Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints

• URL: http://arxiv.org/abs/2401.00978v1
• Date: Tue, 2 Jan 2024 00:38:20 GMT
• Title: Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints
• Authors: Shuang Li, Ke Li, Wei Li, Ming Yang
• Abstract summary: Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. We present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. Our framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population.
• Score: 17.392113376816788
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation has been a building block in designing evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making constraint violation unattainable and potentially misleading for conventional constrained evolutionary multi-objective optimization algorithms. To address this issue, we present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. This framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population. Notably, these two populations operate towards complementary evolutionary directions during their optimization processes. In order to minimize discrepancy, their evolutionary directions alternate, aiding the discovery of feasible solutions. Comparative experiments conducted against five state-of-the-art constrained evolutionary multi-objective optimization algorithms, on 120 benchmark test problem instances with varying properties, as well as two real-world engineering optimization problems, demonstrate the effectiveness and superiority of our proposed framework. Its salient features include faster convergence and enhanced resilience to various Pareto front shapes.

Related papers

• Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learning [132.7040981721302]
  We study the Constrained Convex Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure. Design algorithms for a constrained convex MDP faces several challenges, including handling the large state space.
  arXiv  Detail & Related papers  (2024-02-16T16:35:18Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Evolutionary Solution Adaption for Multi-Objective Metal Cutting Process Optimization [59.45414406974091]
  We introduce a framework for system flexibility that allows us to study the ability of an algorithm to transfer solutions from previous optimization tasks. We study the flexibility of NSGA-II, which we extend by two variants: 1) varying goals, that optimize solutions for two tasks simultaneously to obtain in-between source solutions expected to be more adaptable, and 2) active-inactive genotype, that accommodates different possibilities that can be activated or deactivated. Results show that adaption with standard NSGA-II greatly reduces the number of evaluations required for optimization to a target goal, while the proposed variants further improve the adaption costs.
  arXiv  Detail & Related papers  (2023-05-31T12:07:50Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Do We Really Need to Use Constraint Violation in Constrained Evolutionary Multi-Objective Optimization? [13.833668582211876]
  Constraint violation has been a building block to design evolutionary multi-objective optimization algorithms. This paper develops the corresponding variants that replace the constraint violation by a crisp value. From our experiments on both synthetic and real-world benchmark test problems, we find that the performance of the selected algorithms have not been significantly influenced.
  arXiv  Detail & Related papers  (2022-05-28T06:29:07Z)
• A novel multiobjective evolutionary algorithm based on decomposition and multi-reference points strategy [14.102326122777475]
  Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been regarded as a significantly promising approach for solving multiobjective optimization problems (MOPs) We propose an improved MOEA/D algorithm by virtue of the well-known Pascoletti-Serafini scalarization method and a new strategy of multi-reference points.
  arXiv  Detail & Related papers  (2021-10-27T02:07:08Z)
• On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems [99.59934203759754]
  We introduce a class of first-order methods for smooth constrained optimization. Two distinctive features of our approach are that projections or optimizations over the entire feasible set are avoided. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear.
  arXiv  Detail & Related papers  (2021-07-17T11:45:13Z)
• An Improved Two-Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization [5.760976250387322]
  A recently proposed two-archive evolutionary algorithm for constrained multi-objective optimization (C-TAEA) has be shown as a latest algorithm. We propose an improved version C-TAEA, dubbed C-TAEA-II, featuring an improved update mechanism of two co-evolving archives and an adaptive mating selection mechanism.
  arXiv  Detail & Related papers  (2021-03-10T23:04:02Z)
• Enhanced Innovized Repair Operator for Evolutionary Multi- and Many-objective Optimization [5.885238773559015]
  "Innovization" is a task of learning common relationships among some or all of the Pareto-optimal (PO) solutions in optimisation problems. Recent studies have shown that a chronological sequence of non-dominated solutions also possess salient patterns that can be used to learn problem features. We propose a machine-learning- (ML-) assisted modelling approach that learns the modifications in design variables needed to advance population members towards the Pareto-optimal set.
  arXiv  Detail & Related papers  (2020-11-21T10:29:15Z)
• Application of Compromising Evolution in Multi-objective Image Error Concealment [0.0]
  The Compromising Evolution Method is proposed to modify the Simple Genetic Algorithm by utilizing the notion of compromise. The simulation results show the power of the proposed method solving multi-objective optimizations in a case study of image error concealment.
  arXiv  Detail & Related papers  (2020-11-11T15:22:23Z)
• EOS: a Parallel, Self-Adaptive, Multi-Population Evolutionary Algorithm for Constrained Global Optimization [68.8204255655161]
  EOS is a global optimization algorithm for constrained and unconstrained problems of real-valued variables. It implements a number of improvements to the well-known Differential Evolution (DE) algorithm. Results prove that EOSis capable of achieving increased performance compared to state-of-the-art single-population self-adaptive DE algorithms.
  arXiv  Detail & Related papers  (2020-07-09T10:19:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.