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This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum…
In multidisciplinary optimization the designer needs to find solution to optimization problems which include a number of usually contradicting criteria. Such a problem is mathematically related to the field of nonlinear vector optimization…
What is a systematic way to efficiently apply a wide spectrum of advanced ML programs to industrial scale problems, using Big Models (up to 100s of billions of parameters) on Big Data (up to terabytes or petabytes)? Modern parallelization…
A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is…
Stochastic Multi-Objective Optimization (SMOO) is critical for decision-making trading off multiple potentially conflicting objectives in uncertain environments. SMOO aims at identifying the Pareto frontier, which contains all mutually…
In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and…
Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…
Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is…
We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space…
Pareto set learning (PSL) is an emerging approach for acquiring the complete Pareto set of a multi-objective optimization problem. Existing methods primarily rely on the mapping of preference vectors in the objective space to Pareto optimal…
The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing…
In this paper, we tackle the problem of computing a sequence of rankings with the guarantee of the Pareto-optimal balance between (1) maximizing the utility of the consumers and (2) minimizing unfairness between producers of the items. Such…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
Many machine learning tasks aim to find models that work well not for a single, but for a group of criteria, often opposing ones. One such example is imbalanced data classification, where, on the one hand, we want to achieve the best…
Many problems in scientific and engineering applications contain sparse matrices or graphs as main input objects, e.g. numerical simulations on meshes. Large inputs are abundant these days and require parallel processing for memory size and…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
We consider the problem of quantifying the Pareto optimal boundary in the achievable rate region over multiple-input single-output (MISO) interference channels, where the problem boils down to solving a sequence of convex feasibility…