Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

On the Effect of Connectedness for Biobjective Multiple and Long Path Problems

Recently, the property of connectedness has been claimed to give a strong motivation on the design of local search techniques for multiobjective combinatorial optimization (MOCO). Indeed, when connectedness holds, a basic Pareto local search, initialized with at least one non-dominated solution, allows to identify the efficient set exhaustively. However, this becomes quickly infeasible in practice as the number of efficient solutions typically grows exponentially with the instance size. As a consequence, we generally have to deal with a limited-size approximation, where a good sample set has to be found. In this paper, we propose the biobjective multiple and long path problems to show experimentally that, on the first problems, even if the efficient set is connected, a local search may be outperformed by a simple evolutionary algorithm in the sampling of the efficient set. At the opposite, on the second problems, a local search algorithm may successfully approximate a disconnected efficient set. Then, we argue that connectedness is not the single property to study for the design of local search heuristics for MOCO. This work opens new discussions on a proper definition of the multiobjective fitness landscape.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Dominance Based Crossover Operator for Evolutionary Multi-objective Algorithms

In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates - but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems

Using Comparative Preference Statements in Hypervolume-Based Interactive Multiobjective Optimization

International audienceThe objective functions in multiobjective optimization problems are often non-linear, noisy, or not available in a closed form and evolutionary multiobjective optimization (EMO) algorithms have been shown to be well applicable in this case. Here, our objective is to facilitate interactive decision making by saving function evaluations outside the "interesting" regions of the search space within a hypervolume-based EMO algorithm. We focus on a basic model where the Decision Maker (DM) is always asked to pick the most desirable solution among a set. In addition to the scenario where this solution is chosen directly, we present the alternative to specify preferences via a set of so-called comparative preference statements. Examples on standard test problems show the working principles, the competitiveness, and the drawbacks of the proposed algorithm in comparison with the recent iTDEA algorithm

Optimizing the DFCN Broadcast Protocol with a Parallel Cooperative Strategy of Multi-Objective Evolutionary Algorithms

Proceeding of: 5th International Conference, EMO 2009, Nantes, France, April 7-10, 2009This work presents the application of a parallel coopera- tive optimization approach to the broadcast operation in mobile ad-hoc networks (manets). The optimization of the broadcast operation im- plies satisfying several objectives simultaneously, so a multi-objective approach has been designed. The optimization lies on searching the best configurations of the dfcn broadcast protocol for a given manet sce- nario. The cooperation of a team of multi-objective evolutionary al- gorithms has been performed with a novel optimization model. Such model is a hybrid parallel algorithm that combines a parallel island- based scheme with a hyperheuristic approach. Results achieved by the algorithms in different stages of the search process are analyzed in order to grant more computational resources to the most suitable algorithms. The obtained results for a manets scenario, representing a mall, demon- strate the validity of the new proposed approach.This work has been supported by the ec (feder) and the Spanish Ministry of Education and Science inside the ‘Plan Nacional de i+d+i’ (tin2005-08818-c04) and (tin2008-06491-c04-02). The work of Gara Miranda has been developed under grant fpu-ap2004-2290.Publicad

A practical case of the multiobjective knapsack problem: Design, modelling, tests and analysis

In this paper, we present a practical case of the multiobjective knapsack problem which concerns the elaboration of the optimal action plan in the social and medico-social sector. We provide a description and a formal model of the problem as well as some preliminary computational results. We perform an empirical analysis of the behavior of three metaheuristic approaches: a fast and elitist multiobjective genetic algorithm (NSGA-II), a Pareto Local Search (PLS) algorithm and an Indicator-Based Multi-Objective Local Search (IBMOLS)

ParadisEO-MOEO: A Software Framework for Evolutionary Multi-Objective Optimization

This chapter presents ParadisEO-MOEO, a white-box object-oriented software framework dedicated to the flexible design of metaheuristics for multi-objective optimization. This paradigm-free software proposes a unified view for major evolutionary multi-objective metaheuristics. It embeds some features and techniques for multi-objective resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the problems they are intended to solve. This separation confers a maximum design and code reuse. This general-purpose framework provides a broad range of fitness assignment strategies, the most common diversity preservation mechanisms, some elitistrelated features as well as statistical tools. Furthermore, a number of state-of-the-art search methods, including NSGA-II, SPEA2 and IBEA, have been implemented in a user-friendly way, based on the fine-grained ParadisEO-MOEO components

Experiments on local search for bi-objective unconstrained binary quadratic programming

International audienceThis article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation coefficients, and is addressed by means of a state-of-the-art single-objective tabu search procedure. Next, we design a Pareto local search that iteratively improves a set of solutions based on a neighborhood structure and on the Pareto dominance relation. At last, we hybridize both classes of algorithms by combining a scalarizing and a Pareto local search in a sequential way. A comprehensive experimental analysis reveals the high performance of the proposed approaches, which substantially improve upon previous best-known solutions. Moreover, the obtained results show the superiority of the hybrid algorithm over non-hybrid ones in terms of solution quality, while requiring a competitive computational cost. In addition, a number of structural properties of the problem instances allow us to explain the main difficulties that the different classes of local search algorithms have to face

Evolutionary Multi-Objective Design of SARS-CoV-2 Protease Inhibitor Candidates

Computational drug design based on artificial intelligence is an emerging research area. At the time of writing this paper, the world suffers from an outbreak of the coronavirus SARS-CoV-2. A promising way to stop the virus replication is via protease inhibition. We propose an evolutionary multi-objective algorithm (EMOA) to design potential protease inhibitors for SARS-CoV-2's main protease. Based on the SELFIES representation the EMOA maximizes the binding of candidate ligands to the protein using the docking tool QuickVina 2, while at the same time taking into account further objectives like drug-likeliness or the fulfillment of filter constraints. The experimental part analyzes the evolutionary process and discusses the inhibitor candidates.Comment: 15 pages, 7 figures, submitted to PPSN 202