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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…
Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In…
Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the…
Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly…
Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing expensive black-box functions with multiple objectives. However, existing MOBO methods often struggle with coverage, scalability with respect to the…
We give an efficient algorithm to enumerate all elements of a Pareto front in a multi-objective optimization problem in which the space of values is finite for all objectives. Our algorithm uses a feasibility check for a search space…
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,…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and…
Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…
Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective…
A key task in multi-objective optimization is to compute the Pareto subset or frontier $P$ of a given $d$-dimensional objective space $F$; that is, a maximal subset $P\subseteq F$ such that every element in $P$ is not-dominated (it is not…
In the imprecise geometry model, the input is an imprecise point set, which is a family of regions $F = (R_1, \ldots,R_n)$, where for each $R_i$ one may retrieve the true point $p_i \in R_i$. By preprocessing $F$, we can construct the…
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…
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…
We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods.…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…