An application of the NSGA-II algorithm in Pareto joint inversion of 2D magnetic and gravity data

Joint inversion is a widely used geophysical method that allows model parameters to be obtained from the observed data. Pareto inversion results are a set of solutions that include the Pareto front, which consists of non-dominated solutions. All solutions from the Pareto front are considered the most feasible models from which a particular one can be chosen as the final solution. In this paper, it is shown that models represented by points on the Pareto front do not reflect the shape of the real model. In this contribution, a collective approach is proposed to interpret the geometry of models retrieved in inversion. Instead of choosing single solutions from the Pareto front, all obtained solutions were combined in one “heat map”, which is a plot representing the frequency of points belonging to all returned objects from the solution set. The conducted experiment showed that this approach limits the problem of equivalence and is a promising way of representing the geometry of the model that was retrieved in the inversion process

RIGA: A Regret-Based Interactive Genetic Algorithm

In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms

A fast efficient local search-based algorithm for multi-objective supply chain configuration problem

Supply chain configuration (SCC) plays an important role in supply chain management. This paper focuses on a multi-objective SCC (MOSCC) problem for minimizing both the cost of goods sold and the lead time simultaneously. Some existing population-based methods use the evolution of a population to obtain the optimal Pareto set, but they are time-consuming. In this paper, an Efficient Local Search-based algorithm with rank (ELSrank) is designed to solve the MOSCC problem. Firstly, instead of use of population, two solutions (xA and xB) are generated by the greedy strategy, which have the minimal cost and the minimal time, respectively. They approximately locate in two sides of the Pareto front (PF). Secondly, with the consideration of the problem characteristics, a local search (LS) is proposed to find competitive solutions among the common neighborhood of two given solutions. If xA and xB are chosen to execute the proposed LS, solutions along the link path (the approximate PF) of xA and xB can be found. This way, the solutions along the whole PF can be found. The comparative experiments are conducted on six instances from the real-life MOSCC problems, and the results show that ELSrank performs better than other start-of-the-art algorithms, especially on the large scale problem instances

A Maximum Satisfiability Based Approach to Bi-Objective Boolean Optimization

Many real-world problem settings give rise to NP-hard combinatorial optimization problems. This results in a need for non-trivial algorithmic approaches for finding optimal solutions to such problems. Many such approaches—ranging from probabilistic and meta-heuristic algorithms to declarative programming—have been presented for optimization problems with a single objective. Less work has been done on approaches for optimization problems with multiple objectives. We present BiOptSat, an exact declarative approach for finding so-called Pareto-optimal solutions to bi-objective optimization problems. A bi-objective optimization problem arises for example when learning interpretable classifiers and the size, as well as the classification error of the classifier should be taken into account as objectives. Using propositional logic as a declarative programming language, we seek to extend the progress and success in maximum satisfiability (MaxSAT) solving to two objectives. BiOptSat can be viewed as an instantiation of the lexicographic method and makes use of a single SAT solver that is preserved throughout the entire search procedure. It allows for solving three tasks for bi-objective optimization: finding a single Pareto-optimal solution, finding one representative solution for each Pareto point, and enumerating all Pareto-optimal solutions. We provide an open-source implementation of five variants of BiOptSat, building on different algorithms proposed for MaxSAT. Additionally, we empirically evaluate these five variants, comparing their runtime performance to that of three key competing algorithmic approaches. The empirical comparison in the contexts of learning interpretable decision rules and bi-objective set covering shows practical benefits of our approach. Furthermore, for the best-performing variant of BiOptSat, we study the effects of proposed refinements to determine their effectiveness

Energy aware hybrid flow shop scheduling

Only if humanity acts quickly and resolutely can we limit global warming' conclude more than 25,000 academics with the statement of SCIENTISTS FOR FUTURE. The concern about global warming and the extinction of species has steadily increased in recent years

Many-Objective Genetic Programming for Job-Shop Scheduling

The Job Shop Scheduling (JSS) problem is considered to be a challenging one due to practical requirements such as multiple objectives and the complexity of production flows. JSS has received great attention because of its broad applicability in real-world situations. One of the prominent solutions approaches to handling JSS problems is to design effective dispatching rules. Dispatching rules are investigated broadly in both academic and industrial environments because they are easy to implement (by computers and shop floor operators) with a low computational cost. However, the manual development of dispatching rules is time-consuming and requires expert knowledge of the scheduling environment. The hyper-heuristic approach that uses genetic programming (GP) to solve JSS problems is known as GP-based hyper-heuristic (GP-HH). GP-HH is a very useful approach for discovering dispatching rules automatically. Although it is technically simple to consider only a single objective optimization for JSS, it is now widely evidenced in the literature that JSS by nature presents several potentially conflicting objectives, including the maximal flowtime, mean flowtime, and mean tardiness. A few studies in the literature attempt to solve many-objective JSS with more than three objectives, but existing studies have some major limitations. First, many-objective JSS problems have been solved by multi-objective evolutionary algorithms (MOEAs). However, recent studies have suggested that the performance of conventional MOEAs is prone to the scalability challenge and degrades dramatically with many-objective optimization problems (MaOPs). Many-objective JSS using MOEAs inherit the same challenge as MaOPs. Thus, using MOEAs for many-objective JSS problems often fails to select quality dispatching rules. Second, although the reference points method is one of the most prominent and efficient methods for diversity maintenance in many-objective problems, it uses a uniform distribution of reference points which is only appropriate for a regular Pareto-front. However, JSS problems often have irregular Pareto-front and uniformly distributed reference points do not match well with the irregular Pareto-front. It results in many useless points during evolution. These useless points can significantly affect the performance of the reference points-based algorithms. They cannot help to enhance the solution diversity of evolved Pareto-front in many-objective JSS problems. Third, Pareto Local Search (PLS) is a prominent and effective local search method for handling multi-objective JSS optimization problems but the literature does not discover any existing studies which use PLS in GP-HH. To address these limitations, this thesis's overall goal is to develop GP-HH approaches to evolving effective rules to handle many conflicting objectives simultaneously in JSS problems. To achieve the first goal, this thesis proposes the first many-objective GP-HH method for JSS problems to find the Pareto-fronts of nondominated dispatching rules. Decision-makers can utilize this GP-HH method for selecting appropriate rules based on their preference over multiple conflicting objectives. This study combines GP with the fitness evaluation scheme of a many-objective reference points-based approach. The experimental results show that the proposed algorithm significantly outperforms MOEAs such as NSGA-II and SPEA2. To achieve the second goal, this thesis proposes two adaptive reference point approaches (model-free and model-driven). In both approaches, the reference points are generated according to the distribution of the evolved dispatching rules. The model-free reference point adaptation approach is inspired by Particle Swarm Optimization (PSO). The model-driven approach constructs the density model and estimates the density of solutions from each defined sub-location in a whole objective space. Furthermore, the model-driven approach provides smoothness to the model by applying a Gaussian Process model and calculating the area under the mean function. The mean function area helps to find the required number of the reference points in each mean function. The experimental results demonstrate that both adaptive approaches are significantly better than several state-of-the-art MOEAs. To achieve the third goal, the thesis proposes the first algorithm that combines GP as a global search with PLS as a local search in many-objective JSS. The proposed algorithm introduces an effective fitness-based selection strategy for selecting initial individuals for neighborhood exploration. It defines the GP's proper neighborhood structure and a new selection mechanism for selecting the effective dispatching rules during the local search. The experimental results on the JSS benchmark problem show that the newly proposed algorithm can significantly outperform its baseline algorithm (GP-NSGA-III)

Model-based symbolic design space exploration at the electronic system level: a systematic approach

In this thesis, a novel, fully systematic approach is proposed that addresses the automated design space exploration at the electronic system level. The problem is formulated as multi-objective optimization problem and is encoded symbolically using Answer Set Programming (ASP). Several specialized solvers are tightly coupled as background theories with the foreground ASP solver under the ASP modulo Theories (ASPmT) paradigm. By utilizing the ASPmT paradigm, the search is executed entirely systematically and the disparate synthesis steps can be coupled to explore the search space effectively.In dieser Arbeit wird ein vollständig systematischer Ansatz präsentiert, der sich mit der Entwurfsraumexploration auf der elektronischen Systemebene befasst. Das Problem wird als multikriterielles Optimierungsproblem formuliert und symbolisch mit Hilfe von Answer Set Programming (ASP) kodiert. Spezialisierte Solver sind im Rahmen des ASP modulo Theories (ASPmT) Paradigmas als Hintergrundtheorien eng mit dem ASP Solver gekoppelt. Durch die Verwendung von ASPmT wird die Suche systematisch ausgeführt und die individuellen Schritte können gekoppelt werden, um den Suchraum effektiv zu durchsuchen