Pareto Local Search Algorithm Research Articles

A column generation-based algorithm for gate assignment problem with combinational gates

The gate assignment is a complicated real-world problem occurring in airports. The present paper studies the gate assignment problem with combinational gates. The problem is multi-objective by nature, concerning four objectives. Among those objectives, the number of passengers allocated to nearby gates is aimed to be maximized. The remaining objectives are targeted to be minimized, i.e., the total passenger walking distance, the amount of carbon dioxide emitted by the aircraft assigned to remote gates, and the total distance traveled by the shuttle bus. To solve this problem, we formulate an integer programming model. A column generation-based algorithm based on a set-partitioning model is proposed to solve the problem effectively. In addition, the Pareto Local Search algorithm is adopted to obtain non-dominated solutions. Computational experiments show that the effectiveness of our model is verified through tests with instances of different sizes. The column generation-based algorithm can obtain the optimal solution or the approximately optimal solution with a small gap in a reasonable time. The results of the Pareto Local Search algorithm show the interaction between multiple objectives.

An improved Pareto local search for solving bi-objective scheduling problems in hot rolling mills

Hot rolling scheduling is a complex decision-making optimization problem in the production management of the iron and steel industry. Comprehensively considering temporal and technical constraints of hot rolling production, we formulate a prize-collecting capacitated vehicle routing problem with time windows (PC-CVRPTW) involving special constraints and multiple objectives. Furthermore, this paper develops a Pareto local search (PLS)-based solving algorithm via leveraging problem-specific properties and implements three improvement mechanisms: (1) solution initialization with a greedy strategy; (2) promising solution selection with optimistic hypervolume contribution; (3) hybrid neighborhood exploration integrated variable neighborhood search with constraint programming. To validate the proposed method, computational experiments are conducted on a set of randomly synthetic and realistic industrial instances. The results compared with other variants of PLS and state-of-art algorithms demonstrate that the improved PLS algorithm is effective and can provide promising solutions for bi-objective hot rolling scheduling problems.

Hybrid Multi-Objective Optimization Approach With Pareto Local Search for Collaborative Truck-Drone Routing Problems Considering Flexible Time Windows

The collaboration of drones and trucks for last-mile delivery has attracted much attention. In this paper, we address a collaborative routing problem of the truck-drone system, in which a truck collaborates with multiple drones to perform parcel deliveries and each customer can be served earlier and later than the required time with a given tolerance. To meet the practical demands of logistics companies, we build a multi-objective optimization model that minimizes total distribution cost and maximizes overall customer satisfaction simultaneously. We propose a hybrid multi-objective genetic optimization approach incorporated with a Pareto local search algorithm to solve the problem. Particularly, we develop a greedy-based heuristic method to create initial solutions and introduce a problem-specific solution representation, genetic operations, as well as six heuristic neighborhood strategies for the hybrid algorithm. Besides, an adaptive strategy is adopted to further balance the convergence and the diversity of the hybrid algorithm. The performance of the proposed algorithm is evaluated by using a set of benchmark instances. The experimental results show that the proposed algorithm outperforms three competitors. Furthermore, we investigate the sensitivity of the proposed model and hybrid algorithm based on a real-world case in Changsha city, China.

Many-Objective Pareto Local Search

We propose a new Pareto Local Search Algorithm for the many-objective combinatorial optimization. Pareto Local Search proved to be a very effective tool in the case of the bi-objective combinatorial optimization and it was used in a number of the state-of-the-art algorithms for problems of this kind. On the other hand, the standard Pareto Local Search algorithm becomes very inefficient for problems with more than two objectives. We build an effective Many-Objective Pareto Local Search algorithm using three new mechanisms: the efficient update of large Pareto archives with ND-Tree data structure, a new mechanism for the selection of the promising solutions for the neighborhood exploration, and a partial exploration of the neighborhoods. We apply the proposed algorithm to the instances of two different problems, i.e. the traveling salesperson problem and the traveling salesperson problem with profits with up to 5 objectives showing high effectiveness of the proposed algorithm.

Pareto local search algorithms for the multi-objective beam angle optimisation problem

Due to inherent trade-offs between tumour control and sparing of organs at risk, optimisation problems arising in intensity modulated radiation therapy planning are naturally modelled as multi-objective optimisation problems. Nevertheless, the vast majority of studies in the literature consider single objective approaches to these problems. The beam angle optimisation problem, that we address ion this paper, is one of these problems. It attempts to identify “good” beam angle configurations that allow the delivery of efficient treatment plans. In this paper two bi-objective local search algorithms are developed for the bi-objective beam angle optimisation problem, namely Pareto local search (PLS) and a variation of PLS we call adaptive PLS (aPLS). Both algorithms are able to find a set of (approximately) efficient beam angle configurations. While the PLS algorithm aims to find a set of efficient BACs by performing a very focused search over a specific region of the objective space, the aPLS algorithm aims to produce a set of efficient BACs that are well-distributed over the objective space. We test both algorithms on two prostate cancer cases and compare them to our previously proposed single objective local search algorithm.

A Two-Phase Complete Algorithm for Multi-Objective Distributed Constraint Optimization

A Distributed Constraint Optimization Problem (DCOP) is a fundamental problem that can formalize various applications related to multi-agent cooperation. Many application problems in multi-agent systems can be formalized as DCOPs. However, many real world optimization problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) is an extension of a mono-objective DCOP. Compared to DCOPs, there exists few works on MO-DCOPs. In this paper, we develop a novel complete algorithm for solving an MO-DCOP. This algorithm utilizes a widely used method called Pareto Local Search (PLS) to generate an approximation of the Pareto front. Then, the obtained information is used to guide the search thresholds in a Branch and Bound algorithm. In the evaluations, we evaluate the runtime of our algorithm and show empirically that using a Pareto front approximation obtained by a PLS algorithm allows to significantly speed-up the search in a Branch and Bound algorithm.

On the Biobjective Adjacent Only Quadratic Spanning Tree Problem

Abstract The adjacent only quadratic minimum spanning tree problem is an NP-hard version of the minimum spanning tree where the costs of interaction effects between every pair of adjacent edges are included in the objective function. This paper addresses the biobjective version of this problem. A Pareto local search algorithm is proposed. The algorithm is applied to a set of 108 benchmark instances. The results are compared to the optimal Pareto front generated by a branch and bound algorithm, which is a multiobjective adaptation of a well known algorithm for the mono-objective case.

Stochastic Pareto local search: Pareto neighbourhood exploration and perturbation strategies

Pareto local search (PLS) methods are local search algorithms for multi-objective combinatorial optimization problems based on the Pareto dominance criterion. PLS explores the Pareto neighbourhood of a set of non-dominated solutions until it reaches a local optimal Pareto front. In this paper, we discuss and analyse three different Pareto neighbourhood exploration strategies: best, first, and neutral improvement. Furthermore, we introduce a deactivation mechanism that restarts PLS from an archive of solutions rather than from a single solution in order to avoid the exploration of already explored regions. To escape from a local optimal solution set we apply stochastic perturbation strategies, leading to stochastic Pareto local search algorithms (SPLS). We consider two perturbation strategies: mutation and path-guided mutation. While the former is unbiased, the latter is biased towards preserving common substructures between 2 solutions. We apply SPLS on a set of large, correlated bi-objective quadratic assignment problems (bQAPs) and observe that SPLS significantly outperforms multi-start PLS. We investigate the reason of this performance gain by studying the fitness landscape structure of the bQAPs using random walks. The best performing method uses the stochastic perturbation algorithms, the first improvement Pareto neigborhood exploration and the deactivation technique.