Recommending for a Multi-Sided Marketplace: A Multi-Objective Hierarchical Approach

This thesis aims at developing efficient mathematical methods for solving hierarchical dynamic optimization problems. The main motivation is to model processes in nature, for which there is evidence to assume that they run optimally. We describe models of such processes by optimal control problems (called optimal control models (OCMs)). However, an OCM typically includes unknown parameters that cannot be derived entirely on a theoretical basis, which is in particular the case for the cost function. Therefore, we develop parameter estimation techniques to estimate the unknowns in an OCM from observation data of the process. Mathematically, this leads to a hierarchical dynamic optimization problem with a parameter estimation problem on the upper level and an optimal control problem on the lower level. We focus on multi-stage equality and inequality constrained optimal control problems based on nonlinear ordinary differential equations. The main goal of this thesis is to derive numerically efficient mathematical methods for solving hierarchical dynamic optimization problems, and to use these methods to estimate parameters in high-dimensional OCMs from real-world measurement data. We develop parameter-dependent OCMs for the gait of cerebral palsy patients and able-bodied subjects. The unknown parameters in the OCMs are then estimated from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg by using the mathematical methods developed within this work. The main novelties and contributions of this thesis to the field of hierarchical dynamic optimization are summarized herein. - We establish a novel mathematical method, a so-called direct all-at-once approach, for solving hierarchical dynamic optimization problems based on the direct multiple shooting method and first-order optimality conditions. - Furthermore, we propose an efficient numerical algorithm for large-scale hierarchical dynamic optimization problems, which fully exploits the structures inherited from both the hierarchical setting and the discretization. - Pontryagin's maximum principle is used to analyze solution properties of hierarchical dynamic optimization problems like second-order optimality conditions of the lower-level problem. - In addition, we propose and discuss alternative methods for hierarchical dynamic optimization that are based on derivative-free optimization and a bundle approach. These methods keep the hierarchical problem setting and do not reformulate the lower-level problem using first-order optimality conditions. - We establish a novel lifting method for regularizing mathematical programs with complementarity constraints, which is discussed and numerically investigated by means of a well-known collection of benchmark problems. - Proofs of regularity and convergence results for sequential quadratic programming methods applied to lifted mathematical programs with complementarity constraints are provided. - Efficient state-of-the-art implementations of all mathematical methods derived in this thesis, as well as a benchmark collection of hierarchical dynamic optimization problems are presented. - High-dimensional optimal control gait models for cerebral palsy patients and able-bodied subjects are developed. The mathematical methods derived in this thesis are used to estimate the unknown model parameters from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg. The theoretical and practical results presented in this thesis can be considered an initial motivating step towards answering open questions in current medical research in fields like treatment planning, classification of gaits, or the evaluation of surgeries by means of hierarchical dynamic optimization.

A multi-objective evolutionary approach for the electric vehicle charging stations problem

The emergence of Online-to-Offline (O2O) stores based on delivery platforms (e.g., Uber Eats, DoorDash, and Eleme) provides great convenience to people's lives. In the O2O model, one of the essential problems for merchants is to select a suitable store site, i.e., store site recommendation problem. We argue that the existing works for the traditional brick-and-mortar stores cannot address this problem due to two unique factors in the O2O model including (i) dynamic supply caused by courier capacity and dispatching strategies and (ii) various customer demands caused by delivery distance and customer preferences. To incorporate these new factors, we design <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O^{2}$</tex> SiteRec, a store site recommendation method under the O2O model via multi-graph attention networks, which consists of (i) a courier capacity model based on a multi-semantic relation graph attention network to capture courier capacity; (ii) a heterogeneous multi-graph based recommendation model, where the courier capacity, customer preferences, and context features are fused. We evaluate our method based on one-month real-world data consisting of 39,465 stores and 23.6 million orders from one of the largest O2O platforms in China. Experimental results demonstrate that our method outperforms state-of-the-art baselines in various metrics.

In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behaviorism, combined with the decomposition of the solutions pace was tested on a set of standard multi-objective optimization problems and on a simple but representative case of space trajectory design.

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

Classification is important task of data mining used to extract knowledge from huge volume of data. By nature, classification is multi-objective problem, as it required optimization of multiple objectives simultaneously like accuracy, sensitivity, squared error, precision etc. Traditionally, evolutionary algorithms were used to solve multi-objective classification problem by considering it as single-objective problem, but this approach gives single solution to problem. Therefore, multi-objective evolutionary algorithms are used to solve classification problem. In this paper, we have used Pareto approach to optimize neural network to solve classification problem. Non-dominated sorting genetic algorithm is used to simultaneously optimize accuracy and mean squared error objectives of neural network along with local search. As slow convergence to optimal solutions is major disadvantage of evolutionary algorithm. To speed up convergence to optimal solutions hybrid technique is adopted by augmenting evolutionary technique with local search algorithm. This proposed approach gives set of Pareto optimal solutions which represent different solutions for given classification problem.

This paper addresses the design of a PI controller as a multiobjective problem. For a given plant the design of a PI controller satisfies a given set of specifications and for acceptable design the parameters of the PI controller are to be adjusted so that whole closed loop system satisfies the specifications. A multiobjective optimization approach is implemented here to adjust the parameters of the PI controller and since the design presented here is multiobjective, hence for acceptable design some tradeoff is made among the specifications given. Since the robustness and the performance is not guaranteed both at the same time, due to this reason only some tradeoff is necessary and this paper addresses the contradiction between robustness and performance of PI controller by framing it into a multiobjective optimization problem. The simulation of multiobjective problem generates the Pareto front from which on can make the compromise between performance and robustness. The simulation results derived from the above said approach is applicable for large number of systems.

• First dominance-based multi-objective optimization approach for bias mitigation. • First swarm intelligence approach, also including other interesting techniques. • Study of six real-life scenarios, considering different vital aspects and bias types. • High mitigation of bias, improving fairness and also the original model’s accuracy. • Results surpassing those from other authors’ approaches with remarkable improvements. At present, many decisions, even decisions that affect people’s lives, are increasingly made by decision-making software. For this reason, it is really important to avoid decision-making software being biased, that is, it needs to assure fairness. As decision-making software is generally based on classification models, its bias can be mitigated in three different stages: pre-processing, in-processing, and post-processing. However, despite the importance of fairness on these models, there are very few proposals for the post-processing stage that are able to mitigate bias without reducing the original model’s accuracy. Therefore, this problem should be addressed as a multi-objective problem, optimizing at the same time both fairness and accuracy. Taking this into account, we propose a Multi-Objective Swarm Intelligence approach for BIas Mitigation (MOSIBIM), which combines dominance-based multi-objective optimization (with techniques such as Pareto fronts, niching, and reference points), population-based evolutionary computation, swarm intelligence, and convergence-stagnation differentiation. In order to analyze the improvements that this proposal produces over other approaches in the literature, its results on fairness and accuracy have been compared with the results obtained by other five approaches, optimizing different classification models and in six distinct real-life scenarios which have various types of bias. The results of MOSIBIM show great improvements on fairness in comparison with the other approaches, as it reaches improvement percentages of 91.7 % and, on average, the results are always in the range of 66.6 % to 76.6 % of improvement. Furthermore, the proposed approach has been able to improve the original model’s accuracy in all the studied cases.

To achieve global optimum of product performance, costs and benefits in temperature setting, this article proposes a three - layer hierarchical optimal setting approach for RHFTF's production indexes to get its temperature control model. Layer one uses BFGMMC algorithm to optimize slab settings. Layer two combines T2FRI method for the optimal curve and IKHCD algorithm for missing info between interpolation points. Layer three applies KFCRM algorithm to boost the model's anti interference. The study shows the method enhances model accuracy, optimizes control strategy and meets technical requirements.

The Redundancy Allocation Problem (RAP) is a kind of reliability optimization problems. It involves the selection of components with appropriate levels of redundancy or reliability to maximize the system reliability under some predefined constraints. We can formulate the RAP as a combinatorial problem when just considering the redundancy level, while as a continuous problem when considering the reliability level. The RAP employed in this paper is that kind of combinatorial optimization problems. During the past thirty years, there have already been a number of investigations on RAP. However, these investigations often treat RAP as a single objective problem with the only goal to maximize the system reliability (or minimize the designing cost). In this paper, we regard RAP as a multi-objective optimization problem: the reliability of the system and the corresponding designing cost are considered as two different objectives. Consequently, we can utilize a classical Multi-objective Evolutionary Algorithm (MOEA), named Non-dominated Sorting Genetic Algorithm II (NSGA-II), to cope with this multi-objective redundancy allocation problem (MORAP) under a number of constraints. The experimental results demonstrate that the multi-objective evolutionary approach can provide more promising solutions in comparison with two widely used single-objective approaches on two parallel-series systems which are frequently studied in the field of reliability optimization.

Recent research activity has shown an interest in multi-objective optimization of dynamic processes, both for design and for real-time control; see Liu et al. (2018), Valderrama & Ruiz (2018), and de Sousa Santos et al. (2018) for some recent examples. Many of the methods proposed for these problems are based on converting the multi-objective problem into a single objective through the use of weights. Some works, for instance, Liu et al. (2018), however, consider the multi-objective problem directly but even in these cases, the problem is treated as a single objective problem with other objectives incorporated as constraints. All of these methods may not necessarily generate a satisfactory trade-off or Pareto optimal curve when this trade-off curve is non-convex. In this paper, we illustrate the use of a plant propagation nature inspired algorithm for the solution of design and control problems for dynamic processes. Being population based, it is able to identify an approximation to the Pareto optimal frontier simultaneously. A simple example from the literature is used to demonstrate how this problem can be formulated. The open source, freely available, Fresa application (http://www.ucl.ac.uk/~ucecesf/fresa.html),written in Julia, is used and the discussion concentrates on the problem formulation. The result shows how a multi-objective approach may lead to better insight into the design or control issues. The illustrated problem was originally formulated as a single objective problem. In doing so, information about alternative designs and how these could affect the performance of the system may be hidden. A multi-objective formulation allows the engineer to make better informed design decisions.

An interactive heuristic method for multi-objective combinatorial optimization

In this paper, we propose an improved ideal point setting method in the framework of MOEA/D. MOEA/D decomposes a multi-objective optimisation problem into a number of scalar optimisation problems and optimise them simultaneously. The performance of MOEA/D is highly relate to its decomposition method, and the proposed ideal point setting approach is used in the weighted Tchebycheff (TCH) and penalty-based boundary intersection (PBI) decomposition approach. It expands the region of search in the objective space by transforming the original ideal point into its symmetric point and changes the search direction of each subproblems in MOEA/D. In order to address the proposed ideal point setting method, we design a set of multi-objective problems(MOPs). The proposed method is compared with original MOEA/D-TCH and MOEA/D-PBI on MOPs. The experimental results demonstrate that our proposed ideal point setting method is very effective in terms of both diversity and convergence.

Towards a sustainable power grid: Stochastic hierarchical planning for high renewable integration

An ɛ-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem