Ngoc Hoang Luong

Multi-objective gene-pool optimal mixing evolutionary algorithms

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), with a lean, but sufficient, linkage model and an efficient variation operator, has been shown to be a robust and efficient methodology for solving single objective (SO) optimization problems with superior performance compared to classic genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). In this paper, we bring the strengths of GOMEAs to the multi-objective (MO) optimization realm. To this end, we modify the linkage learning procedure and the variation operator of GOMEAs to better suit the need of finding the whole Pareto-optimal front rather than a single best solution. Based on state-of-the-art studies on MOEAs, we further pinpoint and incorporate two other essential components for a scalable MO optimizer. First, the use of an elitist archive is beneficial for keeping track of non-dominated solutions when the main population size is limited. Second, clustering can be crucial if different parts of the Pareto-optimal front need to be handled differently. By combining these elements, we construct a multi-objective GOMEA (MO-GOMEA). Experimental results on various MO optimization problems confirm the capability and scalability of our MO-GOMEA that compare favorably with those of the well-known GA NSGA-II and the more recently introduced EDA mohBOA.

The multi-objective real-valued gene-pool optimal mixing evolutionary algorithm

The recently introduced Multi-Objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) exhibits excellent scalability in solving a wide range of challenging discrete multi-objective optimization problems. In this paper, we address scalability issues in solving multi-objective optimization problems with continuous variables by introducing the Multi-Objective Real-Valued GOMEA (MO-RV-GOMEA), which combines MO-GOMEA with aspects of the multi-objective estimation-of-distribution algorithm known as MAMaLGaM. MO-RV-GOMEA exploits linkage structure in optimization problems by performing distribution estimation, adaptation, and sampling as well as solution mixing based on an explicitly-defined linkage model. Such a linkage model can be defined a priori when some problem-specific knowledge is available, or it can be learned from the population. The scalability of MO-RV-GOMEA using different linkage models is compared to the state-of-the-art multi-objective evolutionary algorithms NSGA-II and MAMaLGaM on a wide range of benchmark problems. MO-RV-GOMEA is found to retain the excellent scalability of MO-GOMEA through the successful exploitation of linkage structure, scaling substantially better than NSGA-II and MAMaLGaM. This scalability is even further improved when partial evaluations are possible, achieving strongly sub-linear scalability in terms of the number of evaluations.

Scalable and practical multi-objective distribution network expansion planning

We formulate the distribution network expansion planning (DNEP) problem as a multi-objective optimization (MOO) problem with different objectives that distribution network operators (DNOs) would typically like to consider during decision making processes for expanding their networks. Objectives are investment cost, energy loss, total cost, and reliability in terms of the number of customer minutes lost per year. We consider two solvers: the widely-used Non-dominated Sorting Genetic Algorithm NSGA-II and the recently-developed Multiobjective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA). We also develop a scheme to get rid of the notoriously difficult-to-set population size parameter so that these solvers can more easily be used by non-specialists. Experiments are conducted on medium-voltage distribution networks constructed from real data. The results confirm that the MOGOMEA, with the scheme that removes the population size parameter, is a robust and user-friendly MOO solver that can be used by DNOs when solving DNEP.

Application and benchmarking of multi-objective evolutionary algorithms on high-dose-rate brachytherapy planning for prostate cancer treatment

Abstract High-Dose-Rate (HDR) brachytherapy (BT) treatment planning involves determining an appropriate schedule of a radiation source moving through a patients body such that target volumes are irradiated with the planning-aim dose as much as possible while healthy tissues (i.e., organs at risk) should not be irradiated more than certain thresholds. Such movement of a radiation source can be defined by so-called dwell times at hundreds of potential dwell positions, which must be configured to satisfy a clinical protocol of multiple different treatment criteria within a strictly-limited time frame of not more than one hour. In this article, we propose a bi-objective optimization model that intuitively encapsulates in two objectives the complicated high-dimensional multi-criteria nature of the BT treatment planning problem. The resulting Pareto-optimal fronts exhibit possible trade-offs between the coverage of target volumes and the sparing of organs at risk, thereby intuitively facilitating the decision-making process of treatment planners when creating a clinically-acceptable plan. We employ real medical data for conducting experiments and benchmark four different Multi-Objective Evolutionary Algorithms (MOEAs) on solving our problem: the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), the Multi-objective Adapted Maximum-Likelihood Gaussian Model Iterated Density-Estimation Evolutionary Algorithm (MAMaLGaM), and the recently-introduced Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The variation operator that is specific to MO-RV-GOMEA enables performing partial evaluations to efficiently calculate objective values of offspring solutions without incurring the cost of fully recomputing the radiation dose distributions for new treatment plans. Experimental results show that MO-RV-GOMEA is the best performing MOEA that effectively exploits dependencies between decision variables to efficiently solve the multi-objective BT treatment planning problem.

Expanding from Discrete Cartesian to Permutation Gene-pool Optimal Mixing Evolutionary Algorithms

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which includes the Linkage Tree Genetic Algorithm (LTGA), has been shown to scale excellently on a variety of discrete, Cartesian-space, optimization problems. This paper shows that GOMEA can quite straightforwardly also be used to solve permutation optimization problems by employing the random keys encoding of permutations. As a test problem, we consider permutation flowshop scheduling, minimizing the total flow time on 120 different problem instances (Taillard benchmark). The performance of GOMEA is compared with the recently published generalized Mallows estimation of distribution algorithm (GM-EDA). Statistical tests show that results of GOMEA variants are almost always significantly better than results of GM-EDA. Moreover, even without using local search, the new GOMEA variants obtained the best-known solution for 30 instances in every run and even new upper bounds for several instances. Finally, the time complexity per solution for building a dependency model to drive variation is an order of complexity less for GOMEA than for GM-EDA, altogether suggesting that GOMEA also holds much promise for permutation optimization.

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the Interleaved Multi-start Scheme

The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA.

Efficient, effective, and insightful tackling of the high-dose-rate brachytherapy treatment planning problem for prostate cancer using evolutionary multi-objective optimization algorithms

We address the problem of high-dose-rate brachytherapy treatment planning for prostate cancer. The problem involves determining a treatment plan consisting of the so-called dwell times that a radiation source resides at different positions inside the patient such that the prostate volume and the seminal vesicles are covered by the prescribed radiation dose level as much as possible while the organs at risk, e.g., bladder, rectum, and urethra, are irradiated as little as possible. The problem is highly constrained, following clinical requirements for radiation dose distribution while the planning process for treatment planners to design a clinically-acceptable treatment plan is strictly time-limited. In this paper, we propose that the problem can be formulated as a bi-objective optimization problem that intuitively describes trade-offs between target volumes to be radiated and organs to be spared. We solve this problem with the recently-introduced Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA), which is a promising MOEA that is able to effectively exploit dependencies between problem variables to tackle complicated problems in the continuous domain. MO-RV-GOMEA also has the capability to perform partial evaluations if problem structures allow local variations in existing solutions to be efficiently computed, substantially accelerating the overall optimization performance. Experiments on real medical data and comparison with state-of-the-art MOEAs confirm our claims.

Exploring trade-offs between target coverage, healthy tissue sparing, and the placement of catheters in HDR brachytherapy for prostate cancer using a novel multi-objective model-based mixed-integer evolutionary algorithm

Brachytherapy is a form of radiotherapy whereby a radiation source is guided near tumors, using devices such as catheter implants. In the present clinical workflow, catheters are first placed inside or close to the tumor based on clinical expertise. Subsequently, software is used to design a plan for the delivery of radiation. Treatment planning is essentially a multi-objective optimization problem, where conflicting objectives represent radiation delivered to tumor cells and healthy cells. However, current clinical software collapses this information into a single-objective, constrained optimization problem. Moreover, catheter positioning is typically not included. As a consequence, it is hard to obtain insight into the true nature of the trade-offs between key planning objectives and the placement of catheters. Such insights are however crucial in understanding how better treatment plans may be constructed. To obtain such insights, we interface with real-world clinical software and derive potential catheter positions for real-world patients. Selecting and configuring catheters requires mixed-integer optimization. For this reason, we extend the recently-proposed Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT) to tackle multi-objective optimization problems. Our results indicate that clinically acceptable plans of high quality may be achievable with less catheters than typically used in current clinical practice.

Improving the performance of MO-RV-GOMEA on problems with many objectives using tchebycheff scalarizations

The Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA) has been shown to exhibit excellent performance in solving various bi-objective benchmark and real-world problems. We assess the competence of MO-RV-GOMEA in tackling many-objective problems, which are normally defined as problems with at least four conflicting objectives. Most Pareto dominance-based Multi-Objective Evolutionary Algorithms (MOEAs) typically diminish in performance if the number of objectives is more than three because selection pressure toward the Pareto-optimal front is lost. This is potentially less of an issue for MO-RV-GOMEA because its variation operator creates each offspring solution by iteratively altering a currently existing solution in a few decision variables each time, and changes are only accepted if they result in a Pareto improvement. For most MOEAs, integrating scalarization methods is potentially beneficial in the many-objective context. Here, we investigate the possibility of improving the performance of MO-RV-GOMEA by further guiding improvement checks during solution variation in MO-RV-GOMEA with carefully constructed Tchebycheff scalarizations. Results obtained from experiments performed on a selection of well-known problems from the DTLZ and WFG test suites show that MO-RV-GOMEA is by design already well-suited for many-objective problems. Moreover, by enhancing it with Tchebycheff scalarizations, it outperforms M0EA/D-2TCHMFI, a state-of-the-art decomposition-based MOEA.

Efficiency enhancements for evolutionary capacity planning in distribution grids

In this paper, we tackle the distribution network expansion planning (DNEP) problem by employing two evolutionary algorithms (EAs): the classical Genetic Algorithm (GA) and a linkage-learning EA, specifically a Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). We furthermore develop two efficiency-enhancement techniques for these two EAs for solving the DNEP problem: a restricted initialization mechanism to reduce the size of the explorable search space and a means to filter linkages (for GOMEA) to disregard linkage groups during genetic variation that are likely not useful. Experimental results on a benchmark network show that if we may assume that the optimal network will be very similar to the starting network, restricted initialization is generally useful for solving DNEP and moreover it becomes more beneficial to use the simple GA. However, in the more general setting where we cannot make the closeness assumption and the explorable search space becomes much larger, GOMEA outperforms the classical GA.