A benchmark test problem toolkit for multi-objective path optimization

Due to the complexity of multi-objective optimization problems (MOOPs) in general, it is crucial to test MOOP methods on some benchmark test problems. Many benchmark test problem toolkits have been developed for continuous parameter/numerical optimization, but fewer toolkits reported for discrete combinational optimization. This paper reports a benchmark test problem toolkit especially for multi-objective path optimization problem (MOPOP), which is a typical category of discrete combinational optimization. With the reported toolkit, the complete Pareto front of a generated test problem of MOPOP can be deduced and found out manually, and the problem scale and complexity are controllable and adjustable. Many methods for discrete combinational MOOPs often only output a partial or approximated Pareto front. With the reported benchmark test problem toolkit for MOPOP, we can now precisely tell how many true Pareto points are missed by a partial Pareto front, or how large the gap is between an approximated Pareto front and the complete one

Interactive Camera Network Design using a Virtual Reality Interface

Traditional literature on camera network design focuses on constructing automated algorithms. These require problem specific input from experts in order to produce their output. The nature of the required input is highly unintuitive leading to an unpractical workflow for human operators. In this work we focus on developing a virtual reality user interface allowing human operators to manually design camera networks in an intuitive manner. From real world practical examples we conclude that the camera networks designed using this interface are highly competitive with, or superior to those generated by automated algorithms, but the associated workflow is much more intuitive and simple. The competitiveness of the human-generated camera networks is remarkable because the structure of the optimization problem is a well known combinatorial NP-hard problem. These results indicate that human operators can be used in challenging geometrical combinatorial optimization problems given an intuitive visualization of the problem.Comment: 11 pages, 8 figure

Scalable and customizable benchmark problems for many-objective optimization

Solving many-objective problems (MaOPs) is still a significant challenge in the multi-objective optimization (MOO) field. One way to measure algorithm performance is through the use of benchmark functions (also called test functions or test suites), which are artificial problems with a well-defined mathematical formulation, known solutions and a variety of features and difficulties. In this paper we propose a parameterized generator of scalable and customizable benchmark problems for MaOPs. It is able to generate problems that reproduce features present in other benchmarks and also problems with some new features. We propose here the concept of generative benchmarking, in which one can generate an infinite number of MOO problems, by varying parameters that control specific features that the problem should have: scalability in the number of variables and objectives, bias, deceptiveness, multimodality, robust and non-robust solutions, shape of the Pareto front, and constraints. The proposed Generalized Position-Distance (GPD) tunable benchmark generator uses the position-distance paradigm, a basic approach to building test functions, used in other benchmarks such as Deb, Thiele, Laumanns and Zitzler (DTLZ), Walking Fish Group (WFG) and others. It includes scalable problems in any number of variables and objectives and it presents Pareto fronts with different characteristics. The resulting functions are easy to understand and visualize, easy to implement, fast to compute and their Pareto optimal solutions are known.This work has been supported by the Brazilian agencies (i) National Council for Scientific and Technological Development (CNPq); (ii) Coordination for the Improvement of Higher Education (CAPES) and (iii) Foundation for Research of the State of Minas Gerais (FAPEMIG, in Portuguese)