied, yielding simpler but still competitive classifiers.

To support national carbon neutrality goals, China's grid is rapidly decarbonizing. Confronting power volatility and renewable curtailment induced by large-scale wind/PV penetration, this paper introduces an optimal scheduling framework for multi-energy complementary systems integrating thermal, storage, and renewables. Considering the complexity of the multi-energy structure, which involves a large number of decision variables and operational constraints, the model is linearized, and a hierarchical optimization framework is employed. The upper-level model minimizes thermal, storage, and renewable operating costs, using storage for peak-shaving to reduce load fluctuation and enable renewable integration. The lower level minimizes the thermal and storage costs, and curtailment penalties to boost renewable utilization and operational economy. A decomposition-and-coordination solution methodology is adopted to achieve iterative coordination between the two model layers. Finally, the proposed strategy is validated through simulation studies based on an improved IEEE 39-bus test system under multiple scenarios. Simulation results confirm that the proposed methodology substantially improves renewable energy accommodation capacity and overall system economic efficiency, validating the model's effectiveness and practical applicability.

Molecular sequence alignment is one of the most essential tools of the molecular biology. It permits to track changes and similarities between molecular sequences. In this paper the molecular sequence alignment problem is formulated suitable for an evolutionary algorithm (EA), and two problem instances are solved using generalized differential evolution 3 (GDE3), which is a general purpose EA. Regardless of relatively large number of decision variables, the instances were solvable and results were comparable to those by sequence alignment solvers in comparison